Condensate Phase Microscopy

TL;DR

This paper demonstrates a method to detect the phase of a Bose-Einstein condensate wave-function in a 2D optical lattice using phase retrieval algorithms applied to time-of-flight images, enabling phase imaging of ultra-cold atoms.

Contribution

It introduces a novel approach combining phase retrieval algorithms with time-of-flight imaging to measure the phase of condensates in optical lattices, which was previously inaccessible.

Findings

Phase of condensate wave-function can be reconstructed from time-of-flight images.

Method works for Bose-Einstein condensates in triangular optical lattices.

Applicable in the presence of artificial gauge fields.

Abstract

We show that the phase of a Bose-Einstein condensate wave-function of ultra-cold atoms in an optical lattice potential in two-dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave-functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.