Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states

TL;DR

This paper derives the quantum Cramér-Rao bounds for phase estimation in an SU(1,1) interferometer using Gaussian states, revealing conditions for optimal sensitivity and potential to surpass standard quantum limits.

Contribution

It provides analytical expressions for quantum Fisher information in SU(1,1) interferometers with Gaussian inputs, including effects of internal losses and phase shift configurations.

Findings

QCRB varies between single and double arm phase shifts depending on input states.

Optimal sensitivity achieved with a squeezed vacuum in one mode and vacuum in the other.

QCRB can beat the standard quantum limit under low-loss conditions.

Abstract

We theoretically present the quantum Cram\'{e}r-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied and the corresponding analytical expressions of quantum Fisher information with Gaussian input states are presented. Different from the traditional Mach-Zehnder interferometer, the QCRB of single arm case is slightly higher or lower than that of double arms case depending on the input states. With a fixed mean photon number and for pure Gaussian state input, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other. We compare the QCRB with the standard quantum limit and Heisenberg limit. In the case of small internal losses the QCRB can beat the standard quantum limit.