Continuous-wave quantum light control via engineered Rydberg-induced dephasing

TL;DR

This work addresses continuous-wave all-optical single-photon transistors based on Rydberg-atom ensembles, exploring cw operation in both cavity and free-space geometries. The authors develop analytic impedance-matching criteria and engineer probe-induced dephasing to optimize control-photon storage lifetimes and probe-gain, supported by extensive wave-function Monte Carlo simulations. Key outcomes include near-unity impedance matching, cw efficiencies up to about 95% and gains exceeding 300 in some configurations, and robustness across 1D and 3D spatial distributions. The findings indicate a practical path to high-performance cw quantum-light control, with potential applications in optical detectors, quantum memories, and scalable quantum networks.

Abstract

We analyze several implementations of all-optical single-photon transistors (SPTs) operating in the continuous-wave (cw) regime, as presented in the companion paper [Phys. Rev. A 113, L011701 (2026)]. The devices rely on ensembles of Rydberg atoms interacting via van der Waals interactions. Under electromagnetically induced transparency (EIT), a weak probe field is fully transmitted through the atomic ensemble in the absence of control photons. Exciting a collective Rydberg state with a single control photon breaks the EIT condition, thereby strongly suppressing the probe transmission. We show how collective Rydberg interactions in an atomic ensemble, confined either in an optical cavity or in free space, give rise to two distinct probe-induced dephasing mechanisms. These processes localize the control excitations, extend their lifetimes, and increase the device efficiency. We characterize the SPTs in terms of control-photon absorption probability and probe gain, supported by numerical simulations of realistic one- and three-dimensional ensembles. The proposed cw devices complement previously demonstrated SPTs and broaden the toolbox of quantum light manipulation circuitry.

Figures (11)

