Many-body processes in black and gray matter-wave solitons

Abstract

We perform a comparative beyond mean-field study of black and grey solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized densityengineering potential is developed and employed together with phase-imprinting to cleanly initialize grey solitons. Based on our recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which prolongs with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of grey solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analysed in detail. Finally, the role of phase-imprinting for the many-body dynamics is illuminated and additional non-local correlations in pairs of counter-propagating grey solitons are unravelled.

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

“…Having switched off the barrier, we let the interacting manybody system evolve in the box potential. In the course of time, the single density minimum splits into a pair of counter-propagating gray solitons, which are slowly decaying due to quantum-fluctuations [9]. We have shown that a single gray soliton is accompanied by highly localized two-body correlations in the vicinity of the instantaneous soliton position resulting in a bunching of atoms in the soliton flank opposite to its direction of movement (cf.…”

“…e.g. [6][7][8][9]. Due to the increasing population of this orbital, the depth of the characteristic minimum in the reduced one-body density is reduced, i.e.…”

“…1(b) and [9]). Observing numerically that |g 2 (0, 0) − 1| ≪ 1, we may now understand these non-local correlations as a generic property of parity-symmetric systems with essentially two oc-cupied NOs: Denoting the position of the soliton moving to the right/left with x R/L , our above results imply Second, in order to realize a situation with significant deviations of g 2 (0, 0) from unity, we additionally imprint a relative phase of π between the two half-spaces at t = 0 [6][7][8][9]. Thereby, a black soliton is initialized at x = 0.…”

“…By incrementing M , we found in both scenarios discussed below that convergence is ensured on the considered time-scale if M = 4 (cf. [9]). A NO analysis of the full numerical data reveals that two NOs contribute with significant weight while the probability to find an atom in one of the other two NOs does not exceed 0.023 for the time-scales of Fig.…”

“…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.…”