Perfect non-reciprocal reflection amplification in closed loop coherent gain atomic system

Li Guan-Rong; Zheng Yi-Ting; Xu Qiong-Yi; Pei Xiao-Shan; Geng Yue; Yan Dong; Yang Hong

doi:10.7498/aps.73.20240347

Abstract

High-performance non-reciprocal photonic devices can improve the efficiency of optical quantum manipulation, information processing, and quantum simulation effectively. The enhanced optical signal can simultaneously amplify the weak signal output by the quantum system and isolate the sensitive quantum system from the back-scattered external noise, which is the core technology of high-performance photonic devices. In our previous work (2023 Opt. Express 31 38228), we have achieved dynamic control of unidirectional reflection amplification based on four-wave mixing gain and the use of coupling field intensity varying linearly with position. In this work, we design a simple three-level closed loop coherent gain atomic system, setting the intensity of coupling field to be varying with position step shape to break the spatial symmetry of probe susceptibility, and achieving perfect non-reciprocal reflection light amplification. In contrast, the stepped variation of coupling field intensity is easier to adjust in experiment, greatly reducing the difficulty in the experiment. Specifically, the system introduces phase modulation. By changing the phase, the frequency region of probe gain and absorption can be switched, which makes the modulation of reflection amplification more flexible.

Keywords:

Authors and contacts

School of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China

Corresponding author: Yang Hong, yang_hongbj@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12204137, 12126314, 12126351), the Hainan Provincial Banyan Tree Foundation, China (Grant Nos. RSYH20231165828X, RSYH20231165827X), and the Innovation Platform for Academicians of Hainan Province, China (Grant Nos. YSPTZX202215, YSPTZX202207).

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References

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[38]	Abdo B, Sliwa K, Shankar S, Hatridge M, Frunzio L, Schoelkopf R, Devoret M 2014 Phys. Rev. Lett. 112 167701 Google Scholar
[39]	Metelmann A, Clerk A A 2015 Phys. Rev. X 5 021025 Google Scholar
[40]	Koutserimpas T T, Fleury R 2018 Phys. Rev. Lett. 120 087401 Google Scholar
[41]	Sliwa K M, Hatridge M, Narla A, Shankar S, Frunzio L, Schoelkopf R J, Devoret M H 2015 Phys. Rev. X 5 041020 Google Scholar
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[50]	Geng Y, Pei X, Li G, Lin X, Zhang H, Yan D, Yang H 2023 Opt. Express 31 38228 Google Scholar
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Cited By

图 1 (a)三能级$ \Lambda $型相干原子系统; (b)耦合场$ {G_{\mathrm{c}}}(x) $随位置阶梯型变化, $ k = 5 $和$ k = 8 $分别对应红色虚线和蓝色实线, 恒定耦合场$ {G_{\mathrm{c}}} = 25{\text{ MHz}} $对应绿色虚点线; (c)耦合场和微波场竖直方向进入介质, 探测场沿水平方向传播的示意图, 介质长度$ L = 8{\text{ μm}} $

Figure 1. (a) Three-level $ \Lambda $ model coherent atomic system; (b) the intensity of coupling field $ {G_{\mathrm{c}}}(x) $ varies with position by step, $ k = 5 $ and $ k = 8 $ corresponding to red dashed and blue solid respectively, the constant coupling field $ {G_{\mathrm{c}}} = 25{\text{ MHz}} $ corresponding to green dotted line; (c) diagram of the homogeneous atomic medium illuminated by coupling and microwave fields vertical $ x $ axis, and probe field travels along $ x $ direction, the medium length $ L = 8{\text{ μm}}$.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 恒定耦合场$ {G_{\mathrm{c}}} = 25 {\text{MHz}} $时, 各能级粒子数布居随失谐$ {\varDelta _{\text{p}}} $的变化; (b) 阶梯型耦合场$ (k = 8) $时, 各能级粒子数布居随位置的变化; (c), (d) $ \left| 1 \right\rangle $能级与$ \left| 3 \right\rangle $能级粒子数布居差$ {\rho _{11}} - {\rho _{33}} $随位置和失谐的变化以及随位置和相位的变化, 对应阶梯型耦合场$ (k = 8) $. 相关参数: $ \varPhi = {{3\pi } \mathord{\left/ {\vphantom {{3\pi } 2}} \right. } 2} $, $ {N_0} = 3 \times {10^{11}}{\text{ c}}{{\text{m}}^{ - 3}} $, $ {G_{\text{d}}} = 15{\text{ MHz}}, {\text{ }}{G_{\text{p}}} = 0.3{\text{ MHz}} $, $ {\varDelta _{\text{c}}} = 0, {\text{ }}{d_{13}} = 2.0 \times {10^{ - 29}}{\text{ }}{\mathrm{C}} \cdot {\mathrm{m}}, $$ {\text{ }}{\varGamma _{31}} = {\varGamma _{32}} = 6{\text{ MHz}} $

