# Optimal phase measurements with bright and vacuum-seeded SU(1,1) interferometers

## TL;DR

This paper analyzes the phase sensitivity of bright and vacuum-seeded SU(1,1) interferometers, demonstrating a simplified scheme that surpasses classical limits and reaches quantum Fisher information bounds.

## Contribution

It introduces a truncated scheme with one nonlinear interaction that outperforms conventional detection and saturates quantum Fisher information limits.

## Key findings

- Truncated scheme beats conventional intensity detection with bright seed.
- Scheme saturates phase sensitivity bounds set by quantum Fisher information.
- Achieves sub-shot-noise phase sensitivity in vacuum-seeded case.

## Abstract

The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beamsplitters replaced with parametric nonlinear optical processes. We consider the cases of bright and vacuum-seeded SU(1,1) interferometers using intensity or homodyne detectors. A simplified, truncated scheme with only one nonlinear interaction is introduced, which not only beats conventional intensity detection with a bright seed, but can saturate the phase sensitivity bound set by the quantum Fisher information. We also show that the truncated scheme achieves a sub-shot-noise phase sensitivity in the vacuum-seeded case, despite the phase-sensing optical beams having no well-defined phase.