Optimal Strategies for Optical Quantum Memories Using Long-Lived Noble-Gas Spins

TL;DR

This work addresses the challenge of storing quantum light in long-lived noble-gas nuclear spins by analyzing two mediator mechanisms: metastability-exchange with metastable noble-gas atoms and spin-exchange with alkali-metal atoms. Using a compact Bloch-Heisenberg-Langevin framework for a single optical cavity mode, the authors derive analytic storage efficiencies and radial decoherence-free subspaces, and they perform numerically optimized control-pulse protocols across variable signal bandwidths. The key contributions are (i) explicit adiabatic-memory expressions for metastability-exchange and (ii) robust sequential and adiabatic strategies for spin-exchange, supported by extensive numerical optimization showing high efficiencies over wide bandwidths and realistic experimental parameters. Collectively, the results delineate regimes where each interface operates near unity efficiency, enabling hours-long, non-cryogenic optical memories with large time-bandwidth products for quantum networks.

Abstract

Nuclear spins of noble gases exhibit exceptionally long coherence times and can potentially serve as a long-lived storage medium for quantum information. We analyze and compare the performance of two mechanisms for mapping the quantum state of light onto the collective spin state of noble gases. The first mechanism utilizes collisional exchange with the electronic spin state of metastable noble-gas atoms, while the second relies on spin-exchange collisions with ground-state alkali-metal atoms. We describe the operation of an optical quantum memory relying on these two mechanisms using a compact model and study strategies that optimize the memory storage efficiency. Through numerical simulations, we identify optimal sequences for storing optical signals with different signal bandwidths and electronic spin relaxation rates. This work highlights the qualitative difference between the two approaches for using noble gases as long-lived quantum memories at non-cryogenic conditions and outlines the regimes in which they are expected to be efficient.

Figures (6)

• Figure 1: Optical quantum memory using nuclear spins of noble gases.(a) An input optical signal (green) is coherently mapped, via electronic spins, onto the state of noble-gas spins. $\hat{\mathcal{E}}$ denotes the annihilation operator of the optical field in the cavity. $\hat{\mathcal{E}}_{\text{in}}$ ($\hat{\mathcal{E}}_{\text{out}}$) is the annihilation operator for the input (output) optical field. The input pulse has a bandwidth $2B$ where $\tilde{\mathcal{E}}_\text{in}$ is the Fourier transform of the input pulse. Our simple model qualitatively describes platforms where the electronic spins are either (b) of noble gases in a metastable state, e.g.$^3$He, or (c) of alkali-metal atoms in their electronic ground state. $\Omega(t)$ is the Rabi frequency of the optical control field. $J$ is the fixed, magnetic-like coupling between the nuclear and electronic spins; it originates from metastability exchange collisions in (b), and from spin-exchange collisions in (c).
• Figure 2: Numerically-optimized storage efficiency. We present the attained efficiency of the storage sequences for (a) metastability-exchange collisions ($\xi=-1$) and (b) spin-exchange collisions ($\xi=1$). The color scale shows the storage efficiency $\eta_{\infty}$ in the large-cooperativity limit. The limited range of $J/\gamma_{\text{s}}$ in (a) compared with (b) originates from the different nature of the exchange processes. We assume $\gamma_{\textrm{k}}=0$ and $\Delta=0$ in these calculations; see text and Appendix \ref{['appendix:optimal_control_protocol_details']} for details of the numerical optimization protocol. (c-d) Maximal efficiency of the analytical sequences presented in Secs. \ref{['Sec:Metastable']}-\ref{['Sec:Spin-Exchange']}, corresponding to Eq. (\ref{['eq:memory efficiency adiabatic']}) in (c) and Eqs. (\ref{['eq:memory efficiency adiabatic2']}-\ref{['eq:efficiency of the fast storage scheme']}) in (d). Dashed line in (d) indicates the boundary at which the storage sequence change from adiabatic to sequential.
• Figure 3: Optimal storage sequences. (a), (d) Maximal excitation $\langle\hat{\mathcal{S}}^\dagger\hat{\mathcal{S}}\rangle$ of the electron spins during the storage sequence for the numerically optimized solutions for spin exchange collisions (a) and metastability exchange collisions (d). Two distinct regimes of nearly complete excitation (blue) or nearly no excitation (red) are observed for the optimal solutions as a function of the bandwidth $B$ and coupling strength $J$. Dashed lines denote the condition(s) $\max(\langle\hat{\mathcal{S}}^\dagger\hat{\mathcal{S}}\rangle)=0.9$ and $\max(\langle\hat{\mathcal{S}}^\dagger\hat{\mathcal{S}}\rangle)=0.1$ in (a) and $\max(\langle\hat{\mathcal{S}}^\dagger\hat{\mathcal{S}}\rangle)=0.5$ in (d), marking the approximate boundaries of these two regimes, qualitatively showing where the optimal solutions follow the adiabatic or sequential strategies. (b), (c) Particular numerically-optimized solutions, corresponding to the blue diamond and red circle in (a), indicating sequential-like and adiabatic-like storage strategies, respectively. (e), (f) Particular numerically-optimized solutions corresponding to the blue diamond and red circle in (d), indicating solutions with different bandwidth and different electron excitation, where (f) follows an adiabatic solution (see Appendix \ref{['appendix:meta_stable_noble_gass_solutions']}). The optimization parameters used in (a) and (d) are identical to the ones presented in Fig. \ref{['fig:schemes']}(b) and Fig. \ref{['fig:schemes']}(a), respectively. We find that $\delta_{\text{s}}(t)$ (not shown) is near zero throughout the storage sequence, a result of the constant phase of the input pulse, as we discuss in Appendix \ref{['sec:optimized_delta_S']}. The increase in ${\Omega}$ towards the end of the storage sequence in (b) is merely an artifact of the optimizer trying to decouple the alkali and noble-gas spins more efficiently, as there is no constraint on the control field amplitude in the optimization, see Appendix \ref{['appendix:optimal_control_protocol_details']}. Intermediate bandwidth solutions corresponding to the green triangle and the magenta square in (a) are shown in Fig. \ref{['fig:SE_intermediate_solutions']}.
• Figure 4: Numerical verification of the scaling with $C$. The factorization $\eta=\eta_{\infty}C/(C+1)$ (black line) is verified numerically (light blue diamond and light red circle) for two configurations: (a)$B/\gamma_{\textnormal{s}}=10^{3}$ [corresponding to the blue diamond in Fig. \ref{['fig:optimal_storage_strategies']}(a)] and (b)$B/\gamma_{\textnormal{s}}\approx 5.62\cdot 10^{-2}$ [corresponding to the red circle in Fig. \ref{['fig:optimal_storage_strategies']}(a)], both taken at $J/\gamma_{\textnormal{s}}=100$.
• Figure 5: Numerical optimization for storage of exponential, Gaussian, and Lorentzian pulse shapes with bandwidth $2B$ for the spin-exchange configuration ($\xi=1$). (a)$J/\gamma_{\textrm{s}}\approx 100$ and $B/\gamma_{\textrm{s}}\approx 10^{3}$, corresponding to the blue diamond in Fig. \ref{['fig:optimal_storage_strategies']}(a). (b)$J/\gamma_{\textrm{s}}\approx 100$ and $B/\gamma_{\textrm{s}}\approx 5.62\cdot 10^{-2}$, corresponding to the red circle in Fig. \ref{['fig:optimal_storage_strategies']}(a). Top: optical signal. Middle: optical control field (a parameter proportional to its intensity). Bottom: The efficiencies differ between different pulse shapes by no more than $1\%$.