Conditional $\ensuremath{\pi}$-Phase Shift of Single-Photon-Level Pulses at Room Temperature

Conditional $π$ -Phase Shift of Single-Photon-Level Pulses at Room Temperature

Steven Sagona-Stophel, Reihaneh Shahrokhshahi, Bertus Jordaan, Mehdi Namazi, and Eden Figueroa

Phys. Rev. Lett. 125, 243601 – Published 8 December 2020

Abstract

The development of useful photon-photon interactions can trigger numerous breakthroughs in quantum information science, however, this has remained a considerable challenge spanning several decades. Here, we demonstrate the first room-temperature implementation of large phase shifts ( $\approx π$ ) on a single-photon level probe pulse ( $1.5 μ s$ ) triggered by a simultaneously propagating few-photon-level signal field. This process is mediated by ${Rb}^{87}$ vapor in a double- $Λ$ atomic configuration. We use homodyne tomography to obtain the quadrature statistics of the phase-shifted quantum fields and perform maximum-likelihood estimation to reconstruct their quantum state in the Fock state basis. For the probe field, we have observed input-output fidelities higher than 90% for phase-shifted output states, and high overlap (over 90%) with a theoretically perfect coherent state. Our noise-free, four-wave-mixing-mediated photon-photon interface is a key milestone toward developing quantum logic and nondemolition photon detection using schemes such as coherent photon conversion.

Received 28 June 2019
Accepted 15 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.243601

Physics Subject Headings (PhySH)

Optical quantum information processing Quantum gates Quantum optics Quantum state engineering Quantum tomography

Atomic ensemble

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Steven Sagona-Stophel ^*,‡, Reihaneh Shahrokhshahi^‡, Bertus Jordaan, Mehdi Namazi, and Eden Figueroa^†

Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA

^*Corresponding author. stevensagona@gmail.com
^†Corresponding author. eden.figueroa@stonybrook.edu
^‡S. S.-S. and R. S. contributed equally to this work.

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Vol. 125, Iss. 24 — 11 December 2020

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Figure 1
(a) Experimental setup. A sequence of probe ( $Ω_{p}$ ) and signal pulses ( $Ω_{s}$ ) are sent through a room-temperature ${}^{87}{Rb}$ atomic ensemble. The probe output is then measured on a balanced homodyne detector and the associated quadrature and phase values are analyzed. (b) Diagram of our sequence of input pulses. First, we send a pulsed probe field ( $Ω_{p}$ ), with two CW control fields ( $Ω_{c 1}$ , $Ω_{c 2}$ ) creating EIT. Second, we add a pulsed signal $Ω_{s}$ field (in addition to the probe $Ω_{p}$ pulse), creating a double- $Λ$ system. Third, we switch off the probe pulse (leaving the signal pulse on), creating four-wave mixing FWM in the frequency of the probe. (c) Voltage values of the balanced homodyne detector, representing quadrature measurements of the pulse sequence. Across a scan of the phase of the local oscillator of the homodyne, phase information can be extracted from these pulses (as discussed in the SM [24]).
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Figure 2
(a),(b) Comparison between the phase and amplitude of each sinusoidal fit of individual homodyne scans and theoretical values for single-photon-level data. (a) The blue dots represent individual values of $Δ ϕ_{DL} - Δ ϕ_{FWM}$ vs $Δ ϕ_{FWM}$ for each individual homodyne “scan.” The orange dots represent the fitted amplitudes, $A (α_{FWM}, α_{p}, Δ ϕ_{FWM})$ , of each homodyne shot for the DL case. These are compared to their theoretical values (solid orange and dashed blue lines) obtained from Eqs. (21) and (22) in the SM, with $α_{p} = 0.57$ and $α_{FWM} = 0.91$ [24]. No free parameters are used in the theoretical fits. In (b) the blue points represent the phase shift, $Δ ϕ_{DL}$ vs $Δ ϕ_{FWM}$ . Part (c), to reconstruct the quantum state, the quadrature statistics obtained from the outputs must be sorted by their associated $Δ ϕ_{FWM}$ phase shifts. Using the phase information illustrated in (a) and (b), we can collect quadrature statistics associated with different binned phases (as discussed in the SM [24]). Extracted single-photon-level quadrature data are illustrated for the double- $Λ$ (teal) and EIT reference (red)—for different sets of postselected phase shifts (for bins $Δ ϕ_{FWM} \in 0.01, 1.33, - 0.91$ , and $- 2.77 \pm 0.37$ radians). Quadrature values are compared to their averaged fitted values (plotted as a solid line in red and teal).
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Figure 3
Reconstructed density matrices represented as Wigner functions are plotted, illustrating the relationship between inputs and outputs for different postselected phase shifts. The red and purple plots are the input states of the probe and signal. The teal plot is the phase-shifted probe output for (a) 0.3 radians phase shift, (b) $π / 2$ phase shift, and (c) $π$ phase shift.
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Figure 4
(a) For each postselected phase bin, the position in the phase space where the Wigner functions exhibit their maximum values are plotted, illustrating the motion in phase space of the probe output as the global input phase is changed. These maxima are illustrated for the double- $Λ$ states (in teal) and the four-wave mixing (in blue). Additionally, the maximum for the probe-only case is labeled in red for comparison. (b) Plots of mean photon number from reconstructed states, as a function of postselected phase shifts. Photon numbers are plotted as dashed lines for double- $Λ$ (dashed teal), four-wave mixing (dashed blue), EIT-probe (dashed red), and probe input (solid red). (c) Plots of “coherent-state fidelity” (CSF) from reconstructed states, as a function of postselected phase shifts. For each postselected phase shift, the associated reconstructed state is compared to a theoretical, perfect coherent state of the same mean photon number and phase. This is done for quadrature statistics for each pulse sequence (probe-only, double- $Λ$ system, and FWM in red, teal, and blue, respectively). (d) Plots of “phase-aligned, input-output fidelity” (PAIOF) from reconstructed states as a function of postselected phase shifts. The PAIOF fidelity (plotted as a dashed red line) is found by comparing the density matrix overlap between a reference in which the probe is reconstructed without the Rb cell and the phase-shifted double- $Λ$ output state. In calculating the PAIOF, the phase of double- $Λ$ state is shifted to be aligned to the phase of the input. Additionally, a “phase-aligned fidelity” is calculated between reconstructed states obtained between the pulse sequence 1 (probe-only case) and the pulse sequence 2 (double- $Λ$ case) and is plotted as a dashed green line. For comparison, we additionally plot the same phase-aligned fidelity calculations with theoretically perfect coherent states with the same mean photon number (as dotted red and green lines).
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Physical Review Letters

Conditional π-Phase Shift of Single-Photon-Level Pulses at Room Temperature

Steven Sagona-Stophel, Reihaneh Shahrokhshahi, Bertus Jordaan, Mehdi Namazi, and Eden Figueroa

Phys. Rev. Lett. 125, 243601 – Published 8 December 2020

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Conditional $π$ -Phase Shift of Single-Photon-Level Pulses at Room Temperature