Calculation of laser interferometric quantum noise optimal squeezing angle criterion for dynamic unequal-arm heterodyne interferometers
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摘要:
空间引力波探测任务中，干涉仪臂长受轨道动力学影响而动态演化，传统等臂零差模型难以描述外差链路下量子噪声的传递特性。针对空间引力波探测中动态不等臂外差干涉仪导致的激光口噪声与暗口涨落发生非零耦合问题，本文推导了空间引力波探测全频段量子噪声演化模型并得到了最优压缩角自适应调控判据。从含时场算符出发，利用傅里叶变换将时域因果延迟转化为频域相位旋转，导出了频域噪声混合矩阵；结合光力耦合系数描述低频辐射压噪声，推导出了空间引力波探测全频段通用最优压缩角判据。数值仿真表明，在静态相位差达到最大时，传统固定压缩角方案无法抑制混叠噪声，其归一化方差为1.0；本文提出的自适应压缩角方案具有明显的降噪效果，在压缩度
r = 0.5（4.3 dB）和r = 1.0（8.7 dB）时，可将归一化输出相位噪声方差分别压低至0.9046 和0.7483 。利用此判据动态调整压缩方向，可在空间引力波探测全频段内提高量子噪声抑制水平，为空间引力波探测器在动态不等臂环境下的量子噪声抑制提供理论参考。Abstract:In space gravitational wave detection missions, interferometer arm lengths dynamically evolve under the influence of orbital dynamics, making it difficult for traditional equal-arm homodyne models to describe the propagation characteristics of quantum noise in heterodyne links. To address the non-zero coupling between laser-port noise and dark-port fluctuations caused by dynamic unequal-arm heterodyne interferometers in space gravitational wave detection, this paper derives a full-band quantum noise evolution model and obtains an adaptive control criterion for the optimal squeezing angle. Starting from time-dependent field operators, the frequency-domain noise mixing matrix is derived by using the Fourier transform to convert time-domain causal delays into frequency-domain phase rotations. Combined with the optomechanical coupling coefficient to describe low-frequency radiation pressure noise, a universal optimal squeezing angle criterion for the full frequency band of space gravitational wave detection is established. Numerical simulations demonstrate that when the static phase difference reaches its maximum, the traditional fixed squeezing angle scheme fails to suppress the mixed noise, with its normalized variance remaining at 1.0. In contrast, the proposed adaptive squeezing angle scheme exhibits a significant noise reduction effect; at squeezing parameters
r = 0.5 (4.3 dB) andr = 1.0 (8.7 dB), it successfully reduces the normalized output phase noise variance to0.9046 and0.7483 , respectively. Utilizing this criterion to dynamically adjust the squeezing direction can enhance the level of quantum noise suppression across the full frequency band of space gravitational wave detection, providing a theoretical reference for quantum noise mitigation in space gravitational wave detectors under dynamic unequal-arm environments. -
图 1 动态不等臂外差干涉测量示意图
Figure 1. Schematic of dynamic unequal-arm heterodyne interferometric measurement
图 2 激光干涉分束与压缩态注入示意图
Figure 2. Schematic of laser beam splitting and squeezed state injection
图 3 以LISA为例的最优压缩角
$ {\theta }_{opt} $ 随$ {\phi }_{0} $ 和$ \mathit{\Omega } $ 的变化曲面Figure 3. Evolution surface of optimal squeezing angle
$ {\theta }_{opt} $ versus$ {\phi }_{0} $ and$ \mathit{\Omega } $ with LISA as an example
图 4 以LISA为例的固定方案与自适应方案噪声方差对比曲线 (
$ \mathit{\Omega }=1 $ Hz)Figure 4. Comparison of output phase noise variance between fixed and adaptive squeezing schemes with LISA as an example (
$ \mathit{\Omega }=1 $ Hz)
图 5 不同空间引力波探测计划绝对臂长差
$\mathit{\Delta }L$ 下的量子噪声频域响应曲线(${\phi }_{0}=\dfrac{{\text{π}} }{4}$ )Figure 5. Frequency-domain responses of quantum noise mixing ratio under arm-length mismatches
$ \mathit{\Delta }L $ corresponding to different space missions ($ {\phi }_{0}=\dfrac{{\text{π}} }{4} $ ) -
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