Research of radiation characteristics in a parametrically driven cavity

SHANG Xue; CAO Binfang; GUO Miaodi; HE Zhi; ZHOU Chunxiao

doi:10.7498/aps.74.20250223

Abstract

Cavity quantum electrodynamics (QED) serves as a fundamental platform for studying light-matter interactions at a single-particle level and has been extensively investigated in fundamental physics and quantum information. Recent development of parametrically squeezed techniques has demonstrated that they have the remarkable ability to exponentially enhance coherent atom-cavity coupling. However, the full extent to which these techniques can manipulate quantum optical phenomena requires further exploration. This work systematically investigates the influence of optical parametric amplification on single-photon excited atom-cavity systems within a parametrically driven cavity. In the proposed model, optical parametric amplification converts the driving photons into a squeezed cavity mode, which enhances the atom-cavity interaction into the strong coupling region. Through analytical derivation of atomic and cavity radiation spectra, we demonstrate that the optical parametric amplification induces splitting of atomic radiation spectra while exerting negligible effects on spectral intensity. Conversely, the cavity transmission spectrum exhibits both pronounced splitting and nonlinear intensity amplification. Notably, as driving field intensity approaches a critical intensity regime, the cavity radiation spectrum intensity is significantly enhanced. The underlying mechanism is parametric driving amplification, which converts the driving light into a squeezed cavity mode. When this squeezed mode is mapped back to the fundamental mode of the cavity through Bogoliubov squeezing transformation, the pump photons within the squeezed cavity mode are converted into the photons that contribute to the radiation spectrum of the cavity, thereby amplifying its intensity. This parametric enhancement method not only deepens the basic understanding of light-matter interactions, but also establishes a practical framework for improving the single-photon detection sensitivity in cavity-based quantum systems. These findings have broad prospects for quantum sensing and information processing applications.

Keywords:

Authors and contacts

1.
College of Mathematics and Physics, Hunan University of Arts and Sciences, Changde 415000, China
2.
Hunan Provincial Key Laboratory of Optoelectronic Information Integration and Optical Manufacturing Technology, Changde 415000, China
3.
Hunan Province Higher Education Institution’s Key Laboratory of Information Detection and Intelligent Processing Technology, Changde 415000, China
4.
School of Sciences, Xi’An Thchnological University, Xi’an 710021, China
5.
School of Mathematics, Physics and Optoelectronics Engineering, Hubei University of Automotive Technology, Shiyan 442002, China

Corresponding author: ZHOU Chunxiao, zhouchunxiao567@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104150, 12304405), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 24B0639), the Natural Science Foundation of Hunan Province, China (Grant No. 2023JJ30437), the Research Foundation of Hunan University of Art and Science, China (Grant No. 23ZZ04), the Natural Science Foundation of Shaanxi Provincial Department of Education, China (Grant No. 23JKJ0483), the Doctoral Scientific Research Foundation of Hubei University of Automotive Technology, China (Grant No. BK202429), and the Hunan Province’s “14th Five Year Plan” Applied Characteristic Discipline “Electronic Science and Technology”, China.

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References

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[26]	Spillane S M, Kippenberg T J, Painter O J, Vahala K J 2003 Phys. Rev. Lett. 91 043902 Google Scholar
[27]	Lü X Y, Wu Y, Johansson J R, et al. 2015 Phys. Rev. Lett. 114 093602 Google Scholar
[28]	Qin W, Miranowicz A, Li P B, et al. 2018 Phys. Rev. Lett. 120 093601 Google Scholar
[29]	Leroux C, Govia L C G, Clerk A A 2018 Phys. Rev. Lett. 120 093602 Google Scholar
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[43]	Xia K Y, Johnsson M, Knight P L, et al. 2016 Phys. Rev. Lett. 116 023601 Google Scholar
[44]	Serikawa T, Yoshikawa J, Makino K, et al. 2016 Opt. Express 24 28383 Google Scholar
[45]	Vahlbruch H, Mehmet M, Danzmann K, et al. 2016 Phys. Rev. Lett. 117 110801 Google Scholar

Cited By

图 1 原子与参量驱动泵浦腔的相互作用示意图. 腔中包含$ \chi^{(2)} $非线性介质和二能级原子, 其中非线性介质受到振幅$ \varOmega_{{\mathrm{p}}} $, 频率为$ \omega_{{\mathrm{p}}} $, 相位为$ \theta_{{\mathrm{p}}} $的外部驱动场泵浦, 同时原子被单光子激发至激发态. 为了消除光学参量放大带来的额外耗散, 腔耦合了一个压缩参数为$ r_{{\mathrm{e}}} $, 参考相位为$ \theta_{{\mathrm{e}}} $的压缩真空库

Figure 1. The schematic of our proposed method for investigating the interaction between an atom and a parametrically driven cavity. The optical cavity contains a $ \chi^{(2)} $ nonlinear medium and one two-level atom, where the nonlinear medium is pumped by a driving field of amplitude $ \varOmega_{{\mathrm{p}}} $, frequency $ \omega_{{\mathrm{p}}} $ and phase $ \theta_{{\mathrm{p}}} $, and the atom is excited to the excited state by a single photon. In order to eliminate the additional dissipation caused by optical parametric amplification, the cavity couples to a squeezed-vacuum reservoir with the squeezing parameter $ r_{{\mathrm{e}}} $ and a reference phase $ \theta_{{\mathrm{e}}} $.

