Rapid phase estimation of cavity squeezed states via optimal parametric control

Abstract

Ideally, the characterization of non-classical states requires measurements on timescales much shorter than the system’s decoherence time. However, in quantum cavity electrodynamics, photon loss rates are often comparable to measurement rates, which degrades the fidelity of the readout. In this work, we propose an active protocol to accelerate the phase estimation of squeezed vacuum states trapped in a lossy cavity. Instead of relying on passive leakage or linear coherent driving, we excite the system with a time-optimized degenerate parametric drive. This adapted two-photon pump actively amplifies the relevant quantum fluctuations, rapidly projecting the phase information of the squeezed state onto the integrated homodyne photocurrent of the output field before significant decoherence occurs. Because a squeezed vacuum carries no phase information in its first moments, this quadratic control is the minimal resource able to imprint the squeezing angle onto the detected signal. Using a numerical optimal control approach, we derive pumping envelopes that maximize the ability to distinguish between orthogonal squeezed states, achieving approximately a 6.02-fold increase in signal contrast compared to constant excitation schemes. We demonstrate that this active extraction protocol produces a strictly monotonic calibration curve, enabling rapid and unambiguous identification of the squeezed phase angle. Furthermore, robustness analysis confirms that the phase estimate remains reliable even in the presence of intense Gaussian detection noise, providing a practical framework for rapid state verification in open-system quantum technologies.