Phase-Drift Limits and Adaptive Quadrature Readout in Programmable Photonic Processors

Abstract

Phase fluctuations between optical inputs limit programmable photonic processors because their output powers depend on coherent interference. We study the phase-drift penalty that arises when sine and cosine quadratures are measured sequentially rather than simultaneously. The analysis is motivated by measurements from an eight-mode programmable photonic processor, including 35 free-running recordings of 300 s acquired at approximately 125 samples per second per channel. These recordings provide an empirical route for estimating the phase-increment variance at a selected reconfiguration interval. The estimate is defined at the time of the second measurement. For fixed quadrature order, perturbation of the atan2 reconstruction gives $e_{C\to S}=-\delta_\tau\sin^2\phi_0+O(\delta_\tau^2)$ and $e_{S\to C}=-\delta_\tau\cos^2\phi_0+O(\delta_\tau^2)$. Writing $Q_\tau=\operatorname{Var}(\delta_\tau)$, uniform phase averaging gives the first-order drift mean-square error $3Q_\tau/8$. A phase-predicted ordering rule measures the locally less informative quadrature first and the more informative quadrature second. Its uniform first-order penalty is $(3/8-1/\pi)Q_\tau$, which is 84.9 percent below the fixed-order value. We also derive an increment-aware estimator from a local state-space model. Marginalizing the unknown phase increment increases the variance of a stale phase observation by $Q_\tau$, reducing its Fisher information from $I$ to $I/(1+IQ_\tau)$. For ideal balanced Poisson detection, the Fisher information of each quadrature equals its detected signal-photon number. This yields dimensionless architecture boundaries in spatial information and phase-increment variance. Nonlinear Monte Carlo simulations validate the perturbative laws, quantify robustness to prediction error, and compare simultaneous, fixed-order, increment-aware, and adaptive receivers under a common noise model.