Quantum nanophotonic and nanoplasmonic sensing: towards quantum optical bioscience laboratories on chip

2.1 Quantum sensing protocol

Quantum sensing makes use of features of quantum mechanics, such as quantized energy levels, the superposition principle and entanglement, to measure a physical quantity or enhance measurement sensitivity beyond the classical limit. The sensing process involves an object, a detector and a readout system, where the detector interacts with the object and generates a response signal that is measured by the readout device. The size of the object may vary from microscopic (single quantum emitters like atoms, ions, molecules, quantum dots and nitrogen-vacancy centres, and light quanta/photons) to universal (e.g. the gravitational wave produced by the collision of two black holes) in scale. The detectors could be either classical (such as microwaves, optical light and cavities/resonators) or quantum (for instance: internal energy levels of emitters, quantum states of superconducting circuits, and non-classical properties of light). The response signal from the detector must be converted into a physical quantity that is measurable to the readout system. For example, the population of emitters in a certain internal state is indirectly measured by mapping it onto the light power (the number of photons) that can be read out by a photodetector.

As illustrated in Figure 2, the quantum sensing process has three typical steps [28]: (i) Preparation. Due to the nature of quantum mechanics, the full picture of a physical observable associated with the object cannot be captured via a single measurement. Only the expectation value of the observable is meaningful to the measurement. Thus, the detection process should be performed repeatedly under the same preparation conditions many times; (ii) Interaction. Ideally, the detector interacts with the object in a coherent way and the wave function of the coupled system is predictable via the Schrödinger equation. However, in practice, the coherent object-detector interaction is inevitably interrupted by environmental fluctuations, limiting the detection speed and accuracy. Hence, the object-detector coupling strength should be large enough that an efficient response signal is obtained well before the dissipation takes effect; and (iii) Measurement. Fundamental fluctuations are unavoidable and influence the readout outcomes, for which the signal-to-noise ratio must be sufficiently high. Quantum noise, such as photon shot noise and quantum projection noise of emitters, imposes the standard quantum limit (SQL, which scales as 1/N with the number N of photons or emitters) on measurements [1], [30], [31]. Entangling a small quantum system with a large one can efficiently suppress the SQL by means of quantum non-demolition (QND) measurements [32]. Moreover, the SQL of a quantum system composed of N emitters may be overcome by using entangled states of emitters [33], [34], [35]. The ultimate uncertainty of measurements arises from Heisenberg’s uncertainty principle and scales as 1/N [36], [37].

Figure 2:

Quantum sensing process.

The object and detector are isolated and initialized in the known states |ψ_obj(0)⟩ and |ψ_det(0)⟩, respectively, at t = 0. Then, the two states evolve freely for a time duration t₀ and arrive at the prepared states |ψobj(t0)〉=e−iHobjt/ℏ|ψobj(0)〉 and |ψdet(t0)〉=e−iHdett/ℏ|ψdet(0)〉 with the respective Hamiltonians H_obj and H_det. Afterwards, the detector interacts with the object for a duration T. The inevitable environmental fluctuations interrupt the coherent object–detector interaction. Finally, the response signal produced by the detector is measured by a readout device, whose sensitivity is fundamentally limited by quantum mechanics. The sensing process needs to be performed repeatedly to obtain the expectation value of the associated physical observable. Adapted from the study by Vollmer and Yu [29].

2.2 Measurement of photon characteristics

Environmental perturbations inevitably influence the phase ϕ_L (frequency ω_L) and number N_p (intensity) of light quanta. Mapping the photon state onto the density matrix, fluctuation in ϕ_L (ω_L) is related to the non-diagonal elements, which primarily determine the so-called coherence (temporal/spatial correlation) of photons. Enhancing the coherence generally relies on a feedback control loop. In contrast, fluctuation in N_p mainly affects the diagonal elements. Flying single photons enable quantum communication between remotely separated objects. However, fluctuations in ϕ_L and N_p strongly restrict the fidelity of quantum information processing (QIP). Various methods have been exploited to measure both ϕ_L and N_p [1], [21], [28].

Measuring the photon phase ϕ_L: Generally, we measure the light frequency ω_L, instead of ϕ_L, by using a frequency reference which possesses a higher stability and accuracy. The mostly common references are optical resonators. By applying the well-known Pound-Drever-Hall technique [38], the light coherence time can be extended to over 10² s, as shown in the reported studies [39], [40]. However, the resonator’s long-term frequency drift limits the measurement of the slowly varying fluctuation components in ϕ_L. To address this issue, the transition between two internal states of quantum emitters, such as atoms and ions, is usually applied as the frequency reference since the inter-state energy spacing is determined by nature. The light beam is coupled to a pair of emitters’ internal states, inducing the emitters to transfer between these two states, i.e. Rabi oscillation. The fluctuation in ω_L can be derived from measuring the population distribution of emitters. Two approaches, Rabi and Ramsey [41] measurements, are commonly used in the modern optical detection. The sensitivity of such an emitter-population measurement is eventually limited by quantum mechanical principles, i.e. the so-called quantum projection limit (QPL), which is proportional to 1/Ne with the number of quantum emitters N_e (see Box 2). It is worth noting that the QPL can be mitigated down to the fundamental Heisenberg limit (∝1/N_e) by using entangled emitters [47]. The population distribution of emitters needs to be converted into a measurable physical quantity, which is usually the light power (i.e. photon number). The standard quantum limit to photon detection is the so-called shot noise, leading to the measurement sensitivity scaling as 1/Np. In many cases, the light signal is too weak to be measured. Homodyne and heterodyne methods [30], where the weak signal is mixed with a strong local oscillating wave, are generally applied to enhance the signal-to-noise ratio. The fundamental limit of photon-phase measurements is also set by the Heisenberg limit, Δϕ_L = 1/N_p, imposed by the Heisenberg uncertainty principle (see Box 2).

Measuring the photon number N_p: Devices which are capable of precisely counting the number of photons at the single-quantum level are of particular importance to QIP. In particular, for applications in linear optics quantum computation [48], [49], the roles of single photonic qubits encompass information storage, communication and computation. They are also essential in quantum-sensing schemes in which the readout stage requires the detection of small numbers of photons with high time resolution. Several factors are generally used to assess a photodetector: (i) Quantum efficiency (QE), i.e. the ratio of the number of photoelectrons collected by the detector to the number of incident photons; (ii) Dead time (recovery time), i.e. the time interval during which the detector is unable to absorb a second photon after the previous photon-detection event; (iii) Dark count rate, associated with the false detection events caused by the dark current in the detector; (iv) Timing jitter, i.e. the deviation of the time interval between the photon absorption and the electrical-pulse generation of the detector; and (v) Photon number resolution, i.e. the capability of distinguishing the photon number [50].

There are a large number of single photon detection technologies available, but perhaps the most conventional are photomultiplier tubes (PMTs) and single photon avalanche diodes (SPADs or APDs). In a PMT, a photon incident on the photocathode scatters a single electron and this electron is effectively multiplied at the successive dynode stages, giving rise to a macroscopic current in the external circuit. Despite comparatively low detection efficiencies (10–40% typical in the visible region [51]), the timing jitter can be extremely low, e.g. <10 ps in the study by Bortfeldt et al. [52], and PMTs are still widely used in a range of applications [53], [54]. SPADs are based on semiconductor pn junctions reverse biased above the breakdown voltage. Absorption of a photon creating an electron–hole pair leads to an avalanche current which is read out as a digital pulse [55]. Particular advantages include detection in the infra-red region using materials such as InGaAs/InP [56], low timing jitter (30 ps demonstrated in the study by Sanzaro et al. [57]), and room temperature operation [55]. Another semiconductor detector technology is the visible-light photon counter (VLPC), which unlike typical SPADs is capable of resolving the number of detected photons [58]. Choosing between different detector technologies inevitably involves trade-offs between the parameters described above, this is illustrated by the comparison of detector technologies available in 2011 given in the study by Eisaman et al. [51]. Superconducting nanowires (SNs) are a competitive alternative to avalanche diode detectors and offer superior detection efficiency and low dark count rate by comparison [59], [60], [61]. SNs are usually arranged in parallel, with each nanowire connected in series to a resistor. Each branch acts as a superconducting single photon detector [62]. When the nanowire is biased close to its critical current, the absorption of a photon triggers a second-order phase transition to a non-superconducting state, and the bias current is pushed to the external circuit. Divochy et al. demonstrate that in a parallel configuration, the resulting output voltage pulse is proportional to the number of photons [63]. In another experiment, Zen et al. used superconducting magnesium diboride strips to detect 20 keV biomolecular ions at a base temperature of 13 K [64]. SNs require temperatures on the order of a few kelvin to preserve the superconducting state and this makes it challenging to incorporate with other components for lab-on-chip-style biosensing schemes.

2.3 Cavity QED

One of the most fundamental scenarios in quantum optics is the so-called cavity quantum electrodynamics (cavity QED), which studies the properties of quantum emitters interacting with light confined in a high-Q cavity. Inevitable decay sources, spontaneous emission of emitter γ and cavity loss κ, interrupt the coherent emitter-photon interaction, erasing the quantum properties of the system after t > min(γ⁻¹, κ⁻¹). The size of the quantum system, which is measured by the numbers of emitters and photons joining the interface, must be large enough that the system can exhibit/maintain quantum behaviour before the decay sources take effect [65], [66]. In practice, a quantum emitter in its excited |e⟩ state may return back to the ground |g⟩ state via spontaneously emitting a photon with a wave vector k and polarization μ. Indeed, this spontaneous emission is caused by the perturbation from the zero-point energy of the electromagnetic field Esp(−)=∑k,μek,μ∗ℏωk/2ϵ0Veffak,μ†e−ik⋅r0 with the emitter’s location r₀ and the frequency ω_k = c|k|. According to the Fermi’s golden rule, the relevant transition rate is given by

in the electric dipole approximation. In free space, the above equation is further rewritten as

by replacing the summation ∑k(⋅) with an integral Veff(2π)3∫0∞k2dk∫0πsinθdθ∫02πdφ. Here, 〈d⋅Esp(−)〉2=ℏωeg6ϵ0Veff|dge|2 denotes the emitter-vacuum-field coupling intensity. The parameter ρ_vac(ω_eg) with ρvac(ω)=ω2Veffπ2c3 is the density of electromagnetic modes per unit frequency around the transition frequency ω_eg of emitter within the quantization volume V_eff. The spontaneous emission rate of the emitter in free space finally reads as

which actually corresponds to the Einstein’s Α coefficient.