DownLoad: Full-Size Img PowerPoint

图 2 原子的单光子辐射谱, 黑色虚线对应的驱动场强度$ \varOmega_{{\mathrm{p}}} = 0 $, 红色实线对应的驱动场强度$ \varOmega_{{\mathrm{p}}} = 0.799\gamma $, 其他参数取值为$ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, $ \kappa = \gamma $

Figure 2. The radiation spectrum of the atom. The black dashed line and the red solid line are plotted with the driving field driving intensities of $ \varOmega_{{\mathrm{p}}} = 0 $ and $ \varOmega_{{\mathrm{p}}} = 0.799\gamma $, respectively. Other parameters are $ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, $ \kappa = \gamma $.

DownLoad: Full-Size Img PowerPoint

图 3 腔的辐射谱, 黑色虚线对应的驱动场强度$ \varOmega_{{\mathrm{p}}} = 0 $, 红色实线对应的驱动场强度$ \varOmega_{{\mathrm{p}}} = 0.799\gamma $, 其他参数的取值为$ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, $ \kappa = \gamma $

Figure 3. The transmission spectrum of the cavity. The black dashed line and red solid line are plotted with the driving intensities of $ \varOmega_{{\mathrm{p}}} = 0 $ and $ \varOmega_{{\mathrm{p}}} = 0.799\gamma $, respectively. Other parameters are $ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, $ \kappa = \gamma $.

DownLoad: Full-Size Img PowerPoint

图 4 腔的辐射谱　(a)红色实线和黑色虚线分别对应$ \varOmega_{{\mathrm{p}}} = 0 $时耦合强度为$ g = 0.5\gamma $和$ g = 1.62\gamma $时的辐射谱; (b)红色实线对应$ \varOmega_{{\mathrm{p}}} = 0.799\gamma $, $ g = 0.5\gamma $时的辐射谱, 黑色虚线对应$ \varOmega_{{\mathrm{p}}} = 0 $, $ g = 1.62\gamma $时的辐射谱. 其他参数的取值为$ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ \kappa = \gamma $

Figure 4. The transmission spectrum of the cavity: (a) The transmission spectrum with parametric pump field intensity $ \varOmega_{{\mathrm{p}}} = 0 $, where the red solid line and black dashed line are corresponding to the coupling strength of $ g = 0.5\gamma $ and $ g = 1.62\gamma $, respectively. (b) The red solid line is plotted with $ \varOmega_{{\mathrm{p}}} = 0.799\gamma $ and $ g = 0.5\gamma $, while the black dashed line is plotted with $ \varOmega_{{\mathrm{p}}} = 0 $ and $ g = 1.62\gamma $. Other parameters are $ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ \kappa = \gamma $.

DownLoad: Full-Size Img PowerPoint

图 5 原子和腔模的辐射强度随驱动场强度的变化曲线, 嵌入图为根据(20)式得到的放大因子m随驱动场强度的变化曲线, 其他参数为$ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, κ = γ

Figure 5. The intensity of the atomic and cavity mode spectra as a function of the driving field intensity. The inset illustrates the dependence of the amplification factor m on the driving field intensity, which is derived from Eq.(20). Other parameters are $ \varDelta_{{\mathrm{c}}} = 0.8\gamma $, $ \varDelta_{{\mathrm{a}}} = 0 $, $ g = 0.5\gamma $, $ \kappa = \gamma $.

