Nonreciprocal reflection in one-dimensional quasi-periodic defective atomic lattice

XU Qiongyi; ZHANG Jin; ZHENG Yiting; YAN Dong; ZHANG Hanxiao; YANG Hong

doi:10.7498/aps.74.20250270

Abstract

In order to further investigate the non-reciprocity of light propagation in the defective atomic lattices, and due to its effective application in designing novel photonic devices, such as all-optical diodes and isolators, which are powerful tools for information processing and quantum simulation, we innovatively propose to use the Fibonacci sequence to modulate the arrangement of empty lattice cells that form a quasi periodic defective atomic lattices. In the electromagnetically induced transparency window, the probe light is almost not absorbed under the control of a strong coupling field (see Fig. 1). The numerical simulation indicates that a wide nonreciprocal reflection band can be achieved by modulating the number of filled lattice cells, Fibonacci sequence, the period number in a single quasi period (see Fig. 2). These results provide more degrees of freedom for regulating nonreciprocal reflection with wide bandwidth and high contrast, and have potential applications in quantum computing and information processing.

Keywords:

Authors and contacts

1.
School of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China
2.
College of Optoelectronics Science and Engineering, South China Normal University, Guangzhou 510631, China

Corresponding author: YANG Hong, yang_hongbj@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12204137) and the Hainan Province Graduate Innovation Research Project, China (Grant No. Qhys2023-394).

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References

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[23]	Ruesink F, Miri M A, Alù A, Verhagen E 2016 Nat. Commun. 7 13662 Google Scholar
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Cited By

图 1 (a)三能级Lambda型相干原子系统; (b)一维准周期缺陷原子晶格与相干光场的作用; (c)一个满晶格周期中探测场平均极化率实部和虚部随失谐的变化及其与$ - 2\varDelta {\lambda _{{\mathrm{Lat}}}}/{\lambda _{{\mathrm{Lat}}}} \approx 0.0023 $的交点

Figure 1. (a) Three-level Lambda model coherent atomic system; (b) interaction between 1D quasi-periodic atomic lattice and coherent optical field; (c) the real and imaginary parts of average susceptibility in one filled lattice cell v.s. probe detuning, and the intersection with $ - 2\varDelta {\lambda _{{\text{Lat}}}}/{\lambda _{{\text{Lat}}}} \approx 0.0023 $.

DownLoad: Full-Size Img PowerPoint

图 2 (a), (b)展示了左右反射率$ {R_{\mathrm{l}}}_{, {\mathrm{r}}} $随失谐$ {\varDelta _{\mathrm{p}}} $的变化, 分别对应$ n \in \left[ {2, 16} \right] $和$ n \in \left[ {2, 21} \right] $; (c), (d)展示了左右反射率$ {R_{\mathrm{l}}}_{, {\mathrm{r}}} $随失谐$ {\varDelta _{\mathrm{p}}} $和斐波那契数列数量$ b(n) $中最大n值的变化. 其他参数: $ {{{N}}_0} = 7 \times {10^{11}}{\text{ }}{\mathrm{c{m}}^{ - 3}} $, $ \eta = 5 $, $ a = 40 $, $ c = 1 $, $ d = 1500 $, $ {\gamma _{31}} = $$ 6{\text{ MHz}} $, $ {\gamma _{21}} = 0.001{\text{ MHz}} $, $ {\varDelta _{\mathrm{c}}} = 15{\text{ MHz}} $, $ {\varOmega _{\mathrm{c}}} = 36{\text{ MHz}} $, $ {\lambda _{{\mathrm{Lat0}}}} = 781{\text{ nm}} $, $ {\lambda _{\mathrm{p}}} = 780.24{\text{ nm}} $, $ \varDelta {\lambda _{{\mathrm{Lat}}}} = - 0.9{\text{ nm}} $, $ {\boldsymbol d} _{13} = 1.0357 \times $$ {10^{ - 29}}{\text{ }}{\mathrm{C}}{ \cdot} {\mathrm{m}} $