The spontaneous emission of an emitter depends strongly on the environment it resides in. The environment may be tailored by using a high-Q cavity. The resulting density of electromagnetic modes is in Lorentzian shape, ρcav(ω)=2πκκ2/4(ω−ωL)2+κ2/4 with the cavity loss rate κ and quality factor Q = ω_L/κ. Thus, the spontaneous emission rate of an emitter located inside a cavity is expressed as γcav=γFPκ2/4(ωeg−ωL)2+κ2/4, where the so-called Purcell factor [67] is defined as

The factor 3 is originated from the fact that the dipole moment d is randomly oriented with respect to the laboratory frame. The combined emitter-cavity system can be parameterized by the emitter-photon coupling strength g (see Box 3), the saturation photon number Nps=γ2/(2g)2, and the critical excited emitter population Nec=κγ/(2g)2. The concepts of Nps and Nec may be understood from lasing dynamics [69], a process amplifying the coherent photons and maintaining the system’s coherence.

In the weak-coupling regime, g ≪ κ, γ, exploring the quantum properties of the emitter-cavity interaction requires a large system size because Nps≫1 and Nec≫1. In comparison, for Nps≪1 and Nec≪1, the required system size is significantly reduced down to a scale of one emitter and one photon, reaching the strong-coupling regime with g ≫ κ, γ. The single emitter may repeatedly absorb and emit a single photon before the photon irreversibly escapes into the environment. This continuous exchange of excitation between emitters and cavity, known as Rabi oscillation, is imposed on the photons bouncing back and forth between cavity mirrors, resulting in a mode splitting in the spectrum (see Box 3). Thus, the vacuum Rabi splitting can be utilized as a diagnosis tool for the strongly coupled emitter-cavity system. A weak probe beam travels through the cavity with one emitter placed inside. The transmission spectrum of the probe beam exhibits two peaks due to the emitter-cavity interface and each peak is broadened with a spectral width ∼κ, γ. The inter-peak separation is determined by the resonant Rabi strength 2g. Observing the splitting requires g exceeding both κ and γ. Enhancing the emitter-photon coupling strength g may be executed by two approaches (see Box 3): one is to choose a large transition dipole moment |d_ge| of the emitter, and the other is to suppress the cavity-mode volume V_eff while still maintaining a high quality factor Q = ω_L/κ. Unfortunately, the former method is usually infeasible because the spontaneous emission rate γ is proportional to |d_ge|² too, i.e. a larger |d_ge| leads to a larger γ. In contrast, the latter approach can be achieved through exquisite design of the fundamental properties of the cavity. We focus on the critical number of emitters Nec. Using the original expressions of γ and g (see Box 3), one finds that Nec is virtually equal to the reciprocal of the Purcell factor, which was originally introduced as an enhancement factor of the spontaneous emission of a dipole moment placed inside a resonator. Thus, it is natural to employ F_P to measure the emitter-photon coupling. Figure 3 summarizes the F_P factors of different emitter-cavity structures realized in recent experiments. The strong coupling between a single emitter and one photon leads to a value of F_P much greater than unity.

Figure 3:

Purcell factors F_P for different QED structures.

The quantum emitters may be atoms, molecules, QD (quantum dot), NV (nitrogen-vacancy) centre and SQ (superconducting qubit). The resonators include FP (Fabry-Pérot), MT (microtoroid), MS (microsphere), MP (micropillar), PC (photonic crystal), NpoM (nanoparticle-on-mirror) and SC (superconducting) cavities. The arrow crossing sphere represents the transition dipole moment of the quantum emitter. All these QED systems achieved in experiment are in the strong-coupling regime F_P > 1.

The Q factor for different types of cavities varies greatly, strongly dependent on their geometric structures and mechanisms of light confinement. The Q factor for microtoroid and microsphere cavities can be as high as 10⁹ while that for plasmonic cavities is around 10 because of the huge ohmic loss of collective oscillations of surface electrons (Figure 3). Commonly, suppressing the volume V_eff is a general manner to enhance the emitter-cavity interaction.

When the size of emitter is much smaller than the cube of the photon wavelength λL3 (more precisely V_eff), the emitter may be viewed as a point-like dipole located at r_o, which couples to the local electric field of a cavity mode E(r_o). The effective mode volume V_eff may be computed by averaging the whole energy of the cavity mode based on this local value, Veff=∫|Er|2dr/|Ero|2. Since the cavity-mode energy is fixed (i.e. the energy of one photon ℏωL), placing the emitter at the maximum of |E(r)|, |E(r_o)| = max(|E(r)|) leads to the minimal volume and the maximal emitter-cavity coupling strength. In addition, designing the cavity structure to extremely enhance |E(r_o)| makes the single-photon energy ℏωL primarily focused on a small region around r_o, strongly suppressing V_eff.

Plasmonic nanocavities are the most attractive candidate for achieving an extremely large g [74]. The features of surface plasmon resonance enable the electric field to be strongly confined above the surface with a depth much shorter than λ_L, resulting in a huge enhancement of local field. The effective cavity-mode volume may be smaller than λL3≈λeg3 [75], [76], [77]. This well exceeds other types of cavities since diffraction limits the confinement of light to smaller than λL3. Nevertheless, reducing V_eff (enhancing g) is only a part of the story. The Q-factor of plasmonic cavities is only about 10, much lower than other cavity structures. The Purcell factor F_P achieved in recent experiments based on the nanoparticle-on-mirror-plasmonic-cavity structure reaches over 10³ [77], [78], [79], [80], [81]. The enhanced single-photon Rabi frequency g (10¹³∼10¹⁴ s⁻¹) and spontaneous emission rate of emitters prohibits the direct measurement of Rabi flopping due to the limited instrumental response. The vacuum Rabi splitting was first measured in an atom-FP-cavity structure [82], with a ¹³³Cs atomic beam flying through a high-Q optical Fabry-Pérot interferometer.

So far, such a vacuum Rabi splitting has also been performed principally in other diverse emitter-cavity systems, including single atoms interacting with microtoroid cavities [83], the interface between nitrogen-vacancy centres and whispering-gallery waves of a microsphere [84], quantum dots fabricated in a micropillar [85] and photonic crystal cavities [86], superconducting qubits coupled with superconducting resonators, and hybridization of molecules in microcavities [87], [88], [89]. Besides exploiting the fundamental properties of light–matter interface, the strong emitter-cavity coupling is of particular importance to QIP [90], [91], [92] because the relevant quantum operations, e.g. reading, transferring, writing and storing the information between quantum memory (long-lived emitters) and flying qubits (photons), can be accomplished with a high fidelity. It also possesses the potential of wide application in quantum sensing, such as detecting the weak electric/magnetic fields [93], [94] and exploring gravity [95]. Moreover, the recent implementation of the strong interaction between molecules and plasmonic nanoresonators [80], [96] may pave the avenue towards exploring new types of quantum chemistry and molecular reaction [74], [97].

6.1 Nitrogen vacancy centres as quantum emitters

As well as in spin-based sensing, nitrogen vacancy (NV) centres also have applications as single photon emitters [163]. NV centres feature a fluorescence peak around 437 nm; the Hamiltonian for the triplet ground and excited states of NV⁻ share the following form [164]:

where D is the crystal-field splitting (Hz), γ_B is the gyromagnetic ratio (Hz/G), d_∥ is the axial electric-field dipole moment [Hz/(V/cm)], E_∥ is the axial electric field (V/cm), B is the magnetic-field vector, g is the g factor tensor, Sˆ is the vector of electronic spin-1 Pauli operators, A is the hyperfine tensor and Iˆ is the vector of nuclear spin-1 Pauli operators. Emission from an individual NV defect has been shown to produce anti-bunched photon states [165], [166], [167]. The purity of single photon emission in these first demonstrations was high, with second-order correlation functions of g⁽²⁾(0) = 0.26 in bulk diamond [166] and g⁽²⁾(0) = 0.17 in diamond nanocrystals [167]. These nanocrystals have been shown to be biocompatible and have potential sensing and imaging applications within living cells [168]; exploiting both their potential for magnetometry (see also Section 7.1) and sub-diffraction imaging (see also Section 7.5). NV centres have also been proposed as sources of entangled photons [169], [170]. A potential issue with single photon emission from NV centres is a low photon collection efficiency due to the lack of directional emission. Novel fabrication techniques may provide a solution; highly directional single photon emission was achieved by top-down fabrication of diamond nanowires containing individual NV centres [171]. The brush-like array of nanowires also show an order of magnitude greater single photon flux than an ultrapure bulk diamond sample, and at an order of magnitude lower pumping intensity. An alternative approach to directional emission could be to embed emitters in a dielectric antenna structure, as proposed in the study by Lee et al. [172].

NV centres are compatible with integrated photonic circuits; the study by Faraon et al. [173] demonstrates coupling of NV centre fluorescence to diamond-on-silicon waveguides and grating couplers, and the study by Gould et al. [174] shows coupling to waveguides via GaP microdisks. Further to this, the GaP system has been modified to allow the single photon emission frequency to be tuned by an applied bias voltage (Figure 7) [175]. This could compensate for the natural variation in emission frequencies from different NV centres. Femtosecond laser fabrication methods can produce photonic and microfluidic circuits in diamond [163], [176]. Importantly, these reports demonstrate the creation of NV centres on-demand using femtosecond laser pulses. Lenzini et al. give an overall review of progress in diamond integrated circuits for quantum photonics [177]. Together, these fabrication techniques show clear potential for diamond-based systems integrating single photon emitters and microfluidics in on-chip sensors; a potential platform for integrated quantum biosensors.

