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Dynamic resonance fluorescence in solid-state cavity quantum electrodynamics

Nature Photonics volume 18, pages 318–324 (2024)Cite this article

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Abstract

The coherent interaction between a two-level system and electromagnetic fields serves as a foundation for fundamental quantum physics and modern photonic quantum technology. A profound example is resonance fluorescence, where the non-classical photon emission appears in the form of a Mollow-triplet when a two-level system is continuously driven by a resonant laser. Pushing resonance fluorescence from a static to dynamic regime by using short optical pulses generates on-demand emissions of highly coherent single photons. Further increasing the driving strength in the dynamical regime enables the pursuit of exotic non-classical light emission in photon number superposition, photon number entanglement and photon bundle states. However, the long-sought-after spectrum beyond the Mollow-triplet, a characteristic of dynamic resonance fluorescence under strong driving strength, has not yet been observed. Here we report the direct observation and systematic investigations of dynamic resonance fluorescence spectra beyond the Mollow-triplet in a solid-state cavity quantum electrodynamic system. The dynamic resonance fluorescence spectra—with up to five pairs of side peaks, excitation detuning-induced spectral asymmetry, and cavity filtering effects—are observed and quantitatively modelled by a full-quantum model with phonon scattering included. Time-resolved measurements further reveal that the multiple side peaks originate from interference of the emission associated with different temporal positions of the excitation pulses. Our work facilitates the generation of a variety of exotic quantum states of light with dynamic driving of two-level systems.

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Fig. 1: Spectrum of dynamic RF with multiple side peaks from a cQED system.
Fig. 2: Dynamic RF spectra beyond the conventional Mollow-triplet.
Fig. 3: Cavity-enhanced side peaks in the spectra of dynamic RF.
Fig. 4: Time ordering of the side peaks in the spectra of dynamic RF.
Fig. 5: Transition from dynamic RF to static RF.

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Data availability

The data that support the plots within this paper and other findings of this study are available on figshare (https://doi.org/10.6084/m9.figshare.24501241). All other data used in this study are available from the corresponding author on reasonable request.

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Acknowledgements

This research was supported by the National Key Research and Development Program of China (2021YFA1400800, 2018YFA0306101); the National Natural Science Foundation of China (62035017, 12304409); the Guangdong Special Support Program (2019JC05X397); the National Super-Computer Center in Guangzhou; and the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Author notes

  1. These authors contributed equally: Shunfa Liu, Chris Gustin and Hanqing Liu.

Authors and Affiliations

  1. State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China

    Shunfa Liu, Xueshi Li, Ying Yu, Xuehua Wang & Jin Liu

  2. Edward L. Ginzton Laboratory, Stanford University, Stanford, CA, USA

    Chris Gustin

  3. State Key Laboratory for Superlattice and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China

    Hanqing Liu, Haiqiao Ni & Zhichuan Niu

  4. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China

    Hanqing Liu, Haiqiao Ni & Zhichuan Niu

  5. Department of Physics, Engineering Physics, and Astronomy, Queen’s University, Kingston, Ontario, Canada

    Stephen Hughes

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Contributions

J.L. and X.H.W. conceived the project; S.F.L., J.L. and H.Q.L. designed the epitaxial structure and the devices; H.Q.L., Y.Y. and H.Q.N. grew the quantum dot wafers; S.F.L. and X.S.L. fabricated the devices; S.F.L. built the set-up and performed the optical measurements; C.G. performed all the theoretical modelling with input from S.H., and wrote the main theory parts of the paper and the Supplementary Information; S.F.L., J.L. and C.G. analysed the data; J.L. and S.F.L. prepared the main manuscript with inputs from all authors; J.L., S.H., Z.C.N. and X.H.W. supervised the project.

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Correspondence to Xuehua Wang or Jin Liu.

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Extended data

Extended Data Fig. 1 Schematic of the setup for optical characterizations.

The setup consists of 6 functional sections including a cryogenic resonant excitation system, a pulse shaper, a power controller, a spectrometer, an etalon filter, and a lifetime measurement section. The measurements start from shaping the femtosecond (fs) pulses to a picosecond (ps) pulse with tunable wavelength and controllable pulse width between 10 ps and 55 ps by a homemade 4f system and gratings. The power of the shaped ps pulse is then controlled by rotating a polarizer between two fixed polarizers with the same polarization axis and monitored by a power meter. The resonant excitation of the QD is based on a cross-polarization scheme, pairs of the polarizer and half-wave plate are inserted into the excitation and collection optical path for polarization control. RF from QD is coupled to an optical fibre, guided to a spectrometer for spectrum analysis, or used for time-resolved measurement after filtering with an etalon. BS: beam splitter, HWP: half-wave plate, LP filter, PC: polarization controller.

Extended Data Fig. 2 Experimental parameters of the investigated devices.

