Sum sideband effect in hybrid optomechanical system with two-level atom ensemble

LIAO Qinghong; TANG Zhian; AO Jiawen

doi:10.7498/aps.74.20241432

Abstract

Cavity optomechanics, as a cross-discipline between nanophotonics and quantum mechanics, provides a unique platform for investigating optomechanical coupling between photons in microcavities and phonons from mechanical modes. It has a wide range of potential applications in quantum physics, and now it has become a hot topic. A theoretical scheme to enhance the sum sideband generation (SSG) via a two-level atom ensemble is proposed. The effect of the atomic ensemble’s detuning frequency on the efficiency of the SSG is considered by introducing a two-level atom medium. The results indicate that the efficiency of the generating sideband can be significantly enhanced under either red or blue detuning of the atoms, with greater dependence and more pronounced enhancement under the red detuning. In addition, we also consider the effect of pump power, which can effectively enhance the intensity of the output signal by selecting the appropriate pump power. More interestingly, the sensitivity of SSG to atomic detuning also indicates that the precise control of the atomic detuning frequency can achieve the fine-tuning of the SSG process. Furthermore, the cavity-atom coupling strength and atom decay rate are discussed for the transmission characteristics of the sum sideband signals. It is found that the efficiency of SSG can be effectively adjusted by the cavity-atom coupling strength and atom decay rate. The results show that the efficiency of SSG can be significantly improved by optimizing system parameters. The method of enhancing SSG may have potential application prospects in measuring high-precision weak forces and on-chip manipulation of light propagation.

Keywords:

Authors and contacts

1.
Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
2.
Chongqing Research Institute, Nanchang University, Chongqing 402660, China

Corresponding author: LIAO Qinghong, nculqh@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62461035, 62061028), the Key Project of Natural Science Foundation of Jiangxi Province, China (Grant No. 20232ACB202003), the Finance Science and Technology Special “Contract System” Project of Nanchang University of Jiangxi Province, China (Grant No. ZBG20230418015), the Natural Science Foundation of Chongqing, China (Grant No. CSTB2024NSCQ-MSX0412), and the Key Laboratory of Special Artificial Microstructure Materials and Technology Open Project Fund of Shanghai, China (Grant No. ammt2021A-4).

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References

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Cited By

图 1 含有两能级原子系综的复合光力系统模型图

Figure 1. Hybrid optomechanical system model diagram with a two-level atom ensemble.

DownLoad: Full-Size Img PowerPoint

图 2 (a)上和边带和(b)下和边带的效率(对数形式)作为原子失谐频率${\varDelta _1}$和失谐频率${\delta _1}$的函数, 其中${\delta _2} = $$ 0.05{\omega _{\text{m}}}$, 具体参数为$ G/(2\text{π)}=0.4\text{ GHz}/\text{nm} $, ${\gamma }_{\text{m}}/(2\text{π})= $$ 100~\text{Hz} $, $ \varDelta ={\omega }_{\text{m}} $, $ m=10\text{ ng} $, ${\gamma }_{\text{a}}/(2\text{π)}=2.875\text{ MHz} $, $\kappa /\text{(2π}) $$ = 2\text{ MHz} $, ${\omega }_{\text{m}}/\text{(2π)} = 10\text{ MHz} $, ${P}_{1} = {P}_{2} = 0.5\text{ μW} $, ${P}_{\text{c}}= $$ 5\text{ mW} $, ${\lambda }_{\text{c}}=794.98\text{ nm} $

Figure 2. The efficiencies (in logarithmic form) of (a) upper sum sideband generation (USSG) and (b) lower sum sideband generation (LSSG) as a function of the atomic detuning frequency ${\varDelta _1}$ and the detuning frequency ${\delta _1}$, where ${\delta _2} = 0.05{\omega _{\text{m}}}$. The specific parameters are as follows: $ G/(2\text{π)}=0.4\text{ GHz}/\text{nm} $, ${\gamma }_{\text{m}}/(2\text{π})=100\text{ Hz} $, $ \varDelta ={\omega }_{\text{m}} $, $m= $$ 10\text{ ng} $, ${\gamma }_{\text{a}}/(2\text{π)}=2.875\text{ MHz} $, $\kappa /\text{(2π})=2\text{ MHz} $, ${\omega }_{\text{m}}/\text{(2π)}= $$ 10\text{ MHz} $, ${P}_{1}={P}_{2}=0.5\text{ μW} $, ${P}_{\text{c}}=5\text{ mW} $, $ {\lambda }_{\text{c}}=794.98 \text{ nm}$

DownLoad: Full-Size Img PowerPoint

图 3 ${\delta _2} = 0.05{\omega _{\text{m}}}$的USSG (上和边带) (a)和LSSG (下和边带) (b)的效率(对数形式)作为控制功率$ {p_{\text{c}}} $和失谐频率${\delta _1}$的函数, 其他参数与图2一致