Figure 2. (a) $ n \in \left[ {2, 16} \right] $ and (b) $ n \in \left[ {2, 21} \right] $ shows the reflectivities $ {R_{\mathrm{l}}}_{, {\mathrm{r}}} $ v.s. detuning $ {\varDelta _{\mathrm{p}}} $; (c), (d) the reflectivities $ {R_{\mathrm{l}}}_{, {\mathrm{r}}} $ v.s. the number of dissonance and Fibonacci series $ b(n) $ and detuning $ {\varDelta _{\mathrm{p}}} $, respectively. Other relevant parameters: $ {{{N}}_0} = 7 \times {10^{11}}{\text{ }}{\mathrm{c{m}}^{ - 3}} $, $ \eta = 5 $, $ a = 40 $, $ c = 1 $, $ d = 1500 $, $ {\gamma _{31}} = 6{\text{ MHz}} $, $ {\gamma _{21}} = 0.001{\text{ MHz}} $, $ {\varDelta _{\mathrm{c}}} = 15 \;{\mathrm{MHz}} $, $ {\varOmega _{\mathrm{c}}} = 36{\text{ MHz}} $, $ {\lambda _{{\mathrm{Lat0}}}} = 781{\text{ nm}} $, $ {\lambda _{\mathrm{p}}} = $$ 780.24{\text{ nm}} $, $ \varDelta {\lambda _{{\mathrm{Lat}}}} = - 0.9{\text{ nm}} $, ${\boldsymbol d _{13}}= 1.0357 \times {10^{ - 29}}{\text{ }}{\mathrm{C}} {\cdot} {\mathrm{m}} $.

DownLoad: Full-Size Img PowerPoint

图 3 左右反射率$ {R_{\mathrm{l}}}_{, r} $随失谐$ {\varDelta _{\mathrm{p}}} $的变化(a) $ n \in \left[ {2, 7} \right] $; (b) $ n \in \left[ {8, 13} \right] $; (c) $ n \in \left[ {8, 17} \right] $. 相关参数: $ c = 10 $, 其他参数如图2所示

Figure 3. The reflectivities $ {R_{\mathrm{l}}}_{, r} $ v.s. detuning $ {\varDelta _{\mathrm{p}}} $: (a) $ n \in $$ \left[ {2, 7} \right] $; (b) $ n \in \left[ {8, 13} \right] $; (c) $ n \in \left[ {8, 17} \right] $. Here $ c = 10 $, other parameters are shown in Fig 2.

DownLoad: Full-Size Img PowerPoint

图 4 左右反射率$ {R_{\mathrm{l}}}_{, r} $和反射对比度$ {C_{{R}}} $随失谐$ {\varDelta _{\mathrm{p}}} $的变化　(a) $ a = 30 $; (b) $ a = 20 $; (c) $ a = 10 $. 相关参数: $ n \in $$ \left[ {8, 17} \right] $, $ c = 10 $, 其他参数如图2所示

Figure 4. The reflectivities $ {R_{\mathrm{l}}}_{, r} $ and the reflection contrast $ {C_{{R}}} $ v.s. detuning $ {\varDelta _{\mathrm{p}}} $: (a) $ a = 30 $; (b) $ a = 20 $; (c) $ a = 10 $. Here $ n \in \left[ {8, 17} \right] $, $ c = 10 $, other parameters are shown in Fig 2.

DownLoad: Full-Size Img PowerPoint

图 5 左右反射率$ {R_{\mathrm{l}}}_{, r} $和反射对比度$ {C_{{R}}} $随失谐$ {\varDelta _{\mathrm{p}}} $的变化　(a) $ c = 20 $; (b) $ c = 25 $; (c) $ c = 30 $. 相关参数: $ n \in $$ \left[ {8, 17} \right] $, $ a = 20 $, 其他参数如图2所示

Figure 5. The reflectivities $ {R_{\mathrm{l}}}_{, r} $ and the reflection contrast $ {C_{{R}}} $ v.s. detuning $ {\varDelta _{\mathrm{p}}} $: (a) $ c = 20 $; (b) $ c = 25 $; (c) $ c = 30 $. Here $ n \in \left[ {8, 17} \right] $, $ a = 20 $, other parameters are shown in Fig 2.