Figure 7:

NV centre single photon emission coupled to GaP microdisks, with tuneable emission wavelength.

(a) Schematic of NV centre coupled to waveguide via a GaP microdisk. (b) Wavelength shift in single photons coupled into GaP microdisks from NV centres, in response to changing bias voltage Reprinted with permission from the study by Gould et al. [174]. Copyright (2016) by the American Physical Society. (c) SEM image of circuit. Pink: GaP microdisks and waveguides; Yellow: Ti/Au electrodes for applying bias voltage; Grey: diamond substrate. Reprinted with permission from the study by Schmidgall et al. [175]. Copyright (2018) American Chemical Society.

6.2 Quantum dots

Quantum dots (QDs) are semiconductors on the scale of a few nm in all three dimensions which have quantized electronic energy levels. QDs based on CdSe, CdTe and CdS are in widespread use as fluorescent markers in bio-assays and imaging [178], however these applications do not exploit the photon statistics of single photon emission from individual quantum dots. Therefore, we focus here on semiconductor QDs which would be suitable as sources of single photons in integrated biosensing devices.

Semiconductor-based single photon sources consisting of QDs in optical cavities have been studied extensively. These systems are typically based on GaAs and InGaAs semiconductor layers grown by molecular beam epitaxy (MBE), producing sources with second-order correlation functions as low as g⁽²⁾(0) = 10⁻⁴ [121], [122], [179]. QDs can also be integrated into photonic circuits based on silicon waveguides and fabricated using standard CMOS processes by a transfer printing method [180]. Quantum dots in photonic crystal cavities have demonstrated high-purity single photon emission [181], [182]; this work has even led to a commercially available on-chip single photon source using waveguides and grating couplers to extract photons [183].

Organic single photon emitters can be integrated with photonic circuits too; a single dibenzoterrylene fluorophore has been coupled to a silicon nitride waveguide, resulting in anti-bunched emission with g⁽²⁾(0) = 0.01 [184]. In the same way as for diamond-based integrated devices, these techniques could provide a silicon-based platform for integrated quantum optical sensing devices exploiting emission from QDs or organic fluorophores. Optoplasmonic enhancements might also be combined with QD systems, as shown by the demonstration of strong coupling of individual QDs with a plasmonic silver bowtie cavity [185]. Although photon correlation measurements on these systems have not yet been carried out, there is the interesting possibility of exploiting both single photon emission and sub-wavelength field localization in a quantum optoplasmonic system.

6.3 Hexagonal boron nitride defects

Single photon emitters in 2D materials are attractive for achieving more efficient extraction of single photons as compared with emitters embedded in bulk materials. Candidates include defects in semiconducting transition metal dichalcogenides (TMDs) (for example WSe₂) and hexagonal boron nitride (hBN) single crystals [186]. While TMDs require low temperatures for efficient single photon emission, hBN defect centres have been shown to be chemically and thermally stable sources of bright single photon emission, at room temperature [187], [188], [189].

hBN single crystals are a 2D semiconducting material with a large band gap; almost 6 eV [188]. The large band gap is attributed to relatively easy formation of sub-band gap energy defects and highly suppressed non-radiative recombination, which contribute to the capability for room temperature single photon emission [186]. Defects responsible for single photon emission have been proposed to be nitrogen vacancies and anti-site nitrogen vacancies, in which one boron atom adjacent to the vacancy is substituted for nitrogen [188]. The photophysics of the defects is typically modelled using three- or four-level systems, which achieve good fits to experimental second-order correlation functions [188], [191]. These defects can be generated with a high degree of control using oxygen plasma etching and thermal annealing. Wet chemistry techniques for transferring single crystals to substrates have also been developed [192].

Although the zero phonon lines of different emitters may range over 570–800 nm [187], [193], single photon emission from hBN defects can be spectrally tuned using strain [194], [195], [196], photodoping in ionic liquid devices [197] and temperature tuning methods [193]. Localization of emitters and some control over their polarization has been achieved using defects formed at wrinkles in hBN layers [198]. In order to exploit hBN centres in integrated devices, efficient extraction of single photons is required. Two works have shown coupling of hBN emission to optical fibres. One used a tapered fibre to couple single photon emission from hBN flakes with an efficiency of 10% [199]. The second-order correlation function at the output of the fibre was measured to be g⁽²⁾(0) = 0.15. The other study used hBN flakes applied directly to the end of an optical fibre, resulting in an output correlation function of g⁽²⁾(0) = 0.18 and an estimated coupling efficiency also around 10% [200]. It is also possible to fabricate on-chip photonic components directly out of hBN, for example photonic crystal cavities recently produced using reactive ion etching (RIE) and electron beam induced etching (EBIE) fabrication techniques [190] (Figure 8). In Figure 9, we give one of the scanned intensity maps as well as the second-order correlation measurement of a hBN sample. Unlike in diamond NV centres in which spins are currently exploited for magnetic field measurements, the spin properties of hBN defects are not yet well understood. This is partially due to the wide variety of defect types produced in typical hBN fabrication processes. However, magneto-optical effects using hBN defects have been theoretically predicted [201]. Magnetic field-dependent photoluminescence [202] and optical manipulation of defect spins [203] have now been observed in hBN, raising the possibility of 2D material-based magnetometers in the future.

Figure 8:

Quantum emitters in hexagonal boron nitride (hBN) and on-chip fabrication using hBN.

(a) Optical image of hBN flakes, scale bar 50 μm. (b–d) Schematic and SEM images of a photonic crystal cavity fabricated in a suspended multilayer hBN flake, scale bars: 500 nm in (c), 2 μm in (d). Adapted from the study by Kim et al. [190], available under Creative Commons Licence. (e and f) Photoluminescence map of quantum emitters in hBN and photoluminescence spectrum of a single emitter taken at 77 K. Reprinted by permission from Springer Nature: Nature Nanotechnology [188], copyright (2016).

Figure 9:

Photon characterization of quantum emission from hexagonal boron nitride (hBN).

(a) Scanned intensity map of emission from hBN sample at around 570 nm, excited at 532 nm. (b) The second-order correlation g⁽²⁾(τ) function, the g⁽²⁾(0)<0.5 indicates single photon emission.

6.4 Non-linear optical quantum sources and resonators

Non-linear optical processes provide a means of generating non-classical states of light and are in widespread use as sources in quantum sensing schemes. The polarization response of an optical medium can be expanded in powers of the incident light field:

where χ⁽ⁿ⁾ is the nth-order susceptibility of the medium and summation over the indices j, k, l, m, n is implied. Therefore, media with non-zero susceptibilities at second order and higher can support interactions between optical fields at different frequencies. Most common are second-and third-order non-linear interactions, or three- and four-wave mixing, respectively. Only non-centrosymmetric crystals have a non-zero χ⁽²⁾ and can support three-wave mixing, also known as spontaneous parametric down-conversion (SPDC) when a single pump frequency is split into two lower frequencies [204]. Centrosymmetric crystals and amorphous media can have non-zero χ⁽³⁾ but a high susceptibility coefficient is desirable otherwise high pump power is needed for efficient non-linear processes to take place. From a quantum optics perspective, the SPDC non-linear process represents a pump photon being annihilated and a pair of photons created. Non-linear processes are of interest in quantum optics because of the quantum correlations between these paired output photons.

Monolithic non-linear crystals can be integrated in on-chip devices as waveguides, or non-linear cavities can be used, often ring resonators supporting whispering gallery modes (WGM). Whispering gallery mode resonators (WGMRs) have high Q-factors which enhance the efficiency of non-linear conversion processes in WGMRs fabricated from non-linear optical media [205]. Integrating sources of non-classical photon states with other components in photonic circuits is currently of great interest, and the role of non-linear media in this area is covered in the review by Caspani et al. [119]. Waveguides and resonators fabricated from second-order (χ⁽²⁾) non-linear materials can produce photon pairs via spontaneous parametric down conversion (SPDC).

Periodically poled lithium niobate (LiNbO₃) waveguides have been developed as photon pair sources [206] and as sources of polarization-entangled photon pairs by Type-II SPDC [207], [208]. The computational results of the joint spectral intensity as well as the quantum purity estimation of SPDC photon pairs from a 25 mm long periodically poled KTP crystal at a temperature of 50 °C in Type-II phase matching condition is shown in Figure 10. Lithium niobate microdisks have been used to generate entangled pairs which are also shown to be individually quadrature squeezed [107], [209]. Periodically poled lithium niobate microdisk resonators are capable of ultra-bright photon pair generation; a pair generation rate of 36.3 MHz was achieved using only 13.4 μW pump power in the study by Ma et al. [210]. The wavelength of emitted photon pairs can be tuned, for example using thermal and electro-optic tuning. The tuning of photon pair wavelengths to alkali atom hyperfine transitions is demonstrated in the study by Schunk et al. [211]. Alternative χ⁽²⁾ materials include GaAs [212] and AlGaAs [213], both of which have been used to implement waveguide sources of polarization-entangled and counter-propagating photon pairs, respectively. Further to this, an aluminium nitride micro-ring integrated with superconducting single photon detectors via waveguides was demonstrated (Figure 11) in the study by Guo et al. [214]. This demonstrates the potential for quantum optical devices to be completely integrated with both sources and sensors on a chip, although the detectors in this case are mounted on a separate chip in a cryostat.

Figure 10:

Computational analysis of joint spectral intensity and quantum purity of spontaneously parametric down converted photon pairs.

A Type-II SPDC in PPKTP crystal is used as the source for the generation of polarization quantum entangled photon pairs. The pump photon wavelength used here is 775 nm, which gives rise to degenerate signal and idler photons at the communication wavelength of 1550 nm.