Figure 2. (a) Population distribution of each level vs. $ {\varDelta _{\text{p}}} $ with the constant coupling field $ {G_{\mathrm{c}}} = 25{\text{ MHz}} $; (b) population distribution of each level varies with position with stepped coupling field $ (k = 8) $; (c), (d) the population difference $ {\rho _{11}} - {\rho _{33}} $ between level $ \left| 1 \right\rangle $ and level $ \left| 3 \right\rangle $ varies with position $ x $ and detuning $ {\varDelta _{\text{p}}} $ or position $ x $ and relative phase $ \varPhi $ with step coupling field $ (k = 8) $. Other parameters: $ \varPhi = 3\pi /2 $, $ {N_0} = 3 \times {10^{11}}{\text{ c}}{{\text{m}}^{ - 3}} $, $ {G_{\text{d}}} = 15{\text{ MHz}}, {\text{ }}{G_{\text{p}}} = 0.3{\text{ MHz}}, $$ {\varDelta _{\text{c}}} = 0, {\text{ }}{d_{13}} = 2.0 \times {10^{ - 29}}{\text{ }}{\mathrm{C}} \cdot {\mathrm{m}}, {\text{ }}{\varGamma _{31}} = $$ {\varGamma _{32}} = 6{\text{ MHz}} $.

DownLoad: Full-Size Img PowerPoint

图 3 (a), (c), (e) 探测场的左右反射率随失谐$ {\varDelta _{\mathrm{p}}} $的变化, 分别对应恒定场$ {G_{\mathrm{c}}} = 25{\text{ MHz}} $, 阶梯型耦合场$ (k = 5) $和$ (k = 8) $; (b), (d), (f) 探测场左右反射率对比度随失谐$ {\varDelta _{\text{p}}} $的变化; 其他参数与图2相同

Figure 3. (a), (c), (e) Left and right reflectivity of the probe field vs. detuning $ {\varDelta _{\text{p}}} $, corresponding to constant coupling field $ {G_{\mathrm{c}}} = 25{\text{ MHz}} $, stepped coupling field $ (k = 5) $ and $ (k = 8) $, respectively; (b), (d), (f) the corresponding contrast of left and right reflectivity vs. detuning $ {\varDelta _{\text{p}}} $. Other parameters are the same as in Fig 2.

DownLoad: Full-Size Img PowerPoint

图 4 极化率虚部随失谐和相对相位的变化　(a) $ {G_{\text{c}}} = 9{\text{ MHz}} $; (b) $ {G_{\text{c}}} = 16{\text{ MHz}} $; (c) $ {G_{\text{c}}} = 25{\text{ MHz}} $; (d) $ {G_{\text{c}}} = 36{\text{ MHz}} $; 其他参数与图2相同

Figure 4. Changes of the imaginary part of the polarizability with the detuning and relative phase: (a) $ {G_{\text{c}}} = 9{\text{ MHz}} $; (b) $ {G_{\text{c}}} = $$ 16{\text{ MHz}} $; (c) $ {G_{\text{c}}} = 25{\text{ MHz}} $; (d) $ {G_{\text{c}}} = 36{\text{ MHz}} $. Other parameters are the same as in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 5 探测场的左右反射率(a), (b)及其对比度(c), (d)随失谐$ {\varDelta _{\text{p}}} $的变化　(a), (c)阶梯型耦合场对应 $ k = 5 $; (b), (d) 阶梯型耦合场对应$ k = 8 $; 相对相位 $ \varPhi = 7\pi /4 $, 其他参数与图2相同

Figure 5. (a), (b) Left and right reflectivity of the probe field and (c), (d) their contrast vs. detuning $ {\varDelta _{\text{p}}} $: (a), (c) The stepped coupling field corresponding to $ k = 5 $; (b), (d) the stepped coupling field corresponding to $ k = 8 $. The relative phases $ \varPhi = 7{\text{π }}/4 $, other parameters are the same as in Fig. 2.

