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Experimental generation of 9.1 dB HG10 mode squeezed light

LI Zhi BAI Jiandong LIU Kui TANG Jun

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Experimental generation of 9.1 dB HG10 mode squeezed light

LI Zhi, BAI Jiandong, LIU Kui, TANG Jun
cstr: 32037.14.aps.74.20251109
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  • The high-order Hermite-Gaussian (HG) mode squeezed light, as one of the important quantum sources, has significant application in quantum precision measurement and quantum imaging. The enhancement of spatial measurement precision largely depends on the squeezing level of high-order HG-mode quantum states. However, the squeezing level of high-order HG modes is primarily limited by the external pump power in the optical parametric oscillator (OPO) cavity. As is well known, the OPO with dual resonance for both squeezed light and pump light can lower external pump power. The generation of HG10 mode squeezed light differs from that of HG00 mode squeezed light, with an additional Gouy phase shift introduced between the HG20 pump mode and HG10 down-conversion mode within the OPO cavity. In this work, we conduct theoretical analysis and experimental generation of HG10 mode squeezed light at lower external pump power by using a doubly-resonant OPO based on a wedged periodically poled KTiOPO4 (PPKTP) crystal. By precisely controlling both the propagation length of the optical field and temperature in the wedged PPKTP crystal, we simultaneously compensate for the Gouy phase shift between the HG20 and HG10 modes and the astigmatism induced by the frequency-dependent refractive index. This configuration allows for dual resonance of the HG20 pump mode and the HG10 squeezed mode, while operating under the condition close to optimal phase matching. Increasing the reflectivity of the input coupler of OPO cavity enhances the intra-cavity circulating power of the pump light, thereby reducing the required external pump power. Here, the bow-tie-shaped OPO cavity consists of two plane mirrors and two concave mirrors with a curvature radius of 50 mm. The wedged PPKTP is placed in the smallest beam waist of the cavity. The mode converter is employed to generate high-purity HG20 pump mode with a measured purity of 98.0%. The mode-matching effciency of 93.0% is achieved between the high-purity HG20 pump mode and the OPO cavity. The homodyne visibility of the HG10 mode is 98.1%. We experimentally demonstrate the generation of 9.10 dB HG10 mode squeezed light by using a doubly-resonant OPO with only 51 mW of HG20 pump mode, and simultaneously achieve 9.20 dB of squeezing in the HG00 mode with 27 mW of HG00 pump mode. The inferred squeezing levels of both HG10 mode and HG00 mode squeezed light both reach up to 12.15 dB. The quantum technology has solved the pump power limitations in optical parametric oscillators, generating high-order HG mode states with high squeezing level and providing an effective method for enhancing spatial measurement precision.
      Corresponding author: LI Zhi, zhili@nuc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62471443, 12104417), the Fundamental Research Program of Shanxi Province, China (Grant No. 202403021212023), and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province, China (Grant No. 2024L198).
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    Heinze J, Danzmann K, Willke B, Vahlbruch H 2022 Phys. Rev. Lett. 129 031101Google Scholar

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    Pooser R C, Lawrie B 2015 Optica 2 393Google Scholar

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    Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002Google Scholar

    [5]

    孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210Google Scholar

    Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210Google Scholar

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    Roman R V, Fainsin D, Zanin G L, Treps N, Diamanti E, Parigi V 2024 Phys. Rev. Res. 6 043113Google Scholar

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    Shi S P, Tian L, Wang Y J, Zheng Y H, Xie C D, Peng K H 2020 Phy. Rev. Lett. 125 070502Google Scholar

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    Liu X, Shi S P, Wu Y M, Wang X, Tian L, Li W, Wang Y J, Zheng Y H 2025 Sci. China-Phys. Mech. Astron. 68 124211Google Scholar

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    Shi S P, Wang Y J, Tian L, Li W, Wu Y M, Wang Q W, Zheng Y H, Peng K H 2023 Laser Photonics Rev. 17 2200508Google Scholar

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    Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763Google Scholar

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    王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉 2020 69 234204Google Scholar

    Wang J P, Zhang W H, Li R X, Tian L, Wang Y J, Zheng Y H 2020 Acta Phys. Sin. 69 234204Google Scholar

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    Wu L A, Kimble H J, Hall J H, Wu H F 1986 Phys. Rev. Lett. 57 2520Google Scholar

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    Gao L, Zheng L A, Lu B, Shi S P, Tian L, Zheng Y H 2024 Light Sci. Appl. 13 294Google Scholar

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    Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801Google Scholar