Figure 11:

Aluminium nitride micro-ring parametric-down conversion source of correlated photon pairs.

An on-chip source of correlated photon pairs made from an aluminium nitride waveguide on a silicon substrate was coupled to superconducting nanowire single photon detectors (SNSPDs) on a separate chip. High purity heralded single photons were measured using this on-chip setup, showing g⁽²⁾(0) = 0.088 ± 0.004. Adapted from the study by Guo et al. [214].

Examples of quadrature-squeezed light generation in integrated photonic devices are included in the studies by Vaidya et al. and Zhao et al. [215], [216], both of which use four-wave mixing processes in silicon nitride micro-resonators. Squeezed light generation in a room temperature optomechanical cavity was also achieved recently. Rather than using a non-linear optical medium, this system uses effective non-linearity due to the optomechanical interaction to achieve squeezing and has the potential to be miniaturized [217].

Non-linear effects can also be achieved in centrosymmetric materials, using χ⁽³⁾ processes such as four-wave mixing. An AlGaAs waveguide photon pair source is one example [218]. Silicon-based waveguide sources have also been developed [219], including sources of polarization entangled pairs [220]. More complex quantum optical states have recently been produced on-chip, such as four-photon states [221] and on-chip sampling of states with up to eight photons [222]. Due to their potential application to quantum communications, photon pair sources based on silicon micro-ring and micro-disk resonators have been extensively studied [223], [224], [225], [226], [227], [228], [229], [230], [231]. Further to this, silicon micro-ring sources have been developed with higher degrees of photon entanglement including time-energy entanglement [232], [233], [234] and hyper-entanglement (polarization and time-energy) [235]. Simultaneous generation of photon pairs in two communications frequency bands (1310 and 1550 nm) was demonstrated in [236]. Other materials that have been investigated as χ⁽³⁾ WGMR photon pair sources include silicon nitride [237], and recently, indium phosphide membrane micro-rings [238]. A further step towards fully integrated devices is the demonstration that the pump laser could also be placed on a chip. In a work by Wang et al. [239], an electrically injected wafer scale hybrid silicon laser was shown to have comparable performance to a stand-alone laser when pumping a silicon micro-ring photon pair source. Therefore, integrated photonic devices with pump lasers, photon pair sources and single photon detectors all on-chip now appear feasible. The material systems presented here provide sources of non-classical light states: single photons, entangled photon pairs and squeezed light, all with the potential for integration on-chip. Room temperature operation, which is required for integrated sensors in close proximity with biological samples, is offered by all these systems.

6.5 Quantum optical frequency combs

Quantum optical frequency combs (QOFC) combine the advantages of a light source with a large number of phase stable frequency modes of an optical frequency comb (OFC) as well as the photon output embedded with the non-classical quantum property of time-energy entanglement. Because of this peculiar property QOFCs have attracted great interest for on-chip applications such as molecular spectroscopic finger printing as well as to store and process large amounts of quantum information in frequency and time correlations in addition to joint spectral amplitude and phase [240], [241], [242], [243]. OFCs were basically originated as mode locked lasers with optical pulses generated by coherent addition even up to millions of resonant longitudinal optical cavity modes resulting in output optical modes which are harmonically related and phase coherent [244], [245], [246]. OFCs have evolved further with wide band width with the advent of non-linear optical fibers (erbium- and thulium-doped fibers)-based super continuum sources [245]. For the on-chip integration of OFCs with very broad spectra, either supercontinuum generation in optical waveguides or Kerr-comb generation in microresonators are widely used [247].

By means of spontaneous four wave mixing (SFWM) Reimer et al. demonstrated a CMOS compatible micro-ring resonator-based integrated frequency comb source of heralded photon pairs with 200 GHz channel separation and 110 MHz line width [248]. Subsequently, multi-photon entangled quantum states by means of in a QOFC in four-port micro-ring resonators were realized demonstrating how Kerr frequency combs can be well suited to generate several bi- and multi-photon entangled qubits [249] (Figure 12a and b). The micro-ring resonator of this QOFC was pumped with a passive mode-locked fiber laser with a repetition rate of 16.8 MHz and a pulse width of 570 ps. A stabilized unbalanced fiber interferometer with an 11.4 ns delay was used to generate time-bin–entangled qubits where double pulses of equal power were produced with a defined relative phase difference [249]. Further, on chip generation of the higher-dimensional entangled states is also being realized where the photons were created in a coherent superposition of multiple high-purity frequency modes (Figure 12c) [240], [243], [250].

Figure 12:

Integrated generation of time bin multi-photon entangled state in quantum frequency comb through spontaneous four wave mixing (SFWM) [240], [249], [250].

(a) Experimental scheme for generating time-bin–entangled photon pairs on a frequency comb through SFWM based on a micro-ring resonator. Adapted from the study by Reimer et al. [249]. Reprinted with permission from AAAS. (b) Measured density matrix of 4-photon qubit state where achieved fidelity was 64%. Adapted from the study by Reimer et al. [249]. Reprinted with permission from AAAS. (c) Higher-dimensional entangled state generation showing the measured density matrix with quidits, D = 4 where achieved fidelity was 76.6%. Reprinted by permission from Springer Nature: Nature [250], copyright (2017).

7.1 Solid-state spin-based quantum sensing

Quantum sensors based on solid-state spins have demonstrated single molecule resolution [251] and quantum coherence over a large range of temperatures [252], which makes them favourable for applications in the life sciences. High spin-state colour centres arise because of point defects in the bulk structure of wide band gap semiconductors. An important example is the negatively charged nitrogen-vacancy (NV) centre in diamond which consists of a substitutional nitrogen impurity adjacent to a missing carbon atom. NV centres have been integrated into many sensing devices and provide the fundamental mechanism for quantum-based magnetometry [93], [253], [254], thermometry [255], [256] and quantum-enhanced biosensing [257], [258] applications. Petrini et al. discuss the theory of quantum sensing with NV centres in more detail [259], whereas this section provides a summary of the main aims and challenges for solid-state spin-based quantum biosensing.

The electronic structure of group IV defects affects the performance of the sensor. The NV centre is a favourable choice because it features a spin-split ground state accessible by microwave fields, long electron spin coherence times over a large range of temperatures and an internal dynamic that allows for spin initialization and read-out using off-resonant lasers. The performance of the sensor can be further improved in combination with advanced techniques to optimize the spin dephasing time, the readout fidelity and fabrication processes of the NV-based sensor. The optimization techniques for NV diamond magnetometry are reviewed extensively by Barry et al. [260]. Other group IV defects in diamond have also been explored for quantum sensing and are reviewed by Bradac et al. [261]. A promising candidate is the silicon vacancy in diamond, which shows superior spectral properties compared to the NV centre, but an inherently shorter electron spin coherence time [262].

The sensitivity of an NV quantum sensor depends on the location of the NV defect in the lattice. NV centres are most sensitive at or near the surface of the lattice, where it is closest to the sensing target, but quantum coherence is preserved over longer time scales in the lattice bulk. The compromise is between the sensitivity and quantum coherence of the sensor. The direct coupling of an NV centre to nearby spin magnetic dipoles scales as r⁻³, where r is the distance [263] and for scanning magnetometry applications, r also directly sets the spatial resolution [28]. The resolution can be improved without changing the depth of the NV centre in the lattice by coupling the NV centre to electronic spin- ½ qubits on the surface of a high-purity diamond crystal. With proper quantum control, surface electron spins can be coherently manipulated and measured to detect individual proton spins with angstrom resolution [264]. More recently, NV-based sensors have been designed to provide vectorized resolution, for sensing applications in more than one dimension [265].

The fabrication technique also plays an important role in producing stable, high-quality NV centres near the diamond surface. Recently, a new fabrication method has been tested, using plasma immersion ion implantation (PIII) to produce high-quality shallow layers of NV-centres [266]. In conventional NV-centre implantation, accelerated ions penetrate the diamond lattice, causing damage to the shallow layers, which prevents the NV centres from forming. The PIII technique utilizes simultaneous implantation and etching resulting in a shallow good quality implantation layer. Using this fabrication method, most NV centres are within 3.6 nm from the diamond surface and the estimated magnetic sensitivity is around 2.29μT/Hz ⋅μm−2. The creation efficiency of NV ensembles can be further improved by high temperature annealing in vacuum [267] and the stability of the NV charge state can be fine-tuned using different temperatures during the nano-diamond growth period for tailored applications [268].

Improving the performance of solid-state spin-based quantum sensors relies on optimizing the quantum state initialization and readout techniques and finding efficient polarization transfer techniques from electron to nuclear spin. The nuclear hyperpolarization of molecules near or at the surface of a quantum sensor is the basis for nanoscale nuclear magnetic resonance spectroscopy. NV centres in diamond are favourable over other types of quantum defects because the electron spin can be optically initialized almost perfectly even at room temperature. However, it remains a challenge to maximize the dynamic nuclear polarization for the quantum manipulation and detection of small nuclear spins. Some of the most recent approaches to dynamic nuclear polarization include a new PulsePol technique [269] and magic-angle spinning with arbitrary wave-form pulse shaping [270]. Lei et al. also developed a new set of steering pulse sequences for manipulating the quantum coherence times of NV centres [271].

The readout fidelity of a solid-state spin-based quantum sensor can be enhanced by repeating readouts, as described in the quantum sensing protocol. However, the number of repeated readouts is limited by measurement backaction, which changes the quantum state that is measured. Coupling the NV centre electronic spin to its associated ¹⁵N nuclear spin minimizes the measurement backaction effect and results in up to a 13-fold enhancement of the readout fidelity over conventional readout methods [272]. In the case where continuous microwave pulses are used for nuclear magnetic resonance spectroscopy, the readout fidelity can further be improved with quantum logic [273]. Data science deconvolution techniques have also been used to sharpen the readout signal. Aharon et al. demonstrate a deep learning discrimination scheme that outperforms Bayesian methods when verified on noisy nuclear magnetic resonance spectroscopy data [274].

