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Owing to the potential applications in all-optical quantum information processing and quantum optical networks, magnet-free optical non-reciprocity transmission has attracted great interest and has been studied in many fields, such as parity-time-symmetry enhanced nonlinearity, optomechanical systems, photonic crystal, cold atomic Bragg lattices, chiral quantum optics, and hot atoms. In particular, the random thermal motion of hot atoms can be a useful resource to realize optical non-reciprocity. Here in this work, based on the susceptibility-momentum-locking of atomic thermal motion and the strong coupling characteristics of cavities, a magnetic-free optical reciprocity-nonreciprocity transmission conversion scheme is designed and realized through the atom-cavity compound system. Theoretical and experimental analysis show that the coupling field conditions determine the nonreciprocity of the system. Under the action of single traveling-wave field, the nonreciprocity in hot atoms depends on the propagation direction of the coupling field due to the Doppler effect. Therefore, by changing the opening and closing of the opposite coupling field, the two-way single channel optical nonreciprocal transmission based on intracavity electromagnetically induced transparency can be controlled. When the two coupling fields propagate simultaneously in the opposite directions, however, the cavity transmission changes from single-dark-state to double-dark-state peaks, in which the reciprocity outputs depend on the frequency difference between the two coupling fields. By tuning the frequency difference, the two-way multi-channel reciprocal-nonreciprocal transmission regulation based on double dark polar peaks can be realized. The study can be applied to all-optical quantum devices and quantum information processing, such as optical transistors, optical switching and routing, and quantum gate manipulation.
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Keywords:
- optical non-reciprocity /
- double-dark state /
- Doppler shift /
- all-optical switching
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图 1 (a) 实验装置和(b) 实验能级示意图
Figure 1. Schematic diagram of experimental setup (a) and energy levels (b).
图 2 理论模拟注入信号光s1光(红色实线)和s2光(蓝色虚线)的色散 χ'、吸收χ'' 及腔透射谱T 随信号光频率失谐的变化 (a), (b)只有c1光作用时的χ' 和 χ''; (d), (e) 只有c2作用时的χ' 和 χ''; (c), (f) 分别对应只有c1光和只有c2作用时的T. 在计算中参数设置为: (a)—(c)中,
$ {\varOmega _{{c_1}}} = 20{\text{ MHz, }}{\varOmega _{{c_2}}} = 0 $ ; (d)—(f)中,${\varOmega _{{c_1}}} = 0,\;{\varOmega _{{c_2}}} = 20{\text{ MHz}}$ . 其他实验参数为: r = γin = 0.9, γca = 14.4 MHz, γab = 0.3 MHz, L = 526 mm, l = 75 mm,$ {\varDelta _{{c_1}}} = {\varDelta _{{c_2}}} = {\varDelta _{\text{q}}} = 0 $ Figure 2. Theoretical plots of the dispersion χ', absorption χ'' and cavity transmission T of the input s1 (red solid lines) and input s2 (blue dashed lines) versus signal frequency detuning: (a), (b) χ' and χ'' for only c1 used; (d), (e) χ' and χ'' for only c2 used; (c), (f) T corresponding to only c1 and only c2 corresponding to panel (a), (b) and (d), (e), respectively. The parameters used in the calculation are
$ {\varOmega _{{c_1}}} = 20{\text{ MHz, }}{\varOmega _{{c_2}}} = 0 $ for panel (a)–(c);${\varOmega _{{c_1}}} = 0{, }~{\varOmega _{{c_2}}} = 20{\text{ MHz}}$ for panel (d)–(f). The other parameters are r = γin = 0.9, γca = 14.4 MHz, γab = 0.3 MHz, L = 526 mm, l = 75 mm,$ {\varDelta _{{c_1}}} = {\varDelta _{{c_2}}} = {\varDelta _{\text{q}}} = 0 $ .
图 3 理论模拟了当c1光和c2光同时作用时, 不同频差δc下s1光(红色实线)和s2光(蓝色虚线)的色散χ'、吸收χ''及腔透射谱T (a)—(c) δc = 0; (d)—(f) δc = –20 MHz; (g)—(i) δc = –40 MHz. 主要计算参数为
$ {\varOmega _{{c_1}}} = {\varOmega _{{c_2}}} = 20{\text{ MHz}} $ , 其他参数与图2中的相同Figure 3. Theoretical plots of χ', χ'' and T of the input s1 (red solid lines) and input s2 (blue dashed lines) versus signal frequency detuning for different frequency difference δc when coupling lights c1 and c2 are used simultaneously: (a)–(c) δc = 0; (d)–(f) δc = –20 MHz; (g)–(i) δc = –40 MHz. The parameters used in the calculation are
$ {\varOmega _{{c_1}}} = {\varOmega _{{c_2}}} = 20{\text{ MHz}} $ , and other parameters are the same as in Fig. 2.
