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量子存储是实现长距离量子通信的关键步骤, 也是量子信息处理的重要基础. 在满足存储时间长、保真度高的基础上, 实现量子态的异地按需读取对构建实用化量子网络有着重要意义. 本文基于受激拉曼绝热路径(stimulated Raman adiabatic passage, STIRAP)的方法, 提出了通过设计可控脉冲延迟在一维微波波导中实现高保真度的量子态存储与异地按需读取的理论方案. 该方案不仅可以根据需求在异地决定读出时间, 且可以降低原始STIRAP方案所需的脉冲面积, 降低能量消耗. 数值计算的结果表明, 该方案实现的保真度对波导中的平均热光子数及读出脉冲的持续时间均有较强的鲁棒性.On-demand quantum memory is an important step towards practical applications in various quantum information tasks such as long-distance entanglement distribution, quantum computation, and quantum networks. In this work, based on stimulated Raman adiabatic passage (STIRAP) protocol, we introduce a controllable delay between the reading pulse and writing pulse so that the quantum state can be stored in the superconducting waveguide and finally retrieved on demand with high fidelity. Through systematic numerical simulations, we find that if the duration of the writing pulse is set to be in a certain range, the readout unit is capable of retrieving the quantum state stored in the waveguide with high fidelity at any moment after a critical time. Moreover, we also investigate the robustness of our protocol, and find that the fidelity is robust against both the average number of thermal photons in the waveguide and the duration of the reading pulse. The numerical results also show that the pulse area in our protocol is only about one third of that in the original STIRAP protocol. Our protocol provides a practical way to combine the advantages of both on-demand quantum memory and the STIRAP protocol.
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Keywords:
- on-demand quantum state retrieval /
- pulse delay /
- stimulated Raman adiabatic passage /
- microwave waveguide
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图 1 量子态存储与异地读取方案图.
$ {E_{\text{C}}} $ ,$ {E_{\text{L}}} $ 分别代表两端读写腔的电容充电能和电感能量.$ {E_{{\text{C, B}}}} $ 和$ {E_{{\text{L, B}}}} $ 为波导中每个单元的电容充电能和电感能量Fig. 1. Setup for quantum state storage and remote retrieval.
$ {E_{\text{C}}} $ ,$ {E_{\text{L}}} $ are the capacitive and inductive energies of both writing and reading cavities, respectively.$ {E_{{\text{C, B}}}} $ and$ {E_{{\text{L, B}}}} $ are the capacitive and inductive energies for the unit cell within the waveguide.图 2 读出量子态与写入量子态之间的保真度随着读写脉冲持续时间
$ T $ 、读出脉冲延迟$ \Delta T $ 的变化关系图. 这里的读出脉冲与写入脉冲最大强度均为$ A = 0.1\omega $ . 图中所有的时间、频率都以读写腔的频率$ \omega $ 为参考进行无量纲化. 当脉冲写入时间满足$ 100/\omega \lesssim T \lesssim 200/\omega $ 时, 读出脉冲可以在临界时间$ {T_{\text{C}}} $ 之后的任意时刻对量子态进行高保真读取Fig. 2. The fidelity of the scheme as a function of the duration of the pulse
$ T $ and the delay of the reading pulse$ \Delta T $ . The amplitudes of both the writing and reading pulse are$ A = 0.1\omega $ . Each frequency and time scale in this figure are normalized by the bare frequency$ \omega $ of the writing/reading cavities. One can notice that once the duration of the writing pulse satisfies the condition$ 100/\omega \lesssim T \lesssim 200/\omega $ , high-fidelity quantum state retrieval is possible after the critical time$ {T_{\text{C}}} $ .图 3 量子态的存储与读取结果展示 (a)和(b)分别为写入量子态与读出量子态的Wigner准概率分布; (c)所需写入脉冲与读出脉冲的波形以及量子态的读取保真度. 参数取值分别为:
$ T = 150/\omega $ ,$ \Delta T = 400/\omega $ ,$ A = 0.1\omega $ Fig. 3. Numerical results for the storage and the retrieval of a quantum state in a waveguide: (a) and (b) are Wigner distributions of the initial state and the final state, respectively; (c) shows the pulses of our protocol used for storing and retrieving the quantum state. The related parameters are
$ T = 150/\omega $ ,$ \Delta T = 400/\omega $ ,$ A = 0.1\omega $ .图 4 量子态保真度的鲁棒性. 将写入腔的初态制备在1个压缩态
$ \left| {\left. {\psi (0)} \right\rangle = } \right.\left| {\left. {\alpha , r} \right\rangle } \right. $ , 其中$ \alpha = \sqrt 2 $ ,$ r = 0.5 $ . (a)和(b)分别展示了保真度对微波腔中平均热光子数, 以及对读出脉冲持续时间的鲁棒性. 参数取值分别为: 写入脉冲持续时间$ T = 150/\omega $ , 读出脉冲延迟$ \Delta T = 400/\omega $ , 脉冲的最大幅值$ A = 0.1\omega $ Fig. 4. Robustness of the fidelity for the retrieval of the quantum state. The initial state in the writing cavity is prepared to be a squeezed coherent state
$ \left| {\left. {\psi (0)} \right\rangle = } \right.\left| {\left. {\alpha , r} \right\rangle } \right. $ with$ \alpha = \sqrt 2 $ and$ r = 0.5 $ . (a) and (b) show the robustness of the fidelity against the average number of thermal photons inside the waveguide and the duration of the reading pulse, respectively. Here we fix the duration of the writing pulse$ T = 150/\omega $ , the delay of the reading pulse$ \Delta T = 400/\omega $ and the maximum amplitude for both pulses$ A = 0.1\omega $ . -
[1] Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413
Google Scholar
[2] Sun C P, Li Y, Liu X F 2003 Phys. Rev. Lett. 91 147903
Google Scholar
[3] Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photon. 3 706
Google Scholar
[4] Hua Y L, Zhou Z Q, Li C F, Guo G C 2018 Chin. Phys. B 27 020303
Google Scholar
[5] 窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 68 030307
Google Scholar
Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X 2019 Acta Phys. Sin. 68 030307
Google Scholar
[6] Gisin N, Thew R 2007 Nat. Photon. 1 165
Google Scholar
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Google Scholar
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Google Scholar
[9] 周宗权 2022 71 070301
Google Scholar
Zhou Z Q 2022 Acta Phys. Sin. 71 070301
Google Scholar
[10] Gouzien É, Sangouard N 2021 Phys. Rev. Lett. 127 140503
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[30] Specht H P, Nölleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473 190
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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