Reduced density matrices and coherence of trapped interacting bosons

TL;DR

This paper investigates the many-body correlation functions and coherence properties of trapped interacting Bose-Einstein condensates, revealing how trap geometry influences correlations and fragmentation beyond mean-field approximations.

Contribution

It provides a detailed numerical analysis of first- and second-order correlations in Bose-Einstein condensates, highlighting the effects of trap geometry and fragmentation on many-body properties.

Findings

Correlations can be strongly influenced by trap geometry even at weak interactions.

Fragmentation of the condensate can be understood through natural geminals.

Mean-field theory limits are identified and compared with many-body results.

Abstract

The first- and second-order correlation functions of trapped, interacting Bose-Einstein condensates are investigated numerically on a many-body level from first principles. Correlations in real space and momentum space are treated. The coherence properties are analyzed. The results are obtained by solving the many-body Schr\"odinger equation. It is shown in an example how many-body effects can be induced by the trap geometry. A generic fragmentation scenario of a condensate is considered. The correlation functions are discussed along a pathway from a single condensate to a fragmented condensate. It is shown that strong correlations can arise from the geometry of the trap, even at weak interaction strengths. The natural orbitals and natural geminals of the system are obtained and discussed. It is shown how the fragmentation of the condensate can be understood in terms of its natural geminals. The many-body results are compared to those of mean-field theory. The best solution within mean-field theory is obtained. The limits in which mean-field theories are valid are determined. In these limits the behavior of the correlation functions is explained within an analytical model.