For practical applications, it is important that the sensing technology can be integrated into ultra-compact and scalable platforms. Kim et al. demonstrate a chip-scale quantum sensor, which combines NV-based quantum sensing with complementary metal-oxide-semiconductor technology [275]. All the components required for NV-based magnetometry are stacked into a compact 200 × 200 μm footprint. The sensor measures external magnetic fields with a sensitivity of 32.1μT/Hz, with the potential to be improved even further. Another exciting design for NV-based magnetometry is the distributed quantum fibre magnetometer, which allows for distributed magnetic sensing capabilities over extended lengths with a sensitivity of 63±5nT/Hz per site [276].

7.2 From surface plasmons to quantum plasmonic sensing

Plasmon-based sensors are important in biology because they can monitor real-time molecular binding events [277]. Plasmonic sensors typically fall into two main categories; those that are based on propagating surface plasmons and those that are based on localized surface plasmons as shown in Box 4. More recently, with the motivation to reach unprecedented sensitivities, the blueprints for plasmonic-based sensors have become more diverse. Some notable examples are discussed in this section and include hybrid plasmonic-photonic structures and plasmonic structures irradiated with quantum sources of light.

Surface plasmons cannot be directly excited by photons due to the large wavenumber mismatch. Instead, light must be coupled to surface plasmons through a dielectric medium with a high dielectric constant to increase the momentum of the incident light. Traditionally, this is achieved using the Kretschmann-Raether (K-R) configuration [278], whereby the incident light is coupled to a metal film through a glass prism or substrate. Figure 13a and b show adaptations to the traditional K-R configuration that improve the performance of the sensor. Figure 13a shows an example of a sensing device with a wide tunability due to the strong dispersion of hybrid lattice plasmon modes [279], which are a result of patterning the surface with an array of cylinders. Figure 13b shows an example of a sensor that uses optical fibres instead of a prism to couple light to surface plasmons and has the advantage of a more compact configuration for in situ analysis [280]. A comprehensive review of fibre-optic sensors based on the surface plasmon resonance can be found here [284].

Figure 13:

The diverse blueprints for plasmon-based sensing.

(a) Sensing device with a wide tunability due to the strong dispersion of hybrid lattice plasmon modes. Adapted from the study by Sarkar et al. [279]. Copyright © 2015, American Chemical Society. (b) A compact plasmonic sensor for in situ analysis based on photon-plasmon coupling with fibre-optics. Adapted from the study by Li et al. [280]. © The Optical Society. (c) Plasmonic nanoparticle coupled to whispering gallery mode (WGM) for single molecule detection. Adapted from the study by Frustaci and Vollmer [281] under Creative Commons Attribution 4.0 International License. (d) Molecular weighing scale with single molecule sensitivity down to 4 zg. Adapted from the study by Proust et al. [282]. Copyright © 2019, American Chemical Society. (e) Convenient lab-on-chip design for a plasmonic sensor based on hot electrons. Adapted with permission from the study by Wang et al. [283].

The distinctive optical properties of propagating and localized surface plasmons are even more prominent when combined with other optically resonant processes [285], such as Raman spectroscopy [286] or photonic microcavities [146]. In Raman spectroscopy, the near-field signal can be enhanced by introducing plasmonic nanoparticles into the experimental set up, either through core–shell nanoparticles and coated nanostructures [287]; tip-enhanced Raman spectroscopy (TERS) [288] or shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) [289], [290]. Of these, SHINERS has very wide applicability as it can be used for surfaces with any composition and morphology, whereas this is a limitation with the other surface-enhanced Raman spectroscopy techniques [291].

Plasmonic nanostructures combined with optical microcavities or photonic structures also demonstrate extraordinary sensing capabilities. An extensive review of the diverse range of plasmonic-photonic architectures is discussed by Xavier et al. [146]. Some notable examples include WGM resonators coupled to plasmonic nanoparticles, as shown in Figure 13c [281], whereby single molecules in the near field of the resonator can be detected through a resonant frequency shift of the modes [292]. This type of sensor has been used to study single molecules [147], [293] and the conformational dynamics of single proteins, such as DNA polymerase [294]. Another type of plasmonic-photonic nanosensor is shown in Figure 13d and is based on a dielectric photonic microstructure acting as an antenna, which efficiently funnels light towards a plasmonic transducer to enhance the detection sensitivity [282]. This sensor achieves single molecule sensitivity down to 4 zg, which allows this sensor to be used as an optical molecular weighing scale.

Recently, there has also been an interest in hot electron plasmonics for sensing applications [295]. Plasmon decay generates hot electrons, which can be used as a sensing signal if the rate of hot electron generation and collection is faster than the rate of energy dissipation by electron-phonon scattering [296]. Wang et al. propose a sensing device based on the signal from hot electrons, rather than traditional optical measurement, to simplify the conventional sensing configuration [283]. The schematic is shown in Figure 13e and consists of a planar Au-TiO₂-Ti micro-comb structure with 64 Schottky diodes connected in parallel on one 10 mm chip. The sensitivity of the device and the limit of detection are estimated to be 1.87 × 10⁻⁴ RIU/nA and 4.13 × 10⁻³ RIU, respectively. Although these values are not at the known fundamental limits of detection, they are feasible for chemical and biosensing applications, whilst using a very simple lab-on-chip setup.

Since the realization that propagating and localized surface plasmons can transduce squeezed states of light [297], [298], the field of quantum plasmonic sensing has been rapidly expanding. Squeezed states of light suppress the statistical noise in either the amplitude or phase of an optical field at the expense of increased noise in the respective conjugate variable. For plasmonic sensing applications, this quantum property of the optical field can be exploited to detect refractive index changes that would have otherwise been lost in the classically optimized system [156]. A comparison of different specialized quantum states, namely the two-mode squeezed displaced state; the two-mode squeezed vacuum state and the twin Fock state, reveals that all of them can provide a quantum advantage to some extent depending on the parameter regime [299]. Another advantage of quantum plasmonic sensors, specifically for applications in the biosciences, is that they can achieve the same sensitivity as their classical counterparts, but with less optical power, which reduces the chances of damaging the biological specimen under investigation [300].

The quantum nature of plasmons has been observed through numerous experiments, which have been reviewed by Tame et al. [73]. The quantum properties of plasmons include the survival of entanglement; quantum decoherence and loss; wave-particle duality; the quantum size effect and quantum tunnelling. The quantum description of propagating or localized surface plasmons comes from the quantization of the classical modes for the system and can include the effects of loss with either the microscopic Hopfield [301] or macroscopic Green’s function formalism [302]. Including the effects of loss is important for understanding the mechanism for hot carrier generation, which, for biosensing applications, can influence the behaviour of molecules adsorbed to the surface of a quantum plasmonic sensor [295].

Plasmons can also be modelled computationally with varying levels of approximations, depending on the scale of the plasmonic system and geometry considered. For plasmonic nano-gap structures, Zhu et al. assess the appropriate level of theory, based on the size of the nano-gap [303]. Fully quantum calculations using time-dependent density functional theory are computationally intensive and are reserved for plasmonic structures with a size ≲10 nm. In another computational study, the plasmonic properties of a 55-atom silver nanoparticle are simulated using real-time time-dependent density functional theory [304] and the dominant channels for hot-carrier generation are identified, providing a greater insight into plasmon decay mechanisms in quantum plasmonics.

Having given a brief introduction to the field of quantum plasmonics, this section continues with specific examples of quantum plasmonic metrology in the biosciences. Zhou et al. highlight that the field of quantum plasmonics is now moving from fundamental science towards technological applications [290]. Examples of quantum plasmonic devices with potential biosensing applications are summarized in Figure 14. The blueprints for quantum plasmonic sensors are diverse, but some common themes include using quantum states of light with classical detectors, integrating coherent photon-plasmon conversion processes and/or using the quantum tunnelling property of plasmonic nanogap structures. Plasmon rulers exploit the quantum tunnelling property of coupled plasmonic dimers, which consist of two metal nanoparticles separated by a nanoscale gap. The quantum tunnelling regime occurs at dimer separations, S, below which the tunnelling-induced conductance becomes large enough to allow a significant fraction of the plasmon-induced surface charges to tunnel across the gap in half an optical cycle (S ≲ 1 nm) [303]. The concept behind the plasmon ruler is to increase the quantum tunnelling range by connecting the nanoparticle dimer with a DNA linker. This introduces bond tunnelling, which promotes direct charge exchange between the nanoparticle dimer. Lerch and Reinhard [305] demonstrate that by tethering the nanoparticle dimer with a DNA linker, as shown in Figure 14a, the range of coherent charge transfer can be extended to dimer separations of S ≈ 2.8 nm. The plasmon ruler is highly sensitive to changes in the tunnelling current due to ion or protein binding to DNA, which provides a new concept for quantum plasmonic biosensing.

Figure 14:

(a) DNA linker in a plasmonic nanoparticle dimer increases the range of coherent charge transfer. Adapted from the study by Lerch and Reinhard [305] with DNA linker illustration by David S. Goodsell and the RCSB PDB under CC-BY-4.0 license. (b) Plasmonic metasurface increases the conversion efficiency between photons and plasmons for quantum plasmonic detection schemes. Adapted with permission from the study by Dowran et al. [156] © The Optical Society. (c) Hybrid quantum-limited sensor that takes advantage of multiple features from plasmonic, electronic and spectroscopic approaches to maximize sensing capabilities. Adapted from the study by Zhu et al. [306] under Creative Commons Attribution 4.0 International License. (d) Using quantum states of light in plasmonic sensing schemes; plasmonic N00N state in a silver nanowire. Based on the study by Chen et al. [300]. (e) Theoretical proposal for strong coupling between a silver nanowire and silver nanorod across a plasmonic nanogap. Based on the study by Qian et al. [307].

