Insensitivity points and performance of open quantum interferometers under number-conserving & non-conserving Lindblad dynamics

TL;DR

This paper analyzes how environmental noise affects the phase sensitivity of open quantum interferometers, identifying insensitivity points and comparing the impacts of number-conserving and non-conserving Lindblad dynamics.

Contribution

It introduces a detailed study of insensitivity points in quantum interferometers under different Lindblad noise models, revealing their independence from noise intensity and the superiority of number-conserving noise at small N.

Findings

Insensitivity points are independent of noise intensity.

Number-conserving noise can lead to better sensitivity at small particle numbers.

Particle non-conserving noise results in lower achievable sensitivity across all N.

Abstract

We investigate the phase sensitivity of a linear two-mode atom interferometer subject to environmental noise, modeled within the framework of open quantum systems with both number-conserving and non-conserving Lindblad operators. Considering several input states, we first study the cases N=1,2 (N number of particles) and perform numerical simulations for N>2. The sensitivity as a function of the holding time can display divergence points where phase estimation becomes impossible, to which we refer as insensitivity points. We characterize their behavior as the input state, particle number, and noise operator are varied, and we find that their positions are independent of the noise intensity. Moreover, while our fixed measurement scheme may favor number-conserving noise at small N (i.e., having better sensitivity), the Cram\'er-Rao bound reveals that particle non-conserving noise yields strictly lower achievable sensitivity for all particle numbers.