DownLoad: Full-Size Img PowerPoint

[1]	Nimmrichter S, Hornberger K 2013 Phys. Rev. Lett. 110 160403 Google Scholar
[2]	Horodecki R, Horodecki P, Horodecki M, et al. 2009 Rev. Mod. Phys. 81 865 Google Scholar
[3]	单传家, 夏云杰 2006 物理学报 55 1585 Google Scholar Shan C J, Xia Y J 2006 Acta Phys. Sin. 55 1585 Google Scholar
[4]	Wang Q, Chen W, Xavier G, et al. 2008 Phys. Rev. Lett. 100 090501 Google Scholar
[5]	Motes K R, Olson J P, Rabeaux E J, et al. 2015 Phys. Rev. Lett. 114 170802 Google Scholar
[6]	Petrosyan D, Fleischhauer M 2008 Phys. Rev. Lett. 100 170501 Google Scholar
[7]	Ye J, Vernooy D W, Kimble H J 1999 Phys. Rev. Lett. 83 4987 Google Scholar
[8]	Jané E, Plenio M B, Jonathan D 2002 Phys. Rev. A 65 050302(R Google Scholar
[9]	Schuster D I, Bishop L S, Chuang I L 2011 Phys. Rev. A 83 012311 Google Scholar
[10]	Weiher K, Agudelo E, Bohmann M 2019 Phys. Rev. A 100 043812 Google Scholar
[11]	Guo M D, Li H F, Wang F L, et al. 2023 Opt. Lett. 48 4037 Google Scholar
[12]	Garziano L, Macrì V, Stassi R, et al. 2016 Phys. Rev. Lett. 117 043601 Google Scholar
[13]	Kockum F A, Miranowicz A, Liberato S D, et al. 2019 Nat. Rev. Phys. 1 19 Google Scholar
[14]	Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press
[15]	Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633 Google Scholar
[16]	Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565 Google Scholar
[17]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46 Google Scholar
[18]	Peres A, Terno D R 2004 Rev. Mod. Phys. 76 93 Google Scholar
[19]	Ritsch H, Domokos P, Brennecke F, et al. 2013 Rev. Mod. Phys. 85 553 Google Scholar
[20]	Guo M D, Li H F, Li N, et al. 2023 Phys. Rev. A 107 033704 Google Scholar
[21]	Srinivasan K, Painter O 2007 Nature 450 862 Google Scholar
[22]	Carmele A, Kabuss J, Schulze F, Reitzenstein S, Knorr A 2013 Phys. Rev. Lett. 110 013601 Google Scholar
[23]	Liu Y C, Luan X S, Li H K, et al. 2014 Phys. Rev. Lett. 112 213602 Google Scholar
[24]	Xiang Z L, Ashhab S, You J Q, et al. 2013 Rev. Mod. Phys. 85 623 Google Scholar
[25]	Houdré R, Weisbuch C, Stanley R P, Oesterle U, Ilegems M 2000 Phys. Rev. Lett. 85 2793 Google Scholar
[26]	Spillane S M, Kippenberg T J, Painter O J, Vahala K J 2003 Phys. Rev. Lett. 91 043902 Google Scholar
[27]	Lü X Y, Wu Y, Johansson J R, et al. 2015 Phys. Rev. Lett. 114 093602 Google Scholar
[28]	Qin W, Miranowicz A, Li P B, et al. 2018 Phys. Rev. Lett. 120 093601 Google Scholar
[29]	Leroux C, Govia L C G, Clerk A A 2018 Phys. Rev. Lett. 120 093602 Google Scholar
[30]	Forn-Díaz P, Lamata L, Rico E, et al. 2019 Rev. Mod. Phys. 91 025005 Google Scholar
[31]	Qin W, Kockum, A F, Muñoz C S, et al. 2024 Physics Reports 1078 1 Google Scholar
[32]	Muñoz C S, Jaksch D 2021 Phys. Rev. Lett. 127 183603 Google Scholar
[33]	Wang Y, Li C, Sampuli E M, et al. 2019 Phys. Rev. A 99 023833 Google Scholar
[34]	Chen Y H, Qin W, Nori F 2019 Phys. Rev. A 100 012339 Google Scholar
[35]	Wang Y, Wu J L, Han J X, et al. 2020 Phys. Rev. A 102 032601 Google Scholar
[36]	Mollow B R 1969 Phys. Rev. 188 1969 Google Scholar
[37]	Zhou C X, He Z, Cao B F, et al. 2021 J. Opt. Soc. Am. B 38 1359 Google Scholar
[38]	Bhargav A M, Rakshit R K, Das S, et al. 2021 Adv. Quantum Technol. 4 2100008 Google Scholar
[39]	Hadfield R H 2009 Nat. Photonics 3 696 Google Scholar
[40]	Villas-Bôas C J, de Almeida N G, Serra R M, et al. 2003 Phys. Rev. A 68 061801(R Google Scholar
[41]	de Almeida N G, Serra R M, Villas-Bôas C J, et al. 2004 Phys. Rev. A 69 035802 Google Scholar
[42]	Law C K, Zhu S Y, Zubairy M S 1995 Phys. Rev. A 52 4095 Google Scholar
[43]	Xia K Y, Johnsson M, Knight P L, et al. 2016 Phys. Rev. Lett. 116 023601 Google Scholar
[44]	Serikawa T, Yoshikawa J, Makino K, et al. 2016 Opt. Express 24 28383 Google Scholar
[45]	Vahlbruch H, Mehmet M, Danzmann K, et al. 2016 Phys. Rev. Lett. 117 110801 Google Scholar

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