• Figure 1: (a) Sketch of the system, showing the cavity version of the Rydberg-based single-photon transistor. An ensemble of Rydberg atoms in an optical cavity is continuously probed by a weak coherent field with strength $|\alpha_{\mathrm{in,p}}|^2$, which is fully reflected under EIT conditions, while driven by two classical drives $\Omega_\mathrm{c}$ and $\Omega_\mathrm{p}$. Upon sending a control photon $\hat{a}_{\mathrm{in,c}}$ to the cavity, it is converted into a Rydberg excitation, inducing an energy-level shift that modifies the reflection of the probe. (b) Atomic level scheme. The relevant atomic states form two $\Xi$ subsystems (branches): a probe branch ($\{ |g\rangle, |e_\mathrm{p}\rangle, |r_\mathrm{p}\rangle \}$), responsible for EIT-based probing by the input field $\alpha_{\mathrm{in,p}}$ under the drive $\Omega_\mathrm{p}$, and a control branch ($\{ |g\rangle, |e_\mathrm{c}\rangle, |r_\mathrm{c}\rangle \}$), responsible for converting a single-photon pulse into a stored Rydberg excitation $|r_\mathrm{c}\rangle$, which breaks the probe EIT via the interbranch van der Waals interaction $\mathcal{V}_{kl}$.
• Figure 2: First 20 trajectories of the Monte Carlo simulation for 3D Gaussian atomic distribution of $N=1000$ atoms in a cavity with cooperativity $C_\mathrm{c}=100$ and blockaded cooperativity $\overline{C}_\mathrm{b,p}=0.5$. The color of the dot indicate the nature of the jump that occur at the specific time. The parameters are fixed to $\Delta/\gamma_{e_\mathrm{c}} = 180, \kappa_\mathrm{p}=\kappa_\mathrm{c}=\gamma_{e_\mathrm{p}}=\gamma_{e_\mathrm{c}}, \Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} = 5, \Omega_\mathrm{p}/\gamma_{e_\mathrm{c}}=10$, $\delta/\gamma_{e_\mathrm{c}}=1.09$, $|\alpha_{\mathrm{in,p}}|^2/\gamma_{e_\mathrm{c}}=0.33$.
• Figure 3: Impedance matching results for the cavity model with $N=1000$ atoms. (a)-(c) Impedance matching probability $P_{\mathrm{IM}}$ as a function of probe strength for $\mathrm{Re}[\overline{C}_\mathrm{b,p}]\approx0.5$, with multiple curves corresponding to different values of cooperativity $C_\mathrm{c}= 10, 20, 50, 100, 1000, 5000$, shown for different atomic distributions: (a) symmetric ring geometry (b) 1D Gaussian (c) 3D Gaussian. (d)-(f) Numerically optimized dephasing rate (dots) and the theoretical estimate (solid line) versus the blockaded cooperativity, shown for the same values of $C_\mathrm{c}$ and atomic distributions: (d) symmetric ring geometry (e) 1D Gaussian (f) 3D Gaussian. In all panels, lower curves correspond to lower $C_\mathrm{c}$, and the curves for $C_\mathrm{c} = 1000$ and $5000$ nearly overlap. The parameters are fixed to $\kappa_\mathrm{p}=\kappa_\mathrm{c}=\gamma_{e_\mathrm{p}}=\gamma_{e_\mathrm{c}}, \Omega_\mathrm{p}/\gamma_{e_\mathrm{c}}=10, \Delta/\gamma_{e_\mathrm{c}} = 180,\Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} = 5$ for $C_\mathrm{c}=10,20,50,100$, and $\Delta/\gamma_{e_\mathrm{c}} = 4C_\mathrm{c}/5, \Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} =20,45,$ for $C_\mathrm{c}=1000,5000$. The detuning $\delta$ is optimized at each point to enhance $P_{\mathrm{IM}}$.
• Figure 4: Performance of the cavity model with $N = 1000$ atoms. (a)–(c) SPT efficiency as a function of blockaded cooperativity, for control branch cooperativity values $C_\mathrm{c} = 10, 20, 50, 100, 1000, 5000$ (lower curves correspond to lower $C_\mathrm{c}$). Results are shown for different atomic distributions: (a) symmetric ring geometry, (b) 1D Gaussian, (c) 3D Gaussian. (d)–(f) SPT efficiency (solid) and gain (dashed) as functions of cooperativity, with the blockaded cooperativity optimized at each point. Results are shown for different atomic distributions: (d) symmetric ring geometry, (e) 1D Gaussian, (f) 3D Gaussian. The parameters are fixed to $\kappa_\mathrm{p} = \kappa_\mathrm{c} = \gamma_{e_\mathrm{p}} = \gamma_{e_\mathrm{c}}$, with $\Omega_\mathrm{p}/\gamma_{e_\mathrm{c}} = 10$, $\Delta/\gamma_{e_\mathrm{c}} = 180$, and $\Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} = 5$ for $C_\mathrm{c} = 10, 20, 50, 100$; and $\Delta/\gamma_{e_\mathrm{c}} = 4C_\mathrm{c}/5$, $\Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} = 20, 45$ for $C_\mathrm{c} = 1000, 5000$. The detuning $\delta$ and probe strength $|\alpha_{\mathrm{in,p}}|^2$ are optimized at each point to enhance efficiency. Solid curves are polynomial fits provided as guides to the eye; points correspond to simulation data.
• Figure 5: Dissipative processes for the cavity model of $N = 1000$ atoms with a 3D Gaussian distribution. (a) Ratio of the two dephasing rates versus the blockaded cooperativity for a cooperativity $C_\mathrm{c} = 100$. (b) Percentage of unsuccessful trajectories due to spontaneous emission from the probe excited state (dashed line) and decay of the cavity the cavity (solid line) versus the blockaded cooperativity for cooperativity $C_\mathrm{c} = 100$. Solid and dashed curves show fitted polynomials and serve as a guide to the eye. The parameters are fixed to $\kappa_\mathrm{p} = \kappa_\mathrm{c} = \gamma_{e_\mathrm{p}} = \gamma_{e_\mathrm{c}}$, with $\Omega_\mathrm{p}/\gamma_{e_\mathrm{c}} = 10$, $\Delta/\gamma_{e_\mathrm{c}} = 180$, $\Omega_\mathrm{c}/\gamma_{e_\mathrm{c}} = 5$, and $\delta$ varies between $0.14\gamma_{e_\mathrm{c}}$ and $0.1\gamma_{e_\mathrm{c}}$ to provide better impedance matching and $|\alpha_\mathrm{in,p}|^2$ was chosen to optimize impedance matching at each point.