DownLoad: Full-Size Img PowerPoint

[1]	Hu Y Q, Zhang S C, Qi Y H, Lin G W, Niu Y P, Gong S Q 2019 Phys. Rev. Appl. 12 054004 Google Scholar
[2]	Shi Y, Yu Z F, Fan S H 2015 Nat. Photonics 9 388 Google Scholar
[3]	Cao Q T, Wang H, Dong C H, Jing H, Liu R S, Chen X, Ge L, Gong Q, Xiao Y F 2017 Phys. Rev. Lett. 118 033901 Google Scholar
[4]	Shen Z, Zhang Y L, Chen Y, Sun F W, Guo X B, Dong C H 2018 Nat. Commun. 9 1797 Google Scholar
[5]	Shen H Z, Wang Q, Wang J, Yi X X 2020 Phys. Rev. A 101 013826 Google Scholar
[6]	Markelov V A, Novikov M, Turkin A A 1977 JETP Lett. 25 9
[7]	Yu Z, Fan S 2009 Nat. Photonics 3 91 Google Scholar
[8]	Lira H, Yu Z, Fan S, Lipson M 2012 Phys. Rev. Lett. 109 033901 Google Scholar
[9]	Kang M S, Butsch A, Russell P S J 2011 Nat. Photonics 5 549 Google Scholar
[10]	Estep N A, Sounas D L, Soric J, Alu A 2014 Nat. Phys. 10 923 Google Scholar
[11]	Kittlaus E A, Otterstrom N T, Kharel P, Gertler S, Rakich P T 2018 Nat. Photonics 12 613 Google Scholar
[12]	Sohn D B, Kim S, Bahl G 2018 Nat. Photonics 12 91 Google Scholar
[13]	盖云冉, 郑康, 丁春玲 2024 物理学报 73 014201 Google Scholar Gai Y R, Zheng K, Ding C L 2024 Acta Phys. Sin. 73 014201 Google Scholar
[14]	刘妮, 马硕, 梁九卿 2023 物理学报 72 060702 Google Scholar Liu N, Ma S, Liang J Q 2023 Acta Phys. Sin. 72 060702 Google Scholar
[15]	Xu X W, Li Y, Chen A X, Liu Y X 2016 Phys. Rev. A 93 023827 Google Scholar
[16]	Fang K, Luo J, Metelmann A, Matheny M H, Marquardt F, Clerk A A, Painter O 2017 Nat. Phys. 13 465 Google Scholar
[17]	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
[18]	Huang R, Miranowicz A, Liao J Q, Nori F, Jing H 2018 Phys. Rev. Lett. 121 153601 Google Scholar
[19]	Tang L, Tang J S, Chen M Y, Nori F, Xiao M, Xia K Y 2022 Phys. Rev. Lett. 128 083604 Google Scholar
[20]	Hafezi M, Rabl P 2012 Opt. Express 20 7672 Google Scholar
[21]	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
[22]	Peng B, Ozdemir S K, Lei F C, Monifi F 2014 Nat. Phys. 10 394 Google Scholar
[23]	Xia K, Lu G, Lin G, Cheng Y, Niu Y, Gong S, Twamley J 2014 Phys. Rev. A 90 043802 Google Scholar
[24]	Sayrin C, Junge C, Mitsch R, Albrecht B, O’Shea D, Schneeweiss P, Rauschenbeutel A 2015 Phys. Rev. X 5 041036 Google Scholar
[25]	Scheucher M, Hilico A, Will E, Volz J, Rauschenbeutel A 2016 Science 354 1577 Google Scholar
[26]	Lodahl P, Mahmoodian S, Stobbe S, Rauschenbeutel A, Schneeweiss P, Volz J, Zoller P 2017 Nature 541 473 Google Scholar
[27]	Wu J H, Artoni M, La Rocca G C 2015 Phys. Rev. A 91 033811 Google Scholar