Quantum-enhanced plasmonic sensors can also be realized by using quantum states of light. Dowran et al. use a two-mode squeezed displaced state of light (bright entangled twin beams) to demonstrate a quantum-enhanced surface plasmon resonance sensor [156]. A four-wave mixing process is used to generate a probe beam and a conjugate beam. The conjugate beam is sent to a photodetector for a reference intensity measurement, whilst the probe beam passes through the plasmonic sensor for the sample measurement, before arriving at the second photodetector. The plasmonic sensor is patterned by an array of triangular nano-holes, as shown in Figure 14b, and is designed to provide coherent conversion between photons and plasmons, whilst preserving the quantum properties of light. The intensity difference between the measurement and reference beams is subtracted, before passing to a spectrum analyser to demodulate and measure the refractive index shift from the plasmonic sensor. Using this method, it is possible to achieve sensitivities on the order of 10−10RIU/Hz.

Another example of a plasmonic sensor that utilizes quantum states of light is presented by Chen et al. [300]. The experimental setup is similar to Dowran et al. [156], but the plasmonic nanohole array is replaced by the tapered-fibre silver nanowire structure shown in Figure 14d. The structure can efficiently convert between photons and plasmons [308]. Chen et al. experimentally verify that polarization entangled photon pairs can excite a plasmonic N00N state in the silver nanowire and propagate over a distance of 5 μm before reconverting back into photons, whilst preserving high-quality entanglement throughout. They also assess the potential for the device to be used for super-resolution and super-sensitivity measurements and find that after quantifying the losses in the experimental setup, the sensor does not quite meet the criteria for these measurements. Chen et al. suggest that with a twofold coincidence measurement for the two-photon state input and a few improvements to the experimental setup, it would not be impossible to achieve super-sensitivity in the future.

Hybrid sensors take advantage of multiple features from plasmonic, electronic and spectroscopic approaches to maximize sensing capabilities. Zhu et al. demonstrate a hybrid meta-surface sensor with quantum-limited measurement for monolayers of sub-nanometer-sized particles and affinity binding-based quantitative detection of glucose down to 200 pM [306]. They further demonstrate enhanced fingerprinting of minute quantities of glucose and polymer molecules. The metasurface architecture is shown in Figure 14c and shows a monolayer of graphene suspended above a gold nanorod antenna array. The nanoantenna array sits above a platinum mirror, separated by a quartz spacer layer. The sensor operates in air, but there are challenges to integrate the sensor with microfluidic channels due to the stability of monolayer nanomaterials.

Qian et al. propose a sensor based on the strong photon-exciton coupling in a plasmonic nanogap between a silver nanowire and silver nanorod [307]. The proposed setup is shown in Figure 14e. They choose to define the sensitivity of the strongly coupled photon-exciton system according to the Rabi splitting of energy, rather than by the plasmon resonance shift, as it can be directly linked to the dipole moment of the emitter and the electric field corresponding to a single excitation of the silver nanorod. By optimising these parameters for the system, they show that the sensitivity of the quantum plasmon sensing system can exceed that of the traditional plasmon sensing system, which in principle only depends on the resonance spectral shift. Their scheme is yet to be experimentally realized.

Recently, there has been a growing interest in plasmonic strong coupling [309], including sensors based on the strong coupling between plasmonic modes and the optical modes of single emitters [310]. This type of sensor confines light to micro-to pico-sized cavities or gaps, whereby the walls of the cavity are surfaces that support localized or propagating surface plasmon modes. The emitter is positioned inside the cavity or in between the two walls of the nano-gap, such that the optical modes of the emitter can interact with the plasmonic modes of the cavity. The strong coupling regime occurs when the plasmonic and emitting system have overlapping resonant eigenmodes and the strong coupling leads to new hybrid eigenmodes that are distinct from either the individual emitter or plasmonic modes. Plasmonic biosensors based on strong coupling have the potential to achieve superior sensitivity with lower optical power in comparison to the weak coupling case, due to the extreme confinement and amplification of light within the cavity or nano-gap structure.

Several experiments have shown strong coupling in systems that combine plasmonics with photon emitters [80], [311] or quantum dots. Leng et al. assess the properties of a plasmon-emitter system, consisting of a single colloidal quantum dot in the gap between a gold nanoparticle and a silver film [312]. Their results suggest that, in practice, the strong coupling regime is difficult to achieve for this system, since strong coupling is measured for less than 1% of the samples. In a different study, Santhosh et al. investigate strong coupling in plasmonic bowtie-quantum dot systems [185]. Their results show that they were close to achieving strong coupling in the case of a plasmonic bowtie with a single quantum dot. These examples demonstrate the importance of having a consistent definition for strong and weak coupling to compare different experimental results. Pelton et al. propose a uniform method for evaluating and quantifying strong coupling from the scattering spectra, which they derive from strong plasmon-exciton coupling theory [310]. Their analytical expressions can be used to reliably distinguish between Rabi splitting and exciton-induced transparency.

Computational methods are very useful for studying strong coupling in plasmon-emitter systems and can be used to accelerate research in this field. Classical electromagnetism simulations, using finite-difference time-domain methods or finite element methods, have been used to predict and optimize plasmonic-emitter configurations that would lead to strong coupling before doing experiments [313], [314], [315]. The strong coupling regime has also been explored with ab initio computational methods, which model the many-electron interactions of the system. Rossi et al. predict strong coupling between a 201-atom aluminium nanocluster and the molecular resonance of benzene [316]. Ab initio methods can capture the relevant interactions at the quantum level of theory and the relevant electronic transitions can be visualized with additional tools, which provide a greater insight into strong coupling mechanisms.

The strong coupling regime by plasmonics opens new prospects for single molecule detection and quantum optical biosensing. Ojambati et al. [96] recently showed that, with a few additional experimental considerations, it is possible to achieve strong coupling for a molecule-plasmonic system, which is considerably more challenging than for quantum dots due to the Stokes-shifted emission process and the range of vibrational modes. Their results show wavelength-dependent photon statistics in molecular systems, arising from a combination of biexciton excitation, photon-induced tunnelling and multiple excitations of the emitter. These results already show promise for future quantum biosensing applications.

7.3 Quantum-limited single molecule sensors

Tapered optical fibres, or nanofibers, are produced by pulling a single mode optical fibre with heating to reach diameters of hundreds of nm. They have previously been used to achieve nanoparticle trapping [317] (providing higher trapping forces than conventional optical tweezers) and single nanoparticle detection [318]. Mauranyapin et al. have extended the capabilities of fibre sensors to detecting nanoparticles and single biomolecules with quantum-limited precision, by using a heterodyne sensing technique [155]. Silica nanospheres down to 5 nm radius and single BSA (bovine serum albumin) molecules with 3.5 nm Stokes radius were detected in this setup. Dark-field illumination from a probe beam perpendicular to the fibre sensor is scattered by nanoparticles in the fibre’s evanescent field and modulated by a local oscillator propagating in the fibre (Figure 15). The high sensitivity detection was achieved by a heterodyne measurement, balanced at the detector by the pure local oscillator. This measurement scheme was recently developed to use an exposed core fibre sensor [319]. These sensors are more robust (around 120 µm diameter; compared with 500 nm tapered fibres) and can be produced with much longer sensing regions than the <1 mm provided by the previous setup. Detection of silica nanospheres down to 25 nm radius was demonstrated, but using an order of magnitude lower light intensity than the previous technique. The low light intensity used in these experiments is an important feature; since it is up to two orders of magnitude lower than quoted photodamage thresholds these schemes are promising for the observation of biological systems over long timescales.

Figure 15:

Tapered fibre single molecule detection platform.

(a) Sensor geometry; dark-field pump beam (orange) is scattered by nanoparticles into the tapered fibre. Local oscillator (red) propagating in the fibre modulates the scattered signal and is measured by a balanced detector. (b) Detection signal for a single BSA (bovine serum albumin) molecule. (c) Power spectral density of system noise is shown to scale linearly with local oscillator power, consistent with quantum-limited noise. Reprinted by permission from Springer Nature: Nature Photonics [155], copyright (2017).

Crucially, both experiments [155], [319] demonstrate that noise in the system follows a linear scaling with local oscillator power, consistent with quantum-limited noise (Figure 15c). Therefore, these sensors operate at the fundamental limit for a coherent light probe, i.e. are shot-noise-limited. Although sensitivity may be improved by using higher light intensities, this scaling will remain a limit for the technique. Exceeding this performance, as stated in Ref. [155], would require the use of quantum correlated photons.

7.4 Prospects of ultra-sensitive detection with optoplasmonic sensor

State of the art optical label-free micro- and nanosensors are developed to enable the detection of biomolecules at the level of single molecules [293]. Plasmonic nanoparticles and nanostructures are particularly well suited to develop these nanosensors. Their ultra-small modal detection volumes translate into very high detection sensitivities. In 2012, single protein molecule detection in aqueous solution was demonstrated with plasmonic nanorods as small as approximately 37 × 9 nm in the studies by Ament et al. and Zijlstra et al. [320], [321]. In both demonstrations, individual protein binding events were recorded from the shifts of the plasmon resonance spectra. In the most sensitive demonstration that was aided by a photothermal effect [321], the best sensitivity at the shot noise limit was estimated at ∼53 kDa, approximately the molecular weight of streptavidin protein. Many important protein markers for disease have a molecular weight larger than 50 kDa, examples for this are antibodies. With arrays of plasmonic gold nanorods having already demonstrated clinically relevant bulk detection tasks [322], the emerging localized surface plasmon resonance (LSPR) single-molecule sensors are poised to play a very important role in future healthcare applications. Moving beyond the current ∼53 kDa detection limit of LSPR sensors, however, requires new approaches to advance on the uphill road of improving the single-molecule detection of plasmonic nanosensors. One of the very promising and very recent approaches in this regard is based on the use of optical microcavities to read out the response of plasmonic nanosensors, a class of hybrid photonic-plasmonic sensors called optoplasmonic sensors [146].

