Position- and momentum-space two-body correlations in a weakly interacting trapped condensate

TL;DR

This paper analyzes two-body correlations in position and momentum space of a weakly interacting trapped Bose-Einstein condensate, revealing unique features influenced by trap geometry and temperature, with implications for understanding quantum statistical effects.

Contribution

It provides a detailed theoretical study of two-body correlations in trapped BECs using the Bogoliubov approximation, highlighting differences from homogeneous gases and connecting to optical effects.

Findings

Anti-bunching in position space due to repulsive interactions

Bunching signatures in momentum space at equal and opposite momenta

Linewidths of bunching signals linked to trap size and condensate size

Abstract

We investigate the position- and momentum-space two--body correlations in a weakly interacting, harmonically trapped atomic Bose-Einstein condensed gas at low temperatures. The two-body correlations are computed within the Bogoliubov approximation and the peculiarities of the trapped gas are highlighted in contrast to the spatially homogeneous case. In the position space, we recover the anti-bunching induced by the repulsive inter-atomic interaction in the condensed fraction localized around the trap center and the bunching in the outer thermal cloud. In the momentum space, bunching signatures appear for either equal or opposite values of the momentum and display peculiar features as a function of the momentum and the temperature. In analogy to the optical Hanbury Brown and Twiss effect, the amplitude of the bunching signal at close-by momenta is fixed by the chaotic nature of the matter field state and its linewidth is shown to be set by the (inverse of the) finite spatial size of the associated in-trap momentum components. In contrast, the linewidth of the bunching signal at opposite-momenta is only determined by the condensate size.