Transformation of the Talbot effect in response to phase disorder

TL;DR

This paper investigates how phase disorder in Bose-Einstein condensates affects the Talbot effect, revealing the emergence of new spectral peaks due to pairwise interference, supported by analytical derivations.

Contribution

It provides an analytical expression for the density spectrum under arbitrary phase disorder and explains the origin of new peaks from pairwise interferences.

Findings

Phase disorder transforms the Talbot interference pattern.

New spectral peaks arise from pairwise condensate interferences.

Analytical expression derived for the density spectrum with phase disorder.

Abstract

Bose-Einstein condensates initially arranged in a long chain freely expand and interfere. If the initial phases of the condensates are identical, the initial density distribution is restored periodically during the expansion, giving rise to the Talbot effect. Even a slight disorder in the initial phases leads to a transformation of the interference pattern. In response to the phase disorder, the spectrum of the spatial density distribution acquires peaks that are absent in the case of identical phases. We derive an analytical expression for the spectrum of the spatial density distribution for an arbitrary phase disorder. We show that the new peaks emerging due to the phase disorder originate from pairwise interferences of the condensates. The positions of these peaks coincide with the wave vectors of the density modulations (wavelets) generated by such pairwise interferences. The absence of these peaks, when the initial phases are identical, is explained by the mutual destruction of the overlapping wavelets during their summation.