Nonclassical states of light in a nonlinear Michelson interferometer

TL;DR

This paper explores the potential of nonlinear quantum metrology using a Kerr medium in a Michelson interferometer to achieve enhanced measurement sensitivities, analyzing optimal states and practical noise considerations.

Contribution

It provides a detailed analysis of the quantum Cramer-Rao bound in nonlinear interferometry and identifies resilient non-classical states for practical implementation.

Findings

Optimal non-classical states are highly susceptible to photon loss.

Resilient states can still achieve enhanced sensitivities under noise.

Practical schemes for implementing noise-tolerant quantum metrology are discussed.

Abstract

Nonlinear quantum metrology schemes can lead to faster than Heisenberg limited scalings for the measurement uncertainty. We study a Michelson interferometer embedded in a Kerr medium [Luis and Rivas, Phys. Rev. A 92, 022104 (2015)] that leads to non-linear, intensity dependent phase shifts corresponding to relative changes in the lengths of its two arms. The quantum Cramer-Rao bound on the minimum achievable measurement uncertainties is worked out and the requirements, in practice, to saturate the bound are investigated. The choice of input state of light into the interferometer and the read out strategy at the output end are discussed. The ideal, non-classical states of light that must be used to saturate the bound are found to be highly susceptible to photon loss noise. We identify optimal states at each noise level that are both resilient to noise and capable of giving the enhanced sensitivities and discuss practical implementations of the interferometry scheme using such states.