A Multi-path Interferometer with Ultracold Atoms Trapped in an Optical Lattice

TL;DR

This paper demonstrates that a multi-path interferometer with ultracold atoms in an optical lattice can significantly enhance measurement sensitivity for spatially dependent potentials, outperforming traditional two-mode setups.

Contribution

It introduces a multi-path interferometer scheme using ultracold atoms in an optical lattice, showing improved sensitivity scaling with the number of sites and initial state correlations.

Findings

Measurement uncertainty scales as 1/(N(M^j-1))

Sensitivity improves with the number of lattice sites M, especially for linear potentials

Correlated initial states can further enhance estimation precision

Abstract

We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-square fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials and can be further improved by preparing a properly correlated initial state in the lattice.