Nonlinear phase estimation via nonlinear-linear hybrid interferometers

Abstract

Estimating nonlinear phase shifts is useful to analyze many dynamical processes. In this work, with respect to the second-order nonlinear phase shifts, we propose an estimation scheme with a coherent state as the input and balanced homodyne detection as the readout strategy. The measurement setup is a nonlinear-linear hybrid interferometer composed of an optical parametric amplifier and a beam splitter. We analyze the precision and determine the optimal parameters of our scheme. The precision is compared with the quantum Cramér–Rao bound as well as the precision of a conventional nonlinear interferometer. In view of the fact that photon loss is ubiquitous, the effects of transmission loss and detection loss on the precision are addressed. At low gain, our scheme is superior to the scheme using a conventional nonlinear interferometer, and the precision can saturate the quantum Cramér–Rao bound.