Quantum metrology in a nonlinear-interferometer with feedback

TL;DR

This paper introduces a feedback-enhanced nonlinear interferometer for phase estimation, demonstrating improved quantum Fisher information and phase sensitivity, especially in low-loss regimes, with novel feedback schemes and switching strategies.

Contribution

It proposes new feedback schemes for nonlinear interferometers that enhance phase estimation accuracy and introduces a switching method to maintain high QFI at large phases.

Findings

Feedback loops increase quantum Fisher information with each iteration.

The scheme outperforms standard nonlinear interferometers in low-loss conditions.

Switching between squeezing and anti-squeezing improves QFI at large phase values.

Abstract

In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.