Interference of Bose-Einstein condensates in momentum space

TL;DR

This paper proposes an experiment to observe interference fringes in the dynamic structure factor of two spatially separated Bose-Einstein condensates, revealing how measurement induces relative phase coherence.

Contribution

It introduces a method to detect interference in momentum space and demonstrates measurement-induced phase coherence in Bose-Einstein condensates.

Findings

Interference fringes are predicted in the dynamic structure factor at high momentum transfer.

The relative phase between condensates is created through the measurement process.

The experiment links coherence properties to measurable scattering signals.

Abstract

We suggest an experiment to investigate the linear superposition of two spatially separated Bose-Einstein condensates. Due to the coherent combination of the two wave functions, the dynamic structure factor, measurable through inelastic photon scattering at high momentum transfer $q$, is predicted to exhibit interference fringes with frequency period $\Delta\nu = q/md$ where $d$ is the distance between the condensates. We show that the coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates is hence created through the measurement process.