Noise suppression in a temporal-multimode quantum memory entangled with a photon via an asymmetrical photon-collection channel

Ya Li, Ya-fei Wen, Min-jie Wang, Chao Liu, Hai-long Liu, Shu-jing Li, Zhong-xiao Xu, and Hai Wang

Phys. Rev. A 106, 022610 – Published 15 August 2022

Abstract

Quantum interfaces (QIs) that generate entanglement between a multimode atomic memory and a photon form a multiplexed repeater node and could greatly improve quantum repeater rates. Recently, a temporal multimode spin-wave memory entangled with a photon was demonstrated with cold atoms [Wen et al., Phys. Rev. A 100, 012342 (2019)]. However, due to the additional noise generated in a multimode operation, the fidelity of the spin-wave–photon entanglement significantly decreases with the mode number. So far, improvements in the temporal-multimode entanglement fidelity associated with suppressing the additional noise have not been explored. In this work, we propose and experimentally demonstrate a scheme that can suppress the additional noise of a temporally multiplexed QI. The scheme uses an asymmetric channel to retrieve the photons coming from the temporally multiplexed QI. For comparison purposes, we also set up a QI that uses a symmetric channel for photon collection. When the QIs store 14 modes, the measured Bell parameters $S$ for the QIs using the asymmetric and the symmetric photon-collection channels are 2.36 ± 0.03 and 2.24 ± 0.04, respectively, which means that a QI using an asymmetric channel provides a 3% increase in the entanglement fidelity, i.e., a 1.7-fold decrease in the additional noise, compared with a QI using a symmetric channel. In addition, the 14-mode entanglement QIs that use the asymmetric and symmetric collections preserve the violation of a Bell inequality for storage times of up to ∼25 and ∼20 μs, respectively, showing that the asymmetric QI has better entanglement storage performance.

Received 26 January 2022
Revised 5 June 2022
Accepted 20 July 2022

DOI:https://doi.org/10.1103/PhysRevA.106.022610

Physics Subject Headings (PhySH)

Quantum entanglement Quantum networks Quantum repeaters

Quantum Information, Science & Technology

Authors & Affiliations

Ya Li , Ya-fei Wen, Min-jie Wang, Chao Liu, Hai-long Liu, Shu-jing Li, Zhong-xiao Xu, and Hai Wang^*

The State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, People's Republic of China

^*wanghai@sxu.edu.cn

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Vol. 106, Iss. 2 — August 2022

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Images

Figure 1
Overview of the experiment. (a) Experimental setup. A train of write pulses labeled as $W (t_{i})$ ( $i = 1$ to $m$ ), with each pulse coming from a different direction, is applied onto a cloud of cold atoms, with $m$ being up to 14 (for simplicity, we only plot four directions). The asymmetric ( $C H_{1}$ ) and symmetric ( $C H_{2}$ ) channels are set up for collecting Stokes and Anti-Stokes photons. FPGA: programmable gate array; PBS: polarization-beam splitter; PC: phase compensation; HWP: half-wave plate; QWP: quarter-wave plate; D: single photon detector; ASα: Anti-Stokes photons; FP: Fabry-Perot filters. $F C_{S 1}, F C_{S 2}, F C_{AS 1}$ , and $F C_{AS 2}$ : fiber collimators. (b) Asymmetric photon-collection channel. (c) Symmetric photon-collection channel. (d) Relevant atomic levels, where $σ^{+}$ ( $σ^{-}$ ) denotes right (left) circular polarization, $| g 〉 = | 5 S_{^{1 / 2}}, F_{g} = 1 〉, | s 〉 = | 5 S_{^{1 / 2}}, F_{s} = 2 〉, | e_{1} 〉 = | 5 P_{^{1 / 2}}, F_{e_{1}} = 1 〉$ , and $| e_{2} 〉 = | 5 P_{^{1 / 2}}, F_{e_{2}} = 2 〉, m_{F}$ denotes magnetic quantum number. (e) Time sequence of the experimental trial. The clean pulses are used for the optical pumping, which prepares the atoms into the ground level $| g 〉$ .
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Figure 2
Measured excitation probabilities $χ_{α = 1}^{(m)}$ (red circles) and $χ_{α = 1}^{(m)}$ (black squares) as a function of mode number $m$ for the write beam with 100 μW power. Error bars in the experimental data represent 1 standard deviation, which is estimated from the Poissonian detection statistics.
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Figure 3
Measured Bell parameter $S_{α = 1}^{(m)}$ (red circles) $S_{α = 2}^{(m)}$ (blue squares) as a function of mode number $m$ for the excitation probabilities $χ_{α = 1} \approx 1 %$ and $χ_{α = 2} \approx 1 %$ . The red dashed and blue solid curves are the fittings by using Eq. (11). In the fittings, branching ratio $ξ_{s e} = 0.093$ , retrieval efficiencies $γ_{α = 1} = 15.8 %$ and $γ_{α = 2} = 16.7 %$ , the ratios of the solid angles $r_{1} \approx 1.7$ ( $β_{r, α = 1} / β_{w, α = 1} \approx 1 / 1.7$ ) and $r_{2} = 1$ ( $β_{r, α = 2} / β_{w, α = 2} \approx 1$ ), the visibilities for single-mode $V_{α = 1} (1) \approx V {^{'}}_{α = 2} (1) \approx 0.91$ . Error bars in the experimental data represent 1 standard deviation, which is estimated from the Poissonian detection statistics.
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Figure 4
Bell parameter $S_{α = 1}^{(m = 14)}$ ( $S_{α = 2}^{(m = 14)}$ ) as a function of storage time $t$ for the excitation probability $χ_{α = 1} \approx 1 %$ ( $χ_{α = 2} \approx 1 %$ ). The red circles (black squares) depict the measured $S_{α}^{(m = 14)}$ for various storage times $t$ in $C H_{α}$ channel. Error bars in the experimental data represent 1 standard deviation, which is estimated from the Poissonian detection statistics.
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Figure 5
Relevant atomic levels for the proposed scheme.
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Figure 6
Expected results of Bell parameters $S_{α = 1}^{(m)}$ (blue solid curve) and $S_{α = 2}^{(m)}$ (black dashed curve) as a function of mode number $m$ for the proposed scheme with $V_{α = 1} (1) \approx V {^{'}}_{α = 2} (1) \approx 0.95$ . The other parameters are the same as those in Fig. 3.
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