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    Li Z, Guo X L, Sun H X, Liu K, Gao J R 2023 Opt. Express 31 3651Google Scholar

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    Heinze J, Willke B, Vahlbruch H 2022 Phys. Rev. Lett. 128 083606Google Scholar

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    李娟, 李佳明, 蔡春晓, 孙恒信, 刘奎, 郜江瑞 2019 68 034204Google Scholar

    Li J, Li J M, Cai C X, Sun H X, Liu K, Gao J R 2019 Acta Phys. Sin. 68 034204Google Scholar

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    Yesharim O, Tshuva G, Arie A 2024 APL Photonics 9 106116Google Scholar

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    Goodwin-Jones A W, Cabrita R, Korobko M, Beuzekom M V, Brown D D, Fafone V, Heijningen J V, Rocchi A, Schiworski M G, Tacca M 2024 Optica 11 273Google Scholar

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    Treps N, Grosse N, Bowen W P, Fabre C, Bachor H A, Lam P K 2003 Science 301 940Google Scholar

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    Taylor M A, Janousek J, Daria V, Knittel J, Hage B, Bachor H A, Bowen W P 2013 Nat. Photonics 7 229Google Scholar

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    Steinlechner S, Rohweder N O, Korobko M, Töyrä D, Freise A, Schnabel R 2018 Phys. Rev. Lett. 121 263602Google Scholar

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    Zhang C X, Chen Y C, Chen G, Sun H X, Zhang J, Liu K, Yang R G, Gao J R 2024 Phys. Rev. Applied 22 054068Google Scholar

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    Semmler M, Berg-Johansen S, Chille V, Gabriel C, Banzer P, Aiello A, Marquardt C, Leuchs G 2016 Opt. Express 24 7633Google Scholar

    [28]

    Ma L, Guo H, Sun H X, Liu K, Su B D, Gao J R 2020 Photon. Res. 8 1422Google Scholar

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    Lassen M, Delaubert V, Harb C C, Lam P K, Treps N, Bachor H A 2006 J. Eur. Opt. Soc. Rapid Publ. 1 06003Google Scholar

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    Guo J, Cai C X, Ma L, Liu K, Sun H X, Gao J R 2017 Opt. Express 25 4985Google Scholar

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    Stefszky M S, Mow-Lowry C M, Chua S S Y, Shaddock D A, Buchler B C, Vahlbruch H, Khalaidovski A, Schnabel R, Lam P K, Mcclelland D E 2012 Class. Quantum Grav. 29 145015Google Scholar

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    Li Z, Guo H, Liu H B, Li J M, Sun H X, Yang R G, Liu K, Gao J R 2022 Adv. Quantum Technol. 5 2200055Google Scholar

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    Courtois J, Mohamed A, Romanini D 2013 Phys. Rev. A 88 043844Google Scholar

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    Liu P, Li J, Li X H, Xiang X, Wang S F, Liu T, Cao M T, Zhang S G, Cai Y, Dong R F 2024 Opt. Express 32 42784Google Scholar

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    Schönbeck A, Thies F, Schnabel R 2018 Opt. Lett. 43 110Google Scholar

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    Kozlovsky W J, Nabors C D, Byer R 1988 IEEE J. Quantum Electron. 24 913Google Scholar

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    Aoki T, Takahashi G, Furusawa A 2006 Opt. Express 14 6930Google Scholar

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  • 图 1  双共振OPO结构示意图

    Figure 1.  Schematic diagram of doubly-resonant OPO structure.

    图 2  生成$ {\rm H{G_{00}}} $和$ \mathrm{HG_{10}}^{ } $模式压缩光的实验装置图 (QWP, 1/4波片; HWP, 半波片; PBS, 偏振分光棱镜; SG, 信号发生器; LPF, 低通滤波器; PZT, 压电陶瓷; DBS, 双色镜; BS, 50/50分束镜; SHG, 倍频腔; MC, 模式转换腔; OPO, 光学参量振荡器; SA, 频谱分析仪; BHD, 平衡零拍探测系统)

    Figure 2.  Experimental setup for the production of both $ {\rm H{G_{00}}} $ and $ {\rm H{G_{10}}} $ mode squeezed light. QWP, quarter-wave plate; HWP, half-wave plate; PBS, polarizing beam splitter; SG, signal generator; LPF, low-pass filter; PZT, piezo-electric transducer; DBS, dichroic beam splitter; BS, beam splitter; SHG, second harmonic generation; MC, mode converter; OPO, optical parametric oscillator; SA, spectrum analyzer; BHD, balance homodyne detection.

