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

Abstract

is put forward and proven to apply for systems with a non-zero threshold value. It is demonstrated that the model is applicable for general interparticle interaction strengths, particle numbers and threshold values. The model constructs the many-body process from single-particle emission processes. The rates and emission momenta of the single-particle processes are determined by the chemical potentials and energy differences to the threshold value of the potential for systems with different particle numbers. The chemical potentials and these energy differences depend on the interparticle interaction. Both the number of confined particles and their rate of emission thus allow for a control by the manipulation of the interparticle interaction and the threshold. Numerically exact results for two, three and one hundred bosons are shown and discussed. The devised control scheme for the many-body tunneling process performs very well for the dynamics of the momentum density, the correlations, the coherence and of the final state, i.e., the number of particles that remain confined in the potential.

Management of the correlations of UltracoldBosons in triple wells

“…The MCTDHB thus yields descriptions of many-boson systems that allow for correlations to be intrinsically described without any a priori requirements. Coherent systems (states whose one-body RDM has a single contributing eigenvalue) [27] and fragmented systems (states whose one-body RDM has several macroscopic eigenvalues) [28,29] can be described by MCTDHB alike [46][47][48][49][50].…”

Momentum correlations of a few ultracold bosons escaping from an open well

“…While the tunneling of a single particle is well understood [8], and the tunneling of a Bose-Einstein condensate of a large number of particles is well described by a mean-field approximation [9][10][11][12], the escape behavior of interacting few-body systems is a more complicated problem in which the dynamics is nontrivially governed by the interplay between interactions, indistinguishability and quantum correlations [13]. Although significant attention has been already devoted to the dynamical processes of a few particles confined in closed lattice potentials [14][15][16][17], in recent years the significantly different problem of a few particles tunneling into open space has attracted an increasing amount of interest [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…The recent experiments on the tunneling of a few interacting atoms escaping from an effectively one-dimensional potential well [44,45] provide fresh motivation for the study of such tunneling problems. Since the presence of interparticle interactions and quantum correlations affects the tunneling of few-body systems in interesting and complex ways, a deeper understanding of this issue could become important also from a theoretical point of view [18][19][20][21][22][23][24][25][26][27][28][29][30]. * Electronic address: Jacek.Dobrzyniecki@ifpan.edu.pl…”

“…Although the system of two tunneling particles is the simplest possible case of the few-body tunneling problem, many open questions still remain unanswered, and it continues to be explored in recent research [46,47]. In [22,25] the properties of the system were partially studied from the momentum distribution point of view for repulsive interactions. Here we extend this description by also taking the attractive branch of interactions into account.…”

Many-body physics in two-component Bose–Einstein condensates in a cavity: fragmented superradiance and polarization

“…A representative example for a many-body effect is the so-called fragmentation [38,39] of the BEC. Fragmentation can be quantified using the reduced one-body density matrix (RDM); if the RDM has only a single macroscopic eigenvalue the system is said to be condensed [40], while if the RDM has more than one macroscopic eigenvalue the state is said to be fragmented [38,39,41,[42][43][44][45][46][47][48][49][50][51][52][53][54][55]. Fragmentation has been recently demonstrated to emerge in single-component ultracold bosons coupled to a single-mode cavity for pump powers roughly four times as large as the pump power necessary to drive the system from the normal to the superradiant phase [30].…”