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高阶厄米高斯(HG)模压缩态光场作为一种量子光源, 在量子精密测量, 量子成像等领域有重要的应用价值. HG模式量子态增强空间测量精度很大程度上取决于其压缩度. 然而, 利用光学参量振荡器产生高阶HG模压缩光的压缩度主要受泵浦功率限制. 本文理论分析并实验验证利用楔角非线性晶体构成的双共振光学参量振荡器, 在低泵浦功率条件下实现$ {\rm H{G_{10}}} $模压缩态光场的实验制备. 这里, 通过调节光场经历楔角非线性晶体的长度和工作温度, 从而补偿$ {\rm H{G_{20}}} $ 与 $ {\rm H{G_{10}}} $ 模式在腔内的 Gouy 相位差和非线性晶体中不同频率光场引起的像散, 同时实现双共振条件和相位匹配要求. 实验结果表明仅需51mW的 $ {\rm H{G_{20}}} $ 模式泵浦光操控光学参量振荡器产生 9.1 dB 的 $ {\rm H{G_{10}}} $ 模压缩态光场. 该量子技术解决了光学参量振荡器产生高阶横模量子态受泵浦功率限制的问题, 可用于制备高压缩度的高阶HG模压缩态光场, 为提高空间测量精度提供有效手段.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. It is well known that the OPO with double resonance for both squeezed light and pump light enables to lower external pump power. The generation of $ {\rm HG_{10}} $ mode squeezed light differs from that of $ {\rm HG_{00}} $ mode squeezed light, with an additional Gouy phase shift introduced between the $ {\rm HG_{20}} $ pump mode and $ {\rm HG_{10}} $ down-conversion mode within the OPO cavity. In this paper, we present a theoretical analysis and the experimental generation of $ {\rm HG_{10}} $ mode squeezed light at lower external pump power using a doubly-resonant OPO based on a wedged periodically poled $ \rm KTiOP{O_4} $ (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 $ {\rm HG_{20}} $ and $ {\rm HG_{10}} $ modes as well as the astigmatism induced by the frequency-dependent refractive index. This configuration allows double resonance for both the $ {\rm HG_{20}} $ pump mode and the $ {\rm HG_{10}} $ squeezed mode while operating close to optimum phase matching conditions. 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 radius of curvature 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 $ {\rm HG_{20}} $ pump mode with a measured purity of 98.0$ {\text{%}} $. The mode-matching efficiency of 93.0$ {\text{%}} $ is achieved between the high-purity $ {\rm HG_{20}} $ pump mode and the OPO cavity. The homodyne visibility of the $ {\rm HG_{10}} $ mode is 98.1$ {\text{%}} $. We experimentally demonstrate the generation of 9.10 dB $ {\rm HG_{10}} $ mode squeezed light using a doubly-resonant OPO with only 51 mW of $ {\rm HG_{20}} $ pump mode, and simultaneously achieve 9.20 dB of squeezing in the $ {\rm HG_{00}} $ mode with 27 mW of $ {\rm HG_{00}} $ pump mode. The inferred squeezing level of both $ {\rm HG_{10}} $ and $ {\rm HG_{00}} $ mode squeezed light reaches up to 12.15 dB. The quantum technology has solved the pump power limitations in optical parametric oscillators, enabling the generation of high-order HG mode states with high squeezing level and providing an effective method to enhance spatial measurement precision.
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Keywords:
- high-order Hermite-Gaussian mode /
- squeezed state /
- optical parametric oscillator /
- double resonance
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图 2 实验装置图 (QWP, 四分之一波片; 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)
Fig. 2. The 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
Fig. 3. (a) The intensity profile of $ {\rm H{G_{20}}} $ mode; (b) The purity fitting result of $ {\rm H{G_{10}}} $ 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
Fig. 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
Fig. 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.
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