Figure 3. The efficiencies (in logarithmic form) of (a) USSG and (b) LSSG as a function of the control field power $ {p_{\text{c}}} $ and the detuning frequency ${\delta _1}$ for ${\delta _2} = 0.05{\omega _{\text{m}}}$, the other parameters are the same as those in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 4 在不同的原子失谐${\varDelta _1}$下, 输出场和边带的效率$\lg \eta _{\text{s}}^{{ \pm }}$与归一化失谐$ {{{\delta _1}} {/ } {{\omega _{\text{m}}}}} $的函数关系, 其他参数同图2一致

Figure 4. The efficiency $\lg \eta _{\text{s}}^{{ \pm }}$ of the output field sum sideband as a function of the normalized detuning $ {{{\delta _1}} {/ } {{\omega _{\text{m}}}}} $ for different atom detuning ${\varDelta _1}. $ The other parameters are the same as those in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 5 (a), (b)不同${g_{{\text{ac}}}}$值和边带与${\delta _1}$的效率(对数形式), 其中$ {g_{{\text{ac}}}} = 2{\text{π}} \times 2 {\text{ kHz}} $(品红色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 6 {\text{ kHz}} $(蓝色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 8 {\text{ kHz}} $(黑色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 10 {\text{ kHz}} $(绿色实线), $\varDelta = {\varDelta _1} = {\omega _{\text{m}}}$, 其他参数与图2相同

Figure 5. (a), (b) Plots of the efficiency (in logarithmic form) of USSG and LSSG versus ${\delta _1}$ for different values of ${g_{{\text{ac}}}}$, where $ {g_{{\text{ac}}}} = 2{\text{π}} \times 2 {\text{ kHz}} $ (magenta line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 6 {\text{ kHz}} $ (blue line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 8 {\text{ kHz}} $ (black line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times $$ 10 {\text{ kHz}} $ (green line), $\varDelta = {\varDelta _1} = {\omega _{\text{m}}}$, the other parameters are the same as those in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 6 (a), (b)不同${\gamma _a}$值和边带与${\delta _1}$的效率(对数形式), 其中$ {\gamma _a} = 2{\text{π}} \times 2 {\text{ MHz}} $(品红色实线), $ {\gamma _a} = 2{\text{π}} \times 4 {\text{ MHz}} $(绿色实线), $ {\gamma _a} = 2{\text{π}} \times 6 {\text{ MHz}} $(黑色实线), ${g_{{\text{ac}}}} = 2{\text{π}} \times 10 {\text{ kHz}}$, 其他参数与图2相同

Figure 6. (a), (b) Plots of the efficiency (in logarithmic form) of USSG and LSSG versus ${\delta _1}$ for different values of ${\gamma _a}$, where $ {\gamma _a} = 2{\text{π}} \times 2 {\text{ MHz}} $ (magenta line), $ {\gamma _a} = 2{\text{π}} \times 4 {\text{ MHz}} $ (green line), $ {\gamma _a} = 2{\text{π}} \times 6 {\text{ MHz}} $ (black line), ${g_{{\text{ac}}}} = 2{\text{π}} \times $$ 10 {\text{ kHz}}$, the other parameters are the same as those in Fig. 2