DownLoad: Full-Size Img PowerPoint

图 6 (a)左反射率$ {R_{\mathrm{l}}} $和(b)右反射率$ {R_{\mathrm{r}}} $随探测场失谐$ {\varDelta _{\mathrm{p}}} $和强耦合场失谐$ {\varDelta _{\mathrm{c}}} $的变化. 相关参数: $ n \in \left[ {8, 17} \right] $, $ a = $$ 20 $, $ c = 30 $, 其他参数如图2所示

Figure 6. (a) The left reflectivity $ {R_{\mathrm{l}}} $ and (b) the right reflectivity $ {R_{\mathrm{r}}} $ v.s. the probe detuning $ {\varDelta _{\mathrm{p}}} $ and the strong coupling field detuning $ {\varDelta _{\mathrm{c}}} $. Here $ n \in \left[ {8, 17} \right] $, $ a = 20 $, $ c = 30 $, other parameters are shown in Fig 2.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

map

[1]	White A D, Ahn G H, Gasse K V, Yang K Y, Chang L, Bowers J E, Vučković J 2023 Nat. Photonics 17 143 Google Scholar
[2]	Prabu K, Nasre D 2019 Plasmonics 14 1261 Google Scholar
[3]	Xia K Y, Nori F, Xiao M 2018 Phys. Rev. Lett. 121 203602 Google Scholar
[4]	Tian H, Liu J Q, Siddharth A, Wang R N, Blésin T, He J J, Kippenberg T J, Bhave S A 2021 Nat. Photonics 15 828 Google Scholar
[5]	Chan E H W 2014 Opt. Commun. 324 127 Google Scholar
[6]	Litinskaya M, Shapiro E A 2015 Phys. Rev. A 91 033802 Google Scholar
[7]	Shen H Z, Wang Q, Wang J, Yi X X 2020 Phys. Rev. A 101 013826 Google Scholar
[8]	Wu J, Wang Z M, Zhai H, Shi Z X, Wu X H, Wu F 2021 Opt. Mater. Express 11 4058 Google Scholar
[9]	Wang Z Y, Qian J, Wang Y P, Li J, You J Q 2023 Appl. Phys. Lett. 123 153904 Google Scholar
[10]	Chakraborty S, Das C 2023 Phys. Rev. A 108 063704 Google Scholar
[11]	Wang Y M, Xiong W, Xu Z Y, Zhang G Q, You J Q 2022 Sci. China-Phys. , Mech. Astron. 65 260314 Google Scholar
[12]	He X W, Wang Z Y, Han X, Zhang S, Wang H F 2023 Opt. Express 31 43506 Google Scholar
[13]	Yang Y, Guan B, Zhang C L, Liu L C, Liu K 2020 Optoelectron. Sci. Mater. 11606 74
[14]	Kim M K 2015 Opt. Express 23 2040 Google Scholar
[15]	Kawaguchi Y, Alù A, Khanikaev A B 2022 Opt. Mater. Express 12 1453 Google Scholar
[16]	Sounas D L, Alù A 2017 Nat. Photonics 11 774 Google Scholar
[17]	Fleury R, Sounas D L, Alù A 2018 J. Opt. 20 034007 Google Scholar
[18]	Cardin A E, Silva S R, Vardeny S R, Padilla W J, Saxena A, Taylor A J, Kort-Kamp W J M, Chen H T, Dalvit D A R, Azad A K 2020 Nat. Commun. 11 1469 Google Scholar
[19]	Kittlaus E A, Otterstrom N T, Kharel P, Gertler S, Rakich P T 2018 Nat. Photonics 12 613 Google Scholar
[20]	Sohn D B, Kim S, Bahl G 2018 Nat. Photonics 12 91 Google Scholar
[21]	Rodriguez S R K, Goblot V, Zambon N C, Amo A, Bloch J 2019 Phys. Rev. A 99 013851 Google Scholar
[22]	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
[23]	Ruesink F, Miri M A, Alù A, Verhagen E 2016 Nat. Commun. 7 13662 Google Scholar
[24]	Barzanjeh S, Wulf M, Peruzzo M, Kalaee M, Dieterle P B , Painter O, Fink J M 2017 Nat. Commun. 8 953 Google Scholar
[25]	Tang L, Tang J S, Chen M Y, Nori F, Xiao M, Xia K Y 2022 Phys. Rev. Lett. 128 083604 Google Scholar
[26]	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
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[28]	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
