Corrections to the expected signal in quantum metrology using highly anisotropic Bose-Einstein Condensates

TL;DR

This paper examines how different theoretical approximations of a two-mode Bose-Einstein condensate affect the accuracy of parameter estimation in quantum metrology, aiming to improve signal modeling while maintaining computational feasibility.

Contribution

It analyzes the impact of various levels of approximation on the expected signal in quantum metrology with anisotropic BECs, enhancing modeling accuracy.

Findings

Higher-level approximations improve signal estimation accuracy

Simpler models may lead to biased parameter estimates

Enhanced models remain computationally feasible

Abstract

In the quantum metrology protocol described by Tacla et al. [Tacla et al., Phys. Rev. A 82, 053636 (2010)] where a two mode Bose-Einstein condensate (BEC) is used for parameter estimation, the measured quantity is to be obtained by doing a one parameter fit of the observed data to a theoretically expected signal. Here we look at different levels of approximation used to model the two mode BEC to see how the estimate improves when increasing level of detail is added to the theory while at the same time keeping the expected signal computable.