    图 3  (a) $ {\rm H{G_{20}}} $模式强度分布; (b) $ {\rm H{G_{20}}} $模式的纯度拟合结果; (c) $ {\rm H{G_{20}}} $模式的透射光强随OPO腔长的变化结果, 0和1(FSR)对应于$ {\rm H{G_{20}}} $模式的透射峰

    Figure 3.  (a) The intensity profile of $ {\rm H{G_{20}}} $ mode; (b) the purity fitting result of $ {\rm H{G_{20}}} $ mode; (c) the transmitted light intensity of $ {\rm H{G_{20}}} $ mode varies with the OPO cavity length, the transmission peaks of 0 and 1 free spectral range (FSR) correspond to the $ {\rm H{G_{20}}} $ mode.

    图 4  $ {\rm H{G_{00}}} $模式和$ {\rm H{G_{10}}} $模式压缩态光场的噪声功率谱 (a) $ {\rm H{G_{00}}} $模式的最大压缩度及其对应的反压缩度; (b) $ {\rm H{G_{10}}} $模式的最大压缩度及其对应的反压缩度; 曲线i为散粒噪声基准(SNL); 曲线ii为压缩态光场的量子噪声水平随本地光相位扫描的变化结果; 曲线iii为电子学噪声; 频谱分析仪的分辨率带宽(RBW)为300 kHz, 视频带宽(VBW)为2 kHz, 分析频率为3 MHz

    Figure 4.  The noise power spectra of squeezed states for the $ {\rm HG_{00}} $ and $ {\rm HG_{10}} $ modes: (a) The measured squeezing level of the $ {\rm H{G_{00}}} $ mode, along with the respective anti-squeezing level; (b) the measured squeezing level of the $ {\rm H{G_{10}}} $ mode, along with the respective anti-squeezing level; curve i represents the shot noise limit (SNL); curve ii shows the quantum noise level of the squeezed light versus the phase scan of the local oscillator; curve iii indicates the electronic noise; the spectrum analyzer was set with a resolution bandwidth (RBW) of 300 kHz, video bandwidth (VBW) of 2 kHz, and the analysis frequency of 3 MHz.

    图 5  $ {\rm H{G_{10}}} $模式的压缩和反压缩度随泵浦功率的变化结果, 实验结果归一化到真空压缩态

    Figure 5.  The pump power dependence of squeezed and anti-squeezed levels for $ {\rm H{G_{10}}} $ mode, the experimental result is normalized to the vacuum state.

    Baidu
  • [1]

    Heinze J, Danzmann K, Willke B, Vahlbruch H 2022 Phys. Rev. Lett. 129 031101Google Scholar

    [2]

    Acernese F, Agathos M, Aiello L, Ain A, Allocca A, Amato A, Ansoldi S, Antier S, Arène M, et al. 2020 Phys. Rev. Lett. 125 131101Google Scholar

    [3]

    Pooser R C, Lawrie B 2015 Optica 2 393Google Scholar

    [4]

    Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002Google Scholar

    [5]

    孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210Google Scholar

    Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210Google Scholar

    [6]

    Defienne H, Bowen W P, Chekhova M, Lemos G B, Oron D, Ramelow S, Treps N, Faccio D 2024 Nat. Photonics 18 1024Google Scholar

    [7]

    Roman R V, Fainsin D, Zanin G L, Treps N, Diamanti E, Parigi V 2024 Phys. Rev. Res. 6 043113Google Scholar

    [8]

    Shi S P, Tian L, Wang Y J, Zheng Y H, Xie C D, Peng K H 2020 Phy. Rev. Lett. 125 070502Google Scholar

    [9]

    Liu X, Shi S P, Wu Y M, Wang X, Tian L, Li W, Wang Y J, Zheng Y H 2025 Sci. China-Phys. Mech. Astron. 68 124211Google Scholar

    [10]

    Shi S P, Wang Y J, Tian L, Li W, Wu Y M, Wang Q W, Zheng Y H, Peng K H 2023 Laser Photonics Rev. 17 2200508Google Scholar

    [11]

    Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R 2011 Opt. Express 19 25763Google Scholar

    [12]

    王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉 2020 69 234204Google Scholar

    Wang J P, Zhang W H, Li R X, Tian L, Wang Y J, Zheng Y H 2020 Acta Phys. Sin. 69 234204Google Scholar

    [13]

    Wu L A, Kimble H J, Hall J H, Wu H F 1986 Phys. Rev. Lett. 57 2520Google Scholar

    [14]

    Gao L, Zheng L A, Lu B, Shi S P, Tian L, Zheng Y H 2024 Light Sci. Appl. 13 294Google Scholar

