Reduced density matrices and coherence of trapped interacting bosons

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.Comment: 40 pages, 6 figure

Controlling the velocities and the number of emitted particles in the tunneling to open space dynamics

“…Ref. [52]. The momentum space representation is versatile to assess quantum dynamics [30] and will be frequently employed throughout the present study.…”

“…The full wave function which is available in the MCTDHB computations at any given point in time, is a complicated and high dimensional quantity. It is hence a useful practice to rely on reduced density matrices and their diagonals, i.e., densities, for the purpose of visualization [38,39,[50][51][52]. The reduced one-body density matrix is defined as…”

“…The coherence of the quantum many-body state can be analyzed with the aid of Glauber's first order normalized correlation function [38,39,50,52],…”

“…g (2) normalizes the reduced two-body density ρ (2) (x 1 , x 2 |x ′ 1 , x ′ 2 ; t) with the respective densities ρ. ρ (2) is defined as follows [38,39,50,52]:…”

Two-body correlations and natural-orbital tomography in ultracold bosonic systems of definite parity

“…Examples for such phenomena are the Mott-insulating phase, where e.g. an intra-well Tonks-Girardeau transition for a filling factor of two can be understood in the NO framework [4,5], the quantum-fluctuations induced decay of dark solitons [6][7][8][9], where a NO of particular shape is dominantly responsible for the soliton contrast reduction in the reduced one-body density, and fragmented condensates [10][11][12][13], which are defined as many-body states with two or more macroscopically occupied NOs. While there are proposals for the detection of fragmentation and its degree [14,15], the one-body density ρ 1 (r) has, to the best of our knowledge, not yet been unraveled into the * skroenke@physnet.uni-hamburg.de † pschmelc@physnet.uni-hamburg.de contributions |φ i (r)| 2 of the individual NOs by means of a measurement protocol.…”