Nonclassical states of light in a nonlinear Michelson interferometer

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 [Phys. Rev. A 92, 022104 (2015)] that leads to nonlinear, intensity dependent phase shifts corresponding to relative changes in the lengths of its two arms. The quantum Cram\'er-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 readout strategy at the output end are discussed. The ideal nonclassical 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.