    [15]

    Serikawa T, Yoshikawa J I, Makino K, Frusawa A 2016 Opt. Express 24 28383Google Scholar

    [16]

    Wu Y M, Shi S P, Liu X, Tian L, Li W, Wang Y J, Zheng Y H 2025 Phys. Rev. Applied 23 044021Google Scholar

    [17]

    Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801Google Scholar

    [18]

    Li Z, Guo X L, Sun H X, Liu K, Gao J R 2023 Opt. Express 31 3651Google Scholar

    [19]

    Heinze J, Willke B, Vahlbruch H 2022 Phys. Rev. Lett. 128 083606Google Scholar

    [20]

    李娟, 李佳明, 蔡春晓, 孙恒信, 刘奎, 郜江瑞 2019 68 034204Google Scholar

    Li J, Li J M, Cai C X, Sun H X, Liu K, Gao J R 2019 Acta Phys. Sin. 68 034204Google Scholar

    [21]

    Yesharim O, Tshuva G, Arie A 2024 APL Photonics 9 106116Google Scholar

    [22]

    Goodwin-Jones A W, Cabrita R, Korobko M, Beuzekom M V, Brown D D, Fafone V, Heijningen J V, Rocchi A, Schiworski M G, Tacca M 2024 Optica 11 273Google Scholar

    [23]

    Treps N, Grosse N, Bowen W P, Fabre C, Bachor H A, Lam P K 2003 Science 301 940Google Scholar

    [24]

    Taylor M A, Janousek J, Daria V, Knittel J, Hage B, Bachor H A, Bowen W P 2013 Nat. Photonics 7 229Google Scholar

    [25]

    Steinlechner S, Rohweder N O, Korobko M, Töyrä D, Freise A, Schnabel R 2018 Phys. Rev. Lett. 121 263602Google Scholar

    [26]

    Zhang C X, Chen Y C, Chen G, Sun H X, Zhang J, Liu K, Yang R G, Gao J R 2024 Phys. Rev. Applied 22 054068Google Scholar

    [27]

    Semmler M, Berg-Johansen S, Chille V, Gabriel C, Banzer P, Aiello A, Marquardt C, Leuchs G 2016 Opt. Express 24 7633Google Scholar

    [28]

    Ma L, Guo H, Sun H X, Liu K, Su B D, Gao J R 2020 Photon. Res. 8 1422Google Scholar

    [29]

    Lassen M, Delaubert V, Harb C C, Lam P K, Treps N, Bachor H A 2006 J. Eur. Opt. Soc. Rapid Publ. 1 06003Google Scholar

    [30]

    Guo J, Cai C X, Ma L, Liu K, Sun H X, Gao J R 2017 Opt. Express 25 4985Google Scholar

    [31]

    Stefszky M S, Mow-Lowry C M, Chua S S Y, Shaddock D A, Buchler B C, Vahlbruch H, Khalaidovski A, Schnabel R, Lam P K, Mcclelland D E 2012 Class. Quantum Grav. 29 145015Google Scholar

    [32]

    Li Z, Guo H, Liu H B, Li J M, Sun H X, Yang R G, Liu K, Gao J R 2022 Adv. Quantum Technol. 5 2200055Google Scholar

    [33]

    Courtois J, Mohamed A, Romanini D 2013 Phys. Rev. A 88 043844Google Scholar

    [34]

    Liu P, Li J, Li X H, Xiang X, Wang S F, Liu T, Cao M T, Zhang S G, Cai Y, Dong R F 2024 Opt. Express 32 42784Google Scholar

    [35]

    Schönbeck A, Thies F, Schnabel R 2018 Opt. Lett. 43 110Google Scholar

    [36]

    Kozlovsky W J, Nabors C D, Byer R 1988 IEEE J. Quantum Electron. 24 913Google Scholar

    [37]

    Aoki T, Takahashi G, Furusawa A 2006 Opt. Express 14 6930Google Scholar

    [38]

    Zhou Z Y, Liu S L, Li Y, Ding D S, Zhang W, Shi S, Dong M X, Shi B S, Guo G C 2016 Phys. Rev. Lett. 117 103601Google Scholar

    [39]

    Liu S S, Lü Y H, Wang X T, Wang J B, Lou Y B, Jing J T 2024 Phys. Rev. Lett. 132 100801Google Scholar

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  • Received Date:  17 August 2025
  • Accepted Date:  17 September 2025
  • Available Online:  26 September 2025
  • Published Online:  20 November 2025
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