In order to understand the exceptionally high single-molecule sensitivity of optoplasmonic sensors, it is instructive to first review the sensing mechanisms that have been established for optical microcavities based on WGMs [29], [323]. The electric-field operator of a quantized WGM at frequency ω_L takes the general form,

with the normalized mode vector u(r) and the annihilation a and creation a^† operators of intracavity photons. When a tiny particle (e.g. metal nanoparticle and molecules) is located in the vicinity of the microcavity, the evanescent light of a WGM perturbs the distribution of electrons in the particle, which in turn affects the spectral profile of the WGM. Two counter-propagating WGMs (clockwise: cw and counter-clockwise: ccw) are degenerate, i.e. corresponding to the same mode frequency ω_L. The particle interacts with cw and ccw WGMs simultaneously. In general, the particle may be modelled by a two-state (upper |e⟩ and lower |g⟩) system with a transition frequency ω_A. The coupling strength between the light-induced dipole moment d of particle and the cw (ccw) WGM is gcw=−d⋅ucwr0/ℏ (gccw=−d⋅uccwr0/ℏ) with the particle’s location r₀. Besides the particle-WGM coupling, the particle also interacts with the (vacuum) bosonic reservoir, which accounts for the backscattering and Rayleigh scattering of WGM photons. The jth boson mode is characterized by the annihilation b_j and creation bj† operators with the corresponding frequency ω_j. The coupling strength between the particle and the jth boson mode is gj=ωj2ℏϵ0Vvac|d| with the quantization volume V_vac. As a result, the Hamiltonian for some such interacting system is written as

with the particle’s operators σeg=|e〉〈g|, σge=σeg†=|g〉〈e| and σz=|e〉〈e|−|g〉〈g|. According to the Heisenberg equation of motion for an operator, dO/dt=i[H/ℏ,O], one obtains the following equations

where we have artificially inserted the dissipative terms associated with the cavity losses (rate κ) and the decay of particle’s polarization (rate γ). In the weak-coupling limit, the particle stays mainly in the lower state |g⟩, thereby σ_z ∼ −1. Following the Weisskopf-Wigner approach, the equations of motion for the cavity operators can be approximately derived as

Here we have defined the particle’s polarizability α=|d|2ℏ(ωA−ωL−iγ/2), the Rayleigh scattering rate ΓR=(αϵ0)2ωL46π(c/n)3Vcav, and the mode frequency shift Δ=(αϵ0)ωL2Vcav. The WGM volume V_cav is defined based on the light intensity at the location r₀ of particle and φ denotes the phase difference between cw and ccw waves at r₀. The above coupled equations may be extended to a system with multiple particles,

with the fibre taper-cavity coupling strength κ_in and the amplitudes acwin and accwin of the input cw and ccw fields, respectively.

As one can see, the cw and ccw WGMs are coupled with each other through the backscattering and Rayleigh scattering. This, as a result, gives rise to the spectral splitting and broadening in the passive measurement of transmission spectra, as shown in Figure 16. It is worth noting that the splitting distance between two spectral peaks may either increase or decrease as a new particle is bound to the microcavity’s surface because of the phase differences φk (Figure 16b).

Figure 16:

(a) Series of transmission spectra recorded with successive depositions of nanoparticles. (b) Splitting distance versus the number of nanoparticles bound to the microcavity’s surface. Reprinted by permission from Springer Nature: Nature Photonics [323], copyright (2009).

Optical dielectric microcavities such as tiny ∼100 um glass microspheres confine light for an extended time period by the near-total internal reflection of light. The resulting WGM optical resonances exhibit very narrow linewidths and high quality factors up to 10⁹ in air [324]. The dielectric WGM sensors are immersed in liquid sample solution to detect protein molecules as they bind to the surface of the glass microsphere [325], [326]. For example, the binding of BSA protein to the WGM sensor shifts the frequency (wavelength) of the WGM [326] continuously as a protein layer is formed. The WGM frequency shifts are caused by the energy required to polarize the nanosized protein molecules in the layer, with the evanescent field of the WGM. By first-order perturbation, the molecules need only to be characterized by their polarizability α_ex in excess of that of the surrounding medium, which in biosensing is water:

where Δω is the WGM frequency shift, ω is the unperturbed WGM resonance frequency before the protein is adsorbed, α_ex is the excess polarizability of the protein molecule with respect to the solvent, ε_r denotes the refractive index distribution, E₀(r) is the electric field of the WGM, and r_p is the molecule’s position. The above equation is often referred to as the reactive sensing principle (RSP). It allows us to estimate the frequency shifts induced by a variety of biomolecules in different biosensing applications of dielectric WGM sensors [327]. A careful analysis of the WGM detection limits [328] reveals that one has to maximize a figure of merit that is proportional to Q/V in order to achieve a high nanoparticle per-molecule detection sensitivity, where V is the mode volume of the probing WGM.

The equation shown above can be applied to the optoplasmonic sensor, a WGM-plasmonic nanoparticle system, under the assumption that the plasmonic nanoparticle only act to locally enhance the electric field interacting with the molecules. With this in mind one rewrites this RSP equation as

where f²(r_p) = |E₀(r_p)|²/max[ε(r)|E₀(r)|²] is the normalised mode distribution and V_m = ∫_Vε(r)|E₀(r)|²dr/max[ε(r)|E₀(r)|²] is the mode volume [329]. The enhancement factor f²_enh(r_p) = f²(r_p)_{WGM optoplasmonic}/f²(r_p)_{WGM dielectric} signifies the boost of the single-molecule detection signal that is obtained on the hybrid optoplasmonic WGM sensor as compared to the dielectric WGM counterpart without plasmonic nanoparticle, if the Q factor and V_m do not significantly change when forming the WGM-plasmonic nanoparticle system which is most often the case in biosensing [329].

Optoplasmonic WGM sensors can be most easily realized by attaching one or more plasmonic nanoparticles to a WGM glass microsphere cavity [330], [331], [332]. For the optoplasmonic sensing of single DNA molecules, a gold nanoparticle of ∼20–100 nm in size is attached to ∼80 μm diameter WGM microsphere [332]. The self-assembled optoplasmonic sensors enable the detection of single DNA oligomers (11-mers) and intercalating dye molecules <1 kDa in molecular weight [332], demonstrating an optoplasmonic sensor sensitivity that is much improved over the ∼53 kDa detection limit reported for the LSPR nanosenors [321]. On ultra-sensitive optoplasmonic WGM sensors, single-molecules are detected from the shifts of the resonance frequencies of hybrid photonic-plasmonic WGMs. The shifts appear when molecules bind to the metal nanoparticle, where they perturb the sensor system. In the most sensitive single-molecule sensing demonstrations [147], [333], the WGM remains weakly coupled [334], [335] to the plasmon resonance of the attached plasmonic nanoparticle, a gold nanorod. In these demonstrations, the plasmonic nanoparticle, the gold nanorod, provides a dramatic near field enhancement at the single-molecule detection site. The gold nanorods employed in these demonstrations are excited near plasmon resonance with WGM and provide high near field enhancements due to their rod-shaped nanostructures and their high aspect ratio. Experimentally, it was found that single molecules such as BSA (∼66.5 kDa) shift the hybrid-photonic plasmonic WGM by several tens of MHz when the protein molecules bind to the most sensitive detection sites encountered most likely at the tips of the nanorod. The enhancement of the detection signal there is on the order of f²_enh∼10^3–4. For the dielectric WGM microcavity counterpart, the RSP predicts only ∼ kHz of WGM frequency shifts [325]. Given the small single-molecule polarizabilities of proteins such as BSA (∼66.5 kDa) [336] and even much smaller polarizabilities of aminoacids as such as cysteine (∼121 Da) and small molecules such as cysteamine (∼77 Da), all of which have been detected on optoplasmonic WGM sensors [29], the detection signal on the dielectric WGM sensor would be well below the noise floor.

One can conceptually explain the enhancement factor of 10³–10⁴ improvement of optoplasmonic WGM detection limits over those of dielectric WGM microsphere sensors with the plasmonic near-field enhancements provided by the plasmonic nanostructures which are nanorods in all of the highly sensitive demonstrations well below the ∼53 kDa LSPR detection limit. The nanorod-based plasmonic near-field enhancements benefit from the surface roughness of gold nanorods [332] and may result in the factor 10^3–4 of optoplasmonic single-molecule sensitivity enhancements that have been observed. The relative improvements in the sensitivity of optoplasmonic sensors may be approximated by a figure of merit that is proportional to Q/V×E2/E02. The term E2/E02 denotes the maximum near field enhancement that single molecules can explore within a detection site at or near the surface of a plasmonic nanostructure coupled to the WGM microcavity. Note that the Q factor and the mode volume after attaching gold nanorods to the WGM resonator do not change significantly in actual biosensing experiments in water. Dielectric WGM sensors immersed in water for biosensing applications start out with a Q factor on the order of 1 × 10⁷. Their polar mode numbers l [337] are typically in the range of l = 300 to l = 1000 for the WGMs excited in glass microsphere as small as 80 m and at visible to near infrared wavelengths 640 –780 nm. The Q factor drops to approximately 2–3 × 10⁶ after the cavity is modified with one or a few gold nanorods [147], [292], [332], [333].

The plasmonic near field of optoplasmonic sensors defines a detection length scale which can be on the order of the diameter of a protein such as BSA with a diameter of about ∼3–4 nm. Any changes in the chemical structure or physical shape (conformation) of a protein such as an enzyme that remains immobilized within the nanometer-scale plasmonic sensing hotspot can be observed in real-time [281], [294]. Optoplasmonic sensors are thus sensitive to structural changes in protein because the detection signal, the resonance frequency or wavelength shift, changes as the overlap of the protein with the highly localized near field changes. Likewise, any chemical changes in the composition of the immobilized protein or the binding of a substrate to an enzyme or a ligand to a receptor would all contribute to the shifts. The variations of the wavelength shift signal Δλ caused by e.g. conformational (shape) changes of a protein can be estimated from:

The magnitude and sign of these Δλ wavelength shifts are proportional to the changes in the electric field intensity integrated over the volume occupied by the molecule v_m(t) at the times t₁ and t₂, where αex is the excess polarizability of the protein, and v_m (t) is the volume taken up by the protein which depends on the conformation (shape) of the protein adopted at time points t₁ and t₂.