[29]	Zhang Y, Wu J H, Artoni M, La Rocca G C 2021 Opt. Express 29 5890 Google Scholar
[30]	Guo T J, Argyropoulos C 2022 Phys. Rev. B 106 235418 Google Scholar
[31]	Zheng D D, Zhang Y, Liu Y M, Zhang X J, Wu J H 2023 Phys. Rev. A 107 013704 Google Scholar
[32]	Horsley S A R, Artoni M, La Rocca G C 2015 Nat. Photonics 9 436 Google Scholar
[33]	Pei X S, Zhang H X, Pan M M, Geng Y, Li T M, Yang H 2023 Opt. Express 31 14694 Google Scholar
[34]	Peng P S, Thapa G, Zhou J F, Talbayev D 2023 Optica 10 155 Google Scholar
[35]	Guddala S, Kawaguchi Y, Komissarenko F, Kiriushechkina S, Vakulenko A, Chen K, Alù A, Menon V M, Khanikaev A B 2021 Nat. Commun. 12 3746 Google Scholar
[36]	Gao W T, Yang C W, Tan Y T, Ren J 2022 Appl. Phys. Lett. 121 071702 Google Scholar
[37]	Chamanara N, Taravati S, Deck-Léger Z L, Caloz C 2017 Phys. Rev. B 96 155409 Google Scholar
[38]	Hack S A, van der Vegt J J W, Vos W L 2019 Phys. Rev. B 99 115308 Google Scholar
[39]	Yoon T, Bajcsy M 2019 Phys. Rev. A 99 023415 Google Scholar
[40]	Yang H, Zhang T G, Zhang Y, Wu J H 2020 Phys. Rev. A 101 053856 Google Scholar
[41]	Wu J H, Artoni M, La Rocca G C 2017 Phys. Rev. A 95 053862 Google Scholar
[42]	Artoni M, La Rocca G C, Bassani F 2005 Phys. Rev. E 72 046604 Google Scholar
[43]	Li T M, Wang M H, Yin C P, Wu J H, Yang H 2021 Opt. Express 29 31767 Google Scholar
[44]	Yang H, Yang L, Wang X C, Cui C L, Zhang Y, Wu J H 2013 Phys. Rev. A 88 063832 Google Scholar
[45]	Wu J H, Artoni M, La Rocca G C 2015 Phys. Rev. A 91 033811 Google Scholar
[46]	Chaung Y L, Shamsi A, Abbas M, Ziauddin 2020 Opt. Express 28 1701 Google Scholar
[47]	Yang L, Zhang Y, Yan X B, Sheng Y, Cui C L, Wu J H 2015 Phys. Rev. A 92 053859 Google Scholar
[48]	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
[49]	Wang C Q, Jiang X F, Zhao G M, Zhang M Z, Hsu C W, Peng B, Stone A D, Jiang L, Yang L 2020 Nat. Phys. 16 334 Google Scholar
[50]	Finkelstein R, Bali S, Firstenberg O, Novikova I 2023 New J. Phys. 25 035001 Google Scholar
[51]	刘建基, 刘甲琛, 张国权 2023 72 094201 Google Scholar Liu J J, Liu J C, Zhang G Q 2023 Acta Phys. Sin. 72 094201 Google Scholar
[52]	Li T M, Yang H, Wang M H, Yin C P, Zhang T G, Zhang Y 2024 Phys. Rev. Res. 6 023122 Google Scholar
[53]	Yuan J P, Wu C H, Wang L R, Chen G, Jia S T 2019 Opt. Lett. 44 4123 Google Scholar
[54]	Yuan J P, Zhang H F, Wu C H, Wang L R, Xiao L T, Jia S T 2021 Opt. Lett. 46 4184 Google Scholar
[55]	Yuan J P, Zhang H F, Wu C H, Chen G, Wang L R, Xiao L T, Jia S T 2023 Laser Photonics Rev. 17 2200667 Google Scholar
[56]	Schilke A, Zimmermann C, Guerin W 2012 Phys. Rev. A 86 023809.Google Scholar
[57]	Kuraptsev A S, Sokolov I M 2015 Phys. Rev. A 91 053822 Google Scholar
[58]	Artoni M, La Rocca G C 2006 Phys. Rev. Lett. 96 073905 Google Scholar
[59]	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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Vol. 74, Issue 11 - 2025-06-05

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