Optical quantum memory for noble-gas spins based on spin-exchange collisions

Or Katz, Roy Shaham, Eran Reches, Alexey V. Gorshkov, and Ofer Firstenberg

Phys. Rev. A 105, 042606 – Published 12 April 2022

Abstract

Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline and characterize schemes to map the state of photons onto long-lived but optically inaccessible collective states of noble-gas spins. The mapping employs coherent spin-exchange interaction arising from random collisions with alkali vapor. We propose efficient storage strategies in two operating regimes and analyze their performance for several proposed experimental configurations.

Received 19 February 2022
Accepted 30 March 2022

DOI:https://doi.org/10.1103/PhysRevA.105.042606

Physics Subject Headings (PhySH)

Quantum memories Quantum optics

Atomic ensemble

Nuclear spin resonance

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Or Katz ^1,2,*,†, Roy Shaham ^1,2,*, Eran Reches ¹, Alexey V. Gorshkov ³, and Ofer Firstenberg ¹

¹Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
²Rafael Ltd, IL-31021 Haifa, Israel
³Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA

^*These authors contributed equally to this paper.
^†Present address: Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA; or.katz@duke.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 105, Iss. 4 — April 2022

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1

(a) A quantum memory system based on a mixture of noble-gas and alkali spins. The alkali-metal atoms (red) and noble-gas atoms (blue) interact with the quantum signal field $\hat{E}$ in a cavity and with a classical control field. The atomic spins are initially polarized with an auxiliary pumping beam. The signal field in the cavity is coupled to the incoming field ${\hat{E}}_{in}$ , to be stored, and to the output field ${\hat{E}}_{out}$ , retrieved on demand after the memory time. (b) Energy levels of the modeled alkali atom in the laboratory frame. The $Λ$ system consists of two stable ground-level states $| \tilde{↑} 〉$ and $| \tilde{↓} 〉$ , coupled via an excited state $| \tilde{p} 〉$ by the classical control field $E_{c}$ and the quantum signal $\hat{a} = e^{- i ω_{ɛ} t} \hat{E}$ . Initially, the state $| \tilde{↓} 〉$ is populated. (c) Energy levels of the modeled noble-gas atom in the laboratory frame. Initially, the state $| \tilde{⇓} 〉$ is populated.
Reuse & Permissions
Figure 2

Couplings between the collective states for a single input photon. A single photon ${\hat{E}}^{†} | 0 〉$ in the cavity is transferred to the collective noble-gas spin excitation ${\hat{K}}^{†} | 0 〉$ , which acts as the quantum memory, via intermediate excitations of the alkali collective excited-state ${\hat{P}}^{†} | 0 〉$ and ground-state ${\hat{S}}^{†} | 0 〉$ spins. The coupling is controlled by varying the strength of the control field $Ω (t)$ and the detunings $δ_{s} (t)$ and $δ_{k} (t)$ . The exchange coupling rate $J$ and the decay rates $γ_{p}, γ_{s}$ , and $γ_{k}$ are constant. The state $| 0 〉$ corresponds to the maximally polarized spin state and $\hat{P}, \hat{S}$ , and $\hat{K}$ are bosonic field operators.
Reuse & Permissions
Figure 3

Example of storage and retrieval of a short signal pulse using the sequential mapping protocol. We solve numerically Eqs. (31) and (34) for an exponentially shaped input signal field with a single excitation [cf. Eqs. (41)], setting $Δ = δ_{s} = 0$ and using square pulses for the optical control field $γ_{Ω}$ and magnetic detuning $δ_{k}$ as shown in (a) and (b). Here $J = 60 γ_{s}, γ_{s} T = 1.7 \times 10^{- 3}$ , and $C = 100$ . The memory maps the excitation of the input field ${〈 {\hat{E}}_{i n}^{†} {\hat{E}}_{i n} 〉}_{t}$ onto the atomic populations of the alkali ${〈 {\hat{P}}^{†} \hat{P} 〉}_{t}, {〈 {\hat{S}}^{†} \hat{S} 〉}_{t}$ , and the noble gas ${〈 {\hat{K}}^{†} \hat{K} 〉}_{t}$ , which are later retrieved, on demand, into an optical excitation of ${〈 {\hat{E}}_{o u t}^{†} {\hat{E}}_{o u t} 〉}_{t}$ . In the first stage $- \infty \leq t \leq 0$ , the control field maps the signal onto the collective state of the alkali spins via a two-photon process, while the noble gas remains decoupled by setting a large $δ_{k}$ . In the second stage $0 < t \leq T^{'}$ (here $T^{'} / T = 15.6$ ), by tuning $δ_{k} = 0$ , the alkali spins exchange the excitation with the noble-gas spins. Subsequently, the noble-gas spins are decoupled from the alkali spins by increasing $δ_{k}$ again. The optical signal is retrieved into the exponentially shaped output mode [cf. Eqs. (42)] by time reversing the storage sequence, except for a correction of order $γ_{s} T$ to the control field amplitude, $γ_{Ω} (r e t r i e v a l) = γ_{Ω} (s t o r a g e) - 2 γ_{s}$ , which corrects for the effect of nonzero alkali-spin relaxation to first order, as described in the text. The calculated memory efficiency is $η_{tot} = 0.91$ .
Reuse & Permissions
Figure 4