Several demonstrations for the optoplasmonic sensing beyond the ∼53 kDa LSPR detection limit have been reported for optoplasmonic WGM sensors. These demonstrations including the detection of 11-mer oligonucleotides and the small, intercalating <1 kDa dye molecules [332], as well as the sensing of single atomic ions such as Zn²⁺ and Hg²⁺ ions in aqueous solution [333]; and most recently the monitoring of intricate chemical reactions such as the disuflide exchange reaction [147] and the detection of small dithiobis(C2-NTA, ∼772 Da) molecules from effective WGM linewidth shifts [329].

Single cysteamine molecules have been detected at attomolar concentration levels as the ∼77 Da molecules bind to the gold nanorods of a WGM optoplasmonic sensor (Figure 17). The cysteamine molecules link to gold nanorod via their amine group, at the specific buffer conditions used for their immobilization. Once bound, the thiol group of the cysteamine molecule provides a single thiol site for the reversible binding of, i.e. D- and L-cysteine aminoacids. In this way, it becomes possible to find experimental conditions that allow for the repeated probing of a thiolated molecule species such as D- or L-cysteine as these molecules repeatedly bind and unbind at a single thiol sensing site. In this way, the heterogeneity of sensing sites on the optoplasmonic WGM nanosensors can be greatly reduced or removed. This results in signal levels in the single molecule traces [147], which marks an important milestone for demonstrating the laboratories on chip that can potentially identify molecular species. It is a milestone for demonstrating the quantitative analysis of the sensing signals and thereby achieving advanced single-molecule sensing capabilities such as chiral discrimination i.e. of the D and L aminoacids.

Figure 17:

(a) TOP: An optoplasmonic sensor combines the light recirculation in a high Q (Q∼10⁶⁻⁷) whispering-gallery mode (WGM) microsphere cavity with the plasmonic near field enhancements of gold (Au) nanorods (NRs) that are attached to the microcavity. BOTTOM: Optoplasmonic sensor signals that were recorded for individual cysteamine (∼77 Da) molecules binding to the Au NRs. Binding events are detected from femto-meter step-changes in the resonance wavelength or linewidth traces. The detection sensitivity of 300 aM cysteamine required specific buffer conditions, adapted from [147]. (b) TOP: Dielectric WGM cavity sensing mechanism. The WGM resonance changes as single (analyte) nanoparticles diffuse and bind to the dielectric WGM sensor within its evanescent field where the WGM interacts with the nanoparticle, adapted from [330]. BOTTOM: Optoplasmonic WGM sensing mechanism. A plasmonic nanoparticle attached to the WGM sensor and excited by the WGM near the plasmon resonances frequency enhances the intensity of the probing light field at the surface of the nanoparticle. Single molecules are detected with much higher sensitivities if they bind within the region of plasmonic near-field enhancements where, depending on the plasmonic nanoparticle or system, the wavelength shift can be greatly enhanced by a factor of 10³–10⁴ over the shift expected for an all-dielectric microsphere sensor, adapted from [330].

With further technical improvements, it is expected that the optoplasmonic sensors will be able to demonstrate single-molecule sensing capabilities by operating with single photons and at the detection limit set by the quantum noise. The development of the faint-light metrology for single-molecule WGM biosensors operating at the quantum limits will help us implement the most noninvasive optical single-molecule probing techniques. Once single molecules can be probed with single photons it is envisaged that the single photons can be analysed for additional phase or polarization information. The analysis of single photons that have interacted with single molecules may provide us with the possibility for measuring the properties of the molecules that could not have been measured with classical techniques. For example, it is envisaged to realize time averaged single photon-single protein short time scale interactions which could be further improved with ultrafast pulses and they can probe the quantum properties outlined in the first section of this review.

Advancing the sensing capabilities of optical micro and nanosensors even further, beyond the classical limits of detection and beyond the photon shot noise, will require entirely new approaches. Quantum metrology applied to optoplasmonic sensors provides a new avenue to take for advancing single molecule detection capabilities and improving the sensitivity. Moving beyond the classical detection limits, will require the application of quantum-correlated non-classical light sources and quantum measurement schemes described in Sections 4 and 5. Bowen et al. have already demonstrated detection of approx. 50 kDa bovine serum albumin proteins with evanescent optical fibre sensors operating at the photon shot noise (quantum noise) limit [155]. It is envisaged that the optoplasmonic WGM sensors can operate beyond the standard quantum limit (SQL) with the applications of N00N states and squeezed light states. Moving existing biosensing techniques to the quantum-enhanced regime comes with a considerable increase in complexity; for example the need for single photon detectors, single photon timing and counting modules, stringent limits on optical losses, and quantum optical light sources such as non-linear crystal setups. However, the complexity could be significantly reduced with the integration of components on-chip. As demonstrated in Section 6, quantum optical light sources and even entire sensors have the potential to be integrated on-chip, and could therefore become more accessible through collaborations with experts in integrated quantum information technologies and fabrication. Quantum optical laboratories on a chip will enable us to use quantum biosensors such as optoplasmonic WGM sensors to explore Nature’s smallest entities such as single molecules, single photons, pico-Newton forces, molecular chirality, and their interesting physics and applications at unprecedented quantum levels of detection whilst not interfering with the biomolecular activity.

7.5 Quantum optical imaging

Before we close our discussion on the prospects and progress of new generation sensors with unprecedented detection limits driven by quantum phenomena, it will be worthwhile to give a short glimpse of the advances in quantum optical imaging. Ghost imaging was the first experimentally demonstrated imaging technique exploiting quantum correlations between photons [338]. This technique uses entangled photon pairs from a spontaneous parametric down-conversion (SPDC) source. One of each photon pair passes through the object to a bucket detector and the other passes directly to a spatially-resolving detector. Momentum correlations between paired photons allow an image to be formed from coincident signals at the two detectors. Ghost imaging has since been shown to be possible using intensity correlations in purely classical coherent [339]—and even thermal [340], [341]—light sources. Despite this, quantum correlations offer improvements in resolution over classical schemes and the possibility of sub-shot noise sensitivity [342]; see Meda et al. for a review of this area [343].

Imaging schemes relying on quantum correlations include quantum illumination [345], [346], [347], sub-shot noise imaging [19], [20], interaction-free imaging [348] and quantum correlated plenoptic imaging [349], [350]. Rather than working to improve resolution, these techniques typically aim to increase imaging sensitivity, achieving greater image contrast against background thermal noise than is possible using classical imaging. Improved sensitivity allows the imaging of weakly absorbing objects at low light intensities; a regime ideally suited to biological samples prone to photo-damage. As a demonstration of this, Morris et al. [344] reported imaging a wasp wing in a heralded single photon imaging experiment with an average of only 0.45 photons per pixel (Figure 18).

Figure 18:

Heralded single-photon imaging of a wasp wing.

a and c direct imaging b and d reconstructed image using correlations in photon pair detection. Scale bar in a measures 400 µm. Adapted from the study by Morris et al. [344], available under creative commons license 4.0.

A recent development in quantum illumination was the first full-field imaging setup. This achieved up to a factor of 5.5 improvement in image contrast over a setup using illumination with classical light in the presence of thermal background noise [351]. Wide-field microscopy has also been demonstrated with sub-shot noise sensitivity; 80% of the shot-noise level per pixel [20]. By applying median filtering, noise could be reduced further to <30% of the shot-noise level. Imaging can even be performed by measuring photons which have not interacted with the object directly, by using two photon pair sources and detecting photons entangled with those passing through the sample [348]. This could allow detectors to operate in a different frequency band to that incident on the sample, working in a band where the available detector efficiency is higher for example.

Quantum-enhancements to image resolution have also been proposed, for example using entangled two-photon fluorescence microscopy [352]. Typically, high light intensities are required to efficiently detect non-linear fluorescence processes, but by instead exploiting correlations between entangled photon pairs, much lower light intensities could be used. Two-photon fluorescence has been demonstrated using entangled photons illuminating organic fluorophores, including porphyrin dendrimers [162] and annulene systems [353]. A two-photon microscope using entangled photons has also been produced which achieved a signal-to-noise ratio 1.35 times greater than possible at the shot-noise limit [354]. An experiment combining these to produce an entangled two-photon fluorescence microscope could not be found.

Sub-diffraction imaging can also be achieved using the single photon properties of fluorescence from individual NV centres [356], [357] and CdSe/CdS/ZnS colloidal quantum dots [358]. In these reports, nearby single photon emitters are resolved below the diffraction limit by measuring higher-order intensity correlations in the light emitted by fluorescence. Rather than illuminating a sample with entangled photons, this approach performs imaging by measuring the photon statistics of light emitted from the sample itself. The most advanced imaging experiment working on this principle was recently reported by Tenne, Rossman, Rephael et al. [355]. This experiment combined the classical image scanning microscopy (ISM) method with correlation measurements between high time resolution single photon detectors, to image single photon fluorescence emission from CdSe/CdS/ZnS quantum dots. Features in microtubule cell samples containing these nanoparticles were imaged with a resolution four times the diffraction limit, as shown in Figure 19.

Figure 19:

Microtubule imaging using quantum ISM.

Image scanning microscopy (ISM) images of a microtubule sample labelled with fluorescent quantum dots. Different imaging techniques using the same experimental setup are compared, from classical scanning microscopy (CLSM, a) to Fourier reweighted quantum image scanning microscopy (FR Q-ISM, d). Scale bar: 0.5 µm. Reprinted by permission from Springer Nature: Nature Photonics [355], copyright (2018).