图 4 (a), (c) 实验测量了只有c1光和c2光作用下的腔透射谱; (b), (d) 当c2光为脉冲光时在原子共振跃迁中心(Δs = 0)的腔透射强度. (1) 代表s1光的腔透射(红色线), (2) 代表s2光的腔透射(蓝色线), (3) 代表c1光强度(灰色线)和(4)代表c2光强度(黑色线). 主要实验参数为
$ {P_{{c_1}}} = {P_{{c_2}}} = 10\;{\text{mW}} $ ,$ {P_{{s_1}}} = {P_{{s_2}}} = 1.5{\text{ mW}} $ , TCs = 28.5 °C,$ {\delta _c} = {\varDelta _{{c_1}}} = 0 $ Figure 4. (a), (c) Experimental measured cavity transmission for only light c1 (a) and light c2 (c) used. (b), (d) The transmission intensity at the atom resonance center (Δs = 0) when light c2 is as pulsed light. Red curves (1) are the cavity transmission of light s1, blue curves (2) are those of light s2, gray lines (3) and black lines (4) are the intensity of lights c1 and c2, respectively. The main experimental parameters are:
$ {P_{{c_1}}} = {P_{{c_2}}} = 10{\text{ mW}} $ ,$ {P_{{s_1}}} = {P_{{s_2}}} = 1.5{\text{ mW}} $ , TCs = 28.5 °C,$ {\delta _c} = {\varDelta _{{c_1}}} = 0 $ .
图 5 实验测量了c1光和c2光同时作用下的腔透射谱, 其中主要实验参量为(a)
$ {\varDelta _{{c_1}}} = {\delta _c} = 0 $ ; (b)$ {\varDelta _{{c_1}}} = 10{\text{ MHz, }}{\delta _c} = - 20{\text{ MHz}} $ ; (c)$ {\varDelta _{{c_1}}} = 20{\text{ MHz, }}{\delta _c} = - 40{\text{ MHz}} $ . 其他参数与图4相同Figure 5. Experimental measured cavity transmission for lights c1 and c2 simultaneously used. The main experimental parameters are: (a)
$ {\varDelta _{{c_1}}} = {\delta _c} = 0 $ ; (b)$ {\varDelta _{{c_1}}} = 10{\text{ MHz, }}{\delta _c} = - 20{\text{ MHz}} $ ; (c)$ {\varDelta _{{c_1}}} = 20{\text{ MHz, }}{\delta _c} = - 40{\text{ MHz}} $ . The other parameters are the same as in Fig. 4.表 1 不同δc下双暗态极子峰的输出真值表
Table 1. Output truth table of double dark-state peaks under different δc.
