AI 中文总结
本研究建立了评估多模SU(1,1)干涉仪相位灵敏度的理论数值框架，基于波导OPA实现优化设计，揭示不同探测方案下灵敏度的影响因素，为量子增强传感提供支撑。
AI 中文摘要
我们提出了一个综合框架，用于评估在相干-真空输入下，分别采用光子数探测和零差探测的光谱多模SU(1,1)干涉仪的相位灵敏度。光学参量放大器（OPA）采用周期性极化薄膜铌酸锂波导进行模拟，理论模型纳入了基于波导的OPA的固有多模光谱特性。在OPA相同且与施密特（Schmidt）模式无关的相移假设下，我们证明多模SU(1,1)干涉仪等价于施密特基中并行工作的一组独立单模干涉仪，每个干涉仪对应参量过程的一个施密特模式。我们进一步提出了一种基于非对称群速度匹配的优化波导设计，以实现具有近似可分解联合光谱振幅（JSA）的实用OPA。从数值模拟的JSA中提取的施密特系数被纳入理论模型，以评估相位灵敏度。结果表明，多模条件下的灵敏度强烈依赖于测量方案：对于光子数探测，灵敏度的降低源于可用非线性资源在各施密特模式间的重新分配；而零差探测则表现出额外的相干性损失，可通过最优整形本地振荡器（LO）大幅减少。此外，我们表明通过优化注入信号相干态的光谱，以及在零差探测情况下优化本地振荡器的光谱，可在很大程度上缓解性能下降。综上，本工作为分析和优化用于量子增强传感应用的、基于波导OPA的实际多模SU(1,1)干涉仪提供了统一的理论和数值框架。
英文摘要
We present a comprehensive framework for evaluating the phase sensitivity of spectrally multimode SU(1,1) interferometers probed with a coherent-vacuum input, under both number and homodyne detections. The optical parametric amplifiers (OPAs) are simulated using a periodically polled thin-film lithium niobate waveguide. The theoretical model incorporates the intrinsic multimode spectral nature of waveguide-based OPAs. Under the assumptions of identical OPAs and Schmidt-mode-independent phase shifts, we have shown that the multimode SU(1,1) interferometer is equivalent to a collection of independent single-mode interferometers in the Schmidt basis that operate in parallel, each associated with a Schmidt mode of the parametric process. We further present an optimized waveguide design based on asymmetric group-velocity matching to realize a practical OPA with nearly factorizable joint spectral amplitude (JSA). The Schmidt coefficients extracted from the numerically simulated JSA are incorporated into the theoretical model to evaluate the phase sensitivity. The results show that the sensitivity under a multimode condition depends strongly on the measurement scheme. For number detection, the degradation in sensitivity arises from the redistribution of the available nonlinear resource among the Schmidt modes, whereas homodyne detection exhibits an additional coherence penalty that can be substantially reduced by optimally shaping the local oscillator. Moreover, we show that the performance degradation can be to a large extent mitigated by optimizing the spectrum of the injected signal coherent state and, in the case of homodyne detection, the spectrum of the local oscillator. Altogether, this work provides a unified theoretical and numerical framework for analyzing and optimizing realistic multimode SU(1,1) interferometers with waveguide-based OPAs for quantum-enhanced sensing applications.
