Criticality-enhanced global frequency sensing with a monitored Kerr parametric oscillator via extended Kalman filter

TL;DR

This paper demonstrates a method for real-time frequency estimation of a Kerr parametric oscillator using an extended Kalman filter, enhanced by criticality and adaptive control, with robustness to low detection efficiency.

Contribution

It introduces a global sensing protocol leveraging criticality and adaptive control to improve frequency estimation accuracy in nonlinear quantum sensors.

Findings

Frequency estimates form a sharp distribution around the true value.

Criticality enhances the sensitivity of the frequency estimation.

The method remains robust under low detection efficiency.

Abstract

We analyze a global sensing scenario in which the frequency of a monitored Kerr parametric oscillator is estimated assuming limited prior information. The frequency is estimated in real-time by continuously monitoring the oscillator quadrature through homodyne detection and processing the resulting photocurrent with an extended Kalman filter (EKF). Due to the sensor nonlinearity, individual EKF trajectories do not always converge to the true unknown frequency in the long-time limit. However, we show that the statistical distribution of the frequency estimates does exhibit a sharp peak around the true value in the same limit. Leveraging this key statistical property, we develop a global sensing protocol assisted by adaptive control of the sensor parameters to harness critical enhancement. We present numerical evidence that this criticality-enhanced frequency estimation remains robust under low detection efficiency.