δc = 0 δc = –δ δc = –2δ Δs = –δ(δ) Δs = –2δ(0) Δs = –δ(δ) Δs = –3δ Δs = –δ Δs =δ S1-in 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 S2-in 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 S1-out 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 S2-out 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 S = S1-out+ S2-out 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 
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[1] Aplet L J, Carson J W 1964 Appl. Opt. 3 544
Google Scholar
[2] Chang L, Jiang X S, Hua S Y, Yang C, Wen J M, Jiang L, Li G Y, Wang G Z, Xiao M 2014 Nat. Photonics 8 524
Google Scholar
[3] Buddhiraju S, Song A, Papadakis G T, Fan S H 2020 Phys. Rev. Lett. 124 257403
Google Scholar
[4] Estep N A, Sounas D L, Soric J, Alù A 2014 Nat. Phys. 10 923
Google Scholar
[5] Ruesink F, Mathew J P, Miri M A, Verhagen E, Alù A 2018 Nat. Commun. 9 1798
Google Scholar
[6] Shen Z, Zhang Y L, Chen Y, Zou C L, Xiao Y F, Zou X B, Sun F W, Guo G C, Dong C H 2016 Nat. Photonics 10 657
Google Scholar
[7] 张利巍, 李贤丽, 杨柳 2019 68 170701
Google Scholar
Zhang L W, Li X L, Yang L 2019 Acta Phys. Sin. 68 170701
Google Scholar
[8] Lépinay L M, Ockeloen-Korppi C F, Malz D, Sillanpää M A 2020 Phys. Rev. Lett. 125 023603
Google Scholar
[9] Lodahl P, Mahmoodian S, Stobbe S, Rauschenbeutel A, Schneeweiss P, Volz J, Pichler H, Zoller P 2017 Nature 541 473
Google Scholar
[10] Ramezani H, Jha P K, Wang Y, Zhang X 2018 Phys. Rev. Lett. 120 043901
Google Scholar
[11] Scheucher M, Hilico A, Will E, Volz J, Rauschenbeutel A 2016 Science 354 1577
Google Scholar
[12] Kang M S, Butsch A, Russell P S J 2011 Nat. Photonics 5 549
Google Scholar
[13] Wang D W, Zhou H T, Guo M J, Zhang J X, Evers J, Zhu S Y 2013 Phys. Rev. Lett. 110 093901
Google Scholar
[14] Horsley S A R, Wu J H, Artoni M, La Rocca G C 2013 Phys. Rev. Lett. 110 223602
Google Scholar
[15] Sayrin C, Junge C, Mitsch R, Albrecht B, O’Shea D, Schneeweiss P, Volz J, Rauschenbeutel A 2015 Phys. Rev. X 5 041036
Google Scholar
[16] Zhang S C, Hu Y Q, Lin G W, Niu Y P, Xia K Y, Gong J B, Gong S Q 2018 Nat. Photonics 12 744
Google Scholar
[17] Lin G W, Zhang S C, Hu Y Q, Niu Y P, Gong J B, Gong S Q 2019 Phys. Rev. Lett. 123 033902
Google Scholar
[18] Hu Y Q, Zhang S C, Kuang X Y, Qi Y H, Lin G W, Gong S Q, Niu Y P 2020 Opt. Express 28 38710
Google Scholar
[19] Bliokh K Y, Rodríguez-Fortuño F J, Bekshaev A Y, Kivshar Y S, Nori F 2018 Opt. Lett. 43 963
Google Scholar
[20] Song K S, Im S J, Pae J S, Ri C S, Ho K S, Kim C S, Han Y H 2020 Phys. Rev. B 102 115435
Google Scholar
[21] Zhang J X, Zhou H T, Wang D W, Zhu S Y 2011 Phys. Rev. A 83 053841
Google Scholar
[22] Yang P F, Xia X W, He H, Li S K, Han X, Zhang P, Li G, Zhang P F, Xu J P, Yang Y P, Zhang T C 2019 Phys. Rev. Lett. 123 233604
Google Scholar
[23] Kapale K T, Agarwal G S, Scully M O 2005 Phys. Rev. A 72 052304
Google Scholar
[24] Vo C, Riedl S, Baur S, Rempe G, Dürr S 2012 Phys. Rev. Lett. 109 263602
Google Scholar
[25] He L Y, Wang T J, Wang C 2016 Opt. Express 24 15429
Google Scholar
[26] Guo M J, Zhou H T, Wang D, Gao J R, Zhang J X, Zhu S Y 2014 Phys. Rev. A 89 033813
Google Scholar
[27] Tang L, Tang J S, Chen M Y, Nori F, Xiao M, Xia K Y 2022 Phys. Rev. Lett. 128 083604
Google Scholar
[28] Li R B, Deng L, Hagley E W 2014 Phys. Rev. A 90 063806
Google Scholar
[29] Knutson E M, Cross J S, Wyllie S, Glasser R T 2020 Opt. Express 28 22748
Google Scholar
[30] Liu S S, Lou Y B, Jing J T 2019 Phys. Rev. Lett. 123 113602
Google Scholar
[31] Li S J, Pan X Z, Ren Y, Liu H Z, Yu S, Jing J T 2020 Phys. Rev. Lett. 124 083605
Google Scholar
[32] Zhu Y F, Gauthier D J, Morin S E, Wu Q L, Garmichael H J, Mossberg T W 1990 Phys. Rev. Lett. 64 2499
Google Scholar
[33] Sheng J T, Xiao M 2013 Laser Phys. Lett. 10 055402
Google Scholar
[34] Gripp J, Mielke S L, Orozco L A 1996 Phys. Rev. A 54 R3746
Google Scholar
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