[28]	Chaung Y L, Shamsi A, Abbas M 2020 Opt. Express 28 1701 Google Scholar
[29]	Yang L, Zhang Y, Yan X B, Sheng Y, Cui C L, Wu J H 2015 Phys. Rev. A 92 053859 Google Scholar
[30]	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
[31]	Zhang S, Hu Y, Lin G, Niu Y, Xia K, Gong J, Gong S 2018 Nat. Photonics 12 744 Google Scholar
[32]	Lin G, Zhang S, Hu Y, Niu Y, Gong J, Gong S 2019 Phys. Rev. Lett. 123 033902 Google Scholar
[33]	Hu Y, Qi Y, You Y, Zhang S, Lin G, Li X, Niu Y 2021 Phys. Rev. Appl. 16 014046 Google Scholar
[34]	李鑫, 解舒云, 李林帆, 周海涛, 王丹, 杨保东 2022 物理学报 71 184202 Google Scholar Li X, Xie S Y, Li L F, Zhou H T, Wang D, Yang B D 2022 Acta Phys. Sin. 71 184202 Google Scholar
[35]	Heras de las A M, Carusotto I 2021 Phys. Rev. A 104 043501 Google Scholar
[36]	Otterstrom N T, Kittlaus E A, Gertler S, Behunin R O, Lentine A L, Rakich P T 2019 Optica 6 1117 Google Scholar
[37]	Song L N, Wang Z H, Li Y 2018 Opt. Commun. 415 39 Google Scholar
[38]	Abdo B, Sliwa K, Shankar S, Hatridge M, Frunzio L, Schoelkopf R, Devoret M 2014 Phys. Rev. Lett. 112 167701 Google Scholar
[39]	Metelmann A, Clerk A A 2015 Phys. Rev. X 5 021025 Google Scholar
[40]	Koutserimpas T T, Fleury R 2018 Phys. Rev. Lett. 120 087401 Google Scholar
[41]	Sliwa K M, Hatridge M, Narla A, Shankar S, Frunzio L, Schoelkopf R J, Devoret M H 2015 Phys. Rev. X 5 041020 Google Scholar
[42]	Lecocq F, Ranzani L, Peterson G A, Cicak K, Simmonds R W, Teufel J D, Aumentado J 2017 Phys. Rev. Appl. 7 024028 Google Scholar
[43]	Li Y, Huang Y Y, Zhang X Z, Tian L 2017 Opt. Express 25 18907 Google Scholar
[44]	Jiang C, Song L N, Li Y 2018 Phys. Rev. A. 97 053812 Google Scholar
[45]	Ruesink F, Miri M A, Alù A, Verhagen E 2016 Nat. Commun. 7 13662 Google Scholar
[46]	Malz D, Tóth L D, Bernier N R, Feofanov A K, Kippenberg T J, Nunnenkamp A 2018 Phys. Rev. Lett. 120 023601 Google Scholar
[47]	Jiang W, Ma Y, Yuan J, Yin G, Wu W, He S 2017 Laser Photonics Rev. 11 1600253 Google Scholar
[48]	Liu D J, Huang Y, Hu H, Liu L L, Gao D L, Ran L X, Ye D X, Luo Y 2019 IEEE Trans. Antennas Propag. 68 2945 Google Scholar
[49]	Zhang Y, Wu J H, Artoni M, La Rocca G C 2021 Opt. Express 29 5890 Google Scholar
[50]	Geng Y, Pei X, Li G, Lin X, Zhang H, Yan D, Yang H 2023 Opt. Express 31 38228 Google Scholar
[51]	Artoni M, La Rocca G, Bassani F 2005 Phys. Rev. E 72 046604 Google Scholar
[52]	Zhang Y, Xue Y, Wang G, Cui C L, Wang R, Wu J H 2011 Opt. Express 19 2111 Google Scholar

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