(a) Cavity spectrum of device 1 under high-power above-band excitation. A Q-factor of 10584 is acquired by fitting the data with a Lorentz function. Inset: scanning electron microscope (SEM) image of device 1 with a diameter of 2.5 μm. (b) π-pulse RF spectra of the QD in device 1 when QD is on/off-resonance with the cavity mode. (c) Corresponding on/off-resonance lifetimes of the QD at π pulse. (d) Rabi oscillation of device 1 extracted from Fig. 2(b),(e) Parameters of the devices investigated in the main text. The Purcell factors are calculated by using \({{{{\rm{F}}}}}_{{{{\rm{p}}}}}=\frac{{\tau }_{{{{\rm{off}}}}}}{{\tau }_{{{{\rm{on}}}}}}-1\), where τon and τoff are the lifetimes of the QD under resonant and off-resonant conditions, respectively. The extraction efficiencies are calculated with \(\eta =\frac{{{{{\rm{F}}}}}_{{{{\rm{p}}}}}}{{{{{\rm{F}}}}}_{{{{\rm{p}}}}}+1}\times \frac{Q}{{Q}_{0}}\) in which Q is the quality factor of the micropillar and Q0 is the quality factor of the unetched planar cavity.

Extended Data Fig. 3 Laser detuning dependent RF spectra.

(a) Measured laser detuning dependent dynamic RF spectra of device 1 at 4π pulse area. (b) Calculated dynamic RF at 4π pulse area with varied Δx. (c) Measured laser detuning dependent dynamic RF of device 1 at 6π pulse area. (d) Calculated dynamic RF at 6π pulse area with varied Δx. The pulse width is kept for 46 ps for this experiment.

Extended Data Fig. 4 Dynamic RF with varied pulse width τfw (FWHM of the laser pulse) under the condition of Δc = 0 for device 1 at 14 K.

(a) Excitation condition: Δx = 0, τfw = 13 ps. (b) Contour plots of the measured RF spectra [under the condition in (a)] as a function of driving pulse amplitude. The side peaks are labelled with s1 to s2. (c) Log-scale RF spectra [under the condition in (a)] at 4π pulse areas. The position of side peak 1 is pointed out with the dashed line in red. (d) Excitation condition: Δx = 0, τfw = 24 ps. (e) Contour plots of the measured RF spectra [under the condition in (d)] as a function of driving pulse amplitude. (f) Log-scale RF spectra [under a condition in (d)] at 4π pulse areas. (g) Excitation condition: Δx = 0, τfw = 54 ps. (h) Contour plots of the measured RF spectra [under the condition in (g)] as a function of driving pulse amplitude. (i) Log-scale RF spectra [under the condition in (g)] at 4π pulse areas. The side peaks get close to each other and move toward the central peak as the pulse width increases.

Extended Data Fig. 5 Dynamic RF with varied pulse width τfw under the condition of Δc/(2π)= −26 GHz for device 1 at 4 K.

(a) Excitation condition: Δx = 0, τfw = 14 ps. (b) Contour plots of the measured RF spectra [under the condition in (a)] as a function of driving pulse amplitude. The side peaks are labelled with s1 to s3. (c) RF spectra [under the condition in (a)] at 4π and 6π pulse areas. (d) Excitation condition: Δx = 0, τfw = 25 ps. (e) Contour plots of the measured RF spectra [under the condition in (d)] as a function of driving pulse amplitude. (f) RF spectra [under a condition in (d)] at 4π and 6π pulse areas. (g) Excitation condition: Δx = 0, τfw = 54 ps. (h) Contour plots of the measured RF spectra [under the condition in (g)] as a function of driving pulse amplitude. (i) RF spectra [under a condition in (g)] at 4π and 6π pulse areas. Because of the enhancement of the cavity mode, the intensity of the peaks on the left side is comparable with that of the central peak. The side peaks are clearly observable even in the linear scale.

Extended Data Fig. 6 Comparison of different models for reproducing the experimental result in Fig. 3(c).

(a) The TLS is driven directly by the laser with \({H}_{{{{\rm{drive}}}}}(t)=\frac{\Omega (t)}{2}({\sigma }^{+}+{\sigma }^{-})\), we use a naive bad-cavity model to eliminate the cavity mode, and phonons are not considered. (b) A full quantum model with a quantized cavity mode is adopted, with \({H}_{{{{\rm{drive}}}}}(t)=\frac{\Omega (t)}{2}(a+{a}^{{\dagger} })\), and phonons are not considered. The intensity asymmetry of the side peaks due to cavity filtering is reproduced, which agrees well with the experiment. (c) The cavity is driven with \({H}_{{{{\rm{drive}}}}}(t)=\frac{\Omega (t)}{2}(a+{a}^{{\dagger} })\), and phonons are included. This full model gives rise to additional phonon-induced features, also visible in the experiment, as highlighted by the white dotted line. (d) Contour plots of the measured RF spectra as a function of drive pulse amplitude with a pulse width of 54 ps under the condition of Δx = 0 and Δc/(2π)= −26 GHz at 4 K.

Extended Data Fig. 7 Influence of phonons on dynamic RF spectra.

Two additional devices (A and B) at the same sample with Q factors of ~ 7000, Purcell factors of ~ 7, and lifetimes of ~ 80 ps. For device A, QD is in resonance with cavity mode at the temperature of 4 K, and for device B, QD is in resonance with cavity mode at the temperature of 30K. (a) Contour plot of the measured RF spectra as a function of driving pulse amplitude for device A. (b) Rabi oscillation of the main peak in (a). (c) Contours plot of the measured RF spectra as a function of driving pulse amplitude for device B. (d) Rabi oscillation of the main peak in (c).

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and Discussion.

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Liu, S., Gustin, C., Liu, H. et al. Dynamic resonance fluorescence in solid-state cavity quantum electrodynamics. Nat. Photon. 18, 318–324 (2024). https://doi.org/10.1038/s41566-023-01359-x

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