DownLoad: Full-Size Img PowerPoint

[1]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391 Google Scholar
[2]	Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press) pp1–560
[3]	Aspelmeyer M, Meystre P, Schwab K 2012 Phys. Today 65 29
[4]	Forbes A, Dudley A, McLaren M 2016 Adv. Opt. Photonics 8 200 Google Scholar
[5]	陈雪, 刘晓威, 张可烨, 袁春华, 张卫平 2020 物理学报 64 164211 Google Scholar Chen X, Liu X W, Zhang K Y, Yuan C H, Zhang W P 2020 Acta Phys. Sin. 64 164211 Google Scholar
[6]	Xiong H, Wu Y 2018 Appl. Phys. Rev. 5 031305 Google Scholar
[7]	Wang B, Liu Z X, Jia X, Xiong H, Wu Y 2018 Commun. Phys. 1 43 Google Scholar
[8]	Weis S, Rivière R, Deléglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520 Google Scholar
[9]	贺庆 2019 博士学位论文 (武汉: 华中科技大学) He Q 2019 Ph. D. Dissertation(Wuhan: Huazhong University of Science and Technology
[10]	Wang H, Gu X, Liu Y, Miranowicz A, Nori F 2014 Phys. Rev. A 90 023817 Google Scholar
[11]	Kong C, Li S, You C, Xiong H, Wu Y 2018 Sci. Rep. 8 1060 Google Scholar
[12]	Shen R C, Li J, Fan Z Y, Wang Y P, You J Q 2022 Phys. Rev. Lett. 129 123601 Google Scholar
[13]	Xu Y, Liu J Y, Liu W, Xiao Y F 2021 Phys. Rev. A 103 053501 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]	Li J, Wang Y P, You J Q, Zhu S Y 2023 Natl. Sci. Rev 10 nwac247 Google Scholar
[16]	Xiong H, Si L G, Zheng A S, Yang X, Wu Y 2012 Phys. Rev. A 86 013815 Google Scholar
[17]	Xiong H, Si L G, Lü X Y, Yang X, Wu Y 2014 Ann. Phys. 349 43 Google Scholar
[18]	Xiong H, Si L G, Lü X Y, Wu Y 2016 Opt. Express 24 5773 Google Scholar
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[20]	罗均文, 吴德伟, 苗强, 魏天丽 2020 物理学报 69 054203 Google Scholar Luo J W, Wu W D, Miao Q, Wei T L 2020 Acta Phys. Sin. 69 054203 Google Scholar
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[22]	Han Y, Cheng J, Zhou L 2011 J. Phys. B: At. Mol. Opt. Phys. 44 165505 Google Scholar
[23]	Gu K H, Yan D, Wang X, Zhang M L, Yin J Z 2019 J. Phys. B: At. Mol. Opt. Phys. 52 105502 Google Scholar
[24]	Han C M, Wang X, Chen H, Li H R 2020 Opt. Commun. 456 124605 Google Scholar
[25]	谷开慧, 严冬, 张孟龙, 殷景志, 付长宝 2019 物理学报 68 054201 Google Scholar Gu K H, Yan D, Zhang M L, Yin J Z, Fu C B 2019 Acta Phys. Sin. 68 054201 Google Scholar
[26]	廖庆洪, 郑庆华, 鄢秋荣, 刘晔, 张旗 2016 中国激光 43 266 Google Scholar Liao Q H, Zheng Q H, Yan Q R, Liu Y, Zhang Q 2016 Chin. J. Lasers 43 266 Google Scholar
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[29]	Chen S, Jing J 2010 Class. Quantum Grav. 27 225006 Google Scholar
[30]	Peng H B, Chang C W, Aloni S, Yuzvinsky T D, Zettl A 2006 Phys. Rev. Lett. 97 087203 Google Scholar
[31]	Michimura Y, Komori K 2020 Eur. Phys. J. D 74 126 Google Scholar
[32]	Palomaki T A, Teufel J D, Simmonds R W, Lehnert K W 2013 Science 342 710 Google Scholar
[33]	He Y 2016 Phys. Rev. A 94 063804 Google Scholar
[34]	Yasir K A, Liu W M 2016 Sci. Rep. 6 22651 Google Scholar
[35]	Akram M J, Ghafoor F, Khan M M, Saif F 2017 Phys. Rev. A 95 023810 Google Scholar
[36]	Liu L W, Gengzang D J, An X J, Wang P Y 2018 Chin. Phys. B 27 034205 Google Scholar
[37]	Cao C, Mi S C, Gao Y P, He L Y, Yang D , Wang T J , Zhang R, Wang C 2016 Sci. Rep. 6 22920 Google Scholar
[38]	Hao H, Kuzyk M C, Ren J, Zhang F, Duan X, Zhou L, Zhang T, Gong Q, Wang H, Gu Y 2019 Phys. Rev. A 100 023820 Google Scholar
[39]	Wang M, Kong C, Sun Z Y, Zhang D, Wu Y Y, Zheng L L 2021 Phys. Rev. A 104 033708 Google Scholar
[40]	Nagy D, Szirmai G, Domokos P 2013 Eur. Phys. J. D 67 1 Google Scholar
[41]	Morsch O, Oberthaler M 2006 Rev. Mod. Phys. 78 179 Google Scholar
[42]	Li M, Chen C L 2014 Acta Phys. Sin. 63 043201 Google Scholar
[43]	Su X, Huang Y M, Xiong H 2019 IEEE Access 7 133832 Google Scholar
[44]	Xiong H, Fan Y W, Yang X X, Wu Y 2016 Appl. Phys. Lett. 109 061108 Google Scholar
[45]	Liu S, Liu B, Yang W X 2019 Opt. Express 27 3909 Google Scholar
[46]	Wang X Y, Si L G, Lu X H, Wu Y 2019 Opt. Express 27 29297 Google Scholar
[47]	Xiong H, Huang Y M, Wu Y 2021 Phys. Rev. A 103 043506 Google Scholar
[48]	Lu X H, Si L G, Wang X Y, Wu Y 2021 Opt. Express 29 4875 Google Scholar
[49]	Liao Q H, Ao J W, Song M L, Qiu H Y 2023 Opt. Express 31 27508 Google Scholar
[50]	Wang X, Ren F F, Han S, Han H Y, Yan D 2023 Acta Phys. Sin. 72 094203 [王鑫, 任飞帆, 韩嵩, 韩海燕, 严冬 2023 物理学报 72 094203]Google Scholar Wang X, Ren F F, Han S, Han H Y, Yan D 2023 Acta Phys. Sin. 72 094203 Google Scholar
[51]	Eftekhari F, Tavassoly M K, Behjat A, Faghihi M J 2024 OPT LASER TECHNOL 168 109934 Google Scholar
[52]	Singh S K, Peng J X, Asjad M, Mazaheri M 2021 J. Phys. B: At. Mol. Opt. Phys. 54 215502 Google Scholar
[53]	Chen B, Shang L, Wang X F, Chen J B, Xue H B, Liu X, Zhang J 2019 Phys. Rev. A 99 063810 Google Scholar

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Vol. 74, Issue 8 - 2025-04-20

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