Example of storage and retrieval of a long pulse using the adiabatic mapping protocol. We numerically solve Eqs. (54) and (55) for an exponentially shaped signal field containing a single excitation [cf. Eqs. (41)] for $Δ = δ_{s} = 0$ and for the square-profile control fields $γ_{Ω}$ and $δ_{k}$ in (a) and (b). Here $J = 60 γ_{s}, γ_{s} T = 17$ , and $C = 100$ . The mapping of the input excitations ${〈 {\hat{E}}_{i n}^{†} {\hat{E}}_{i n} 〉}_{t}$ onto the atomic populations ${〈 {\hat{P}}^{†} \hat{P} 〉}_{t}, {〈 {\hat{S}}^{†} \hat{S} 〉}_{t}$ , and ${〈 {\hat{K}}^{†} \hat{K} 〉}_{t}$ is realized during storage, and the mapping onto ${〈 {\hat{E}}_{o u t}^{†} {\hat{E}}_{o u t} 〉}_{t}$ is realized during retrieval. The noble-gas spins adiabatically follow the input optical pulse, maintaining ${〈 {\hat{S}}^{†} \hat{S} 〉}_{t} ≪ 1$ throughout the protocol. The optical pulse is retrieved by time reversing the storage sequence, yielding a total memory efficiency of $η_{tot} = 0.98$ .
Reuse & Permissions
Figure 5

Emergence of a decay rate $γ_{J}$ from the collective noble-gas spin $\hat{K}$ during adiabatic retrieval. The picture is similar for adiabatic storage. (a) The optical cavity field $\hat{E}$ couples to the collective optical dipole $\hat{P}$ , which couples to the collective alkali spin $\hat{S}$ , which couples to the collective noble-gas spin $\hat{K}$ , with corresponding rates $G, Ω$ , and $J$ . The optical field decays into the desired output field ${\hat{E}}_{out}$ with rate $κ$ . The rates $γ_{p}, γ_{s}$ , and $γ_{k}$ encompass both relaxation and coupling to other (undesired) modes (not shown). (b) In the fast-cavity limit ( $κ ≫ G$ ), the cavity field adiabatically follows the optical dipole, giving rise to a decay rate $C γ_{p}$ from the optical dipole into the output field. This good decay rate $C γ_{p}$ competes with bad decay rate $γ_{p}$ , contributing a factor of $C γ_{p} / (C γ_{p} + γ_{p})$ to the retrieval efficiency. (c) For moderate control fields ( $C γ_{p} ≫ Ω$ ), the optical dipole adiabatically follows the alkali spin, giving rise to a decay rate $γ_{Ω}$ from the alkali spin. This good decay rate $γ_{Ω}$ competes with bad decay rate $γ_{s}$ , contributing a factor of $γ_{Ω} / (γ_{Ω} + γ_{s})$ to the retrieval efficiency. (d) For $γ_{Ω} + γ_{s} ≫ J$ (corresponding to $T ≫ 1 / J$ , since $T \sim 1 / γ_{J}$ ), the alkali spin adiabatically follows the noble-gas spin, giving rise to a decay rate $γ_{J}$ from the noble gas spin. This good decay rate $γ_{J}$ competes with bad decay rate $γ_{k}$ , contributing a factor of $γ_{J} / (γ_{J} + γ_{k})$ to the retrieval efficiency.
Reuse & Permissions
Figure 6

Effective diffusion-induced decay rate of the uniform mode of alkali spins as a function of the coupling duration $1 / γ_{E}$ .
Reuse & Permissions
Figure 7

Mode overlap of the uniform spin distribution with the signal and control fields in the cavity, cf. Eq. (C3), for the first seven modes. The condition $| k_{ɛ} - k_{c} | R ≪ 1$ is typically satisfied.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information