Nonlinear interferometry with Bose-Einstein condensates

TL;DR

This paper investigates a nonlinear interferometry scheme using Bose-Einstein condensates, demonstrating through simulations that it can surpass traditional sensitivity limits under realistic conditions.

Contribution

It provides numerical validation of a proposed BEC-based nonlinear interferometry method achieving super-Heisenberg scaling.

Findings

Confirms $1/N^{3/2}$ sensitivity scaling through simulations.

Shows two modes share the same spatial wave function during measurement.

Analyzes the impact of wave function spreading on measurement precision.

Abstract

We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than $1/N$ in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of $N$ atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the BEC ground-state wave function on the ideal $1/N^{3/2}$ scaling. Numerical integration of the coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme.