Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions

Doganov, Rostislav A.; Klaiman, Shachar; Alon, Ofir E.; Streltsov, Alexej I.; Cederbaum, Lorenz S.

doi:10.1103/physreva.87.033631

Cited by 52 publications

(67 citation statements)

References 60 publications

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“…In contrast, the mechanism described by Girardeau whereby the particles can avoid feeling the interaction remains a possibility. In our previous work [20], considering two, three, and four particles [21] in a two dimensional harmonic trap [2,[22][23][24][25][26][27][28][29][30], we showed that interacting bosons avoid feeling the interaction by becoming correlated in such a way that the probability of two particles being at the same position vanishes [31].…”

Section: Introductionmentioning

confidence: 99%

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

2018

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Abstract:The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.

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Section: Introductionmentioning

confidence: 99%

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

2018

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“…the frequency of the isotropic external oscillator and = ( ) The two-body s-wave interaction is modeled by a finite-range Gaussian shaped function[96][97][98] …”

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Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates

et al. 2017

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The beyond mean-field dynamics of a bent dark soliton embedded in a two-dimensional repulsively interacting Bose-Einstein condensate is explored. We examine the case of a single bent dark soliton comparing the mean-field dynamics to a correlated approach, the Multi-Configuration Time-Dependent Hartree method for Bosons. Dynamical snaking of this bent structure is observed, signaling the onset of fragmentation which becomes significant during the vortex nucleation. In contrast to the mean-field approximation "filling" of the vortex core is observed, leading in turn to the formation of filled-core vortices, instead of the mean-field vortex-antivortex pairs. The resulting smearing effect in the density is a rather generic feature, occurring when solitonic structures are exposed to quantum fluctuations. Here, we show that this filling owes its existence to the dynamical building of an antidark structure developed in the next-to-leading order orbital. We further demonstrate that the aforementioned beyond mean-field dynamics can be experimentally detected using the variance of single shot measurements. Additionally, a variety of excitations including vortices, oblique dark solitons, and open ring dark soliton-like structures building upon higher-lying orbitals is observed. We demonstrate that signatures of the higher-lying orbital excitations emerge in the total density, and can be clearly captured by inspecting the one-body coherence. In the latter context, the localization of one-body correlations exposes the existence of the multi-orbital vortex-antidark structure.

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“…The short-range repulsive interaction between the bosons is modeled by a Gaussian function [49,50] W (r − r ′ ) = λ 0 e −(r−r ′ ) 2 /2σ 2 2πσ 2 with a width σ = 0.25. The interaction parameter λ 0 is taken to be positive to describe repulsive bosons.…”

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Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

et al. 2014

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A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs. [4][5][6]. While three-dimensional trapped BECs have been extensively studied since their discovery, the static and time-dependent properties of their two-dimensional counterparts are comparatively less explored.One of the most popular scenarios studied with ultracold bosonic atoms, both experimentally and theoretically, is the splitting of a BEC by a central barrier into two spatially-disjoint clouds, e.g., Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It is a common practice that in order to produce a fragmented BEC in the splitting process, the ground state must be fragmented. This renders high barriers and strong interaction strengths necessary. Previous works dealt with splitting of a BEC in one or three spatial dimensions. To the best of our knowledge, splitting of a BEC in two spatial dimensions has not been explored experimentally or theoretically on the many-body level.In the present work we investigate theoretically, on an accurate many-body level, the physics of splitting a twodimensional (2D) BEC. A natural approach is to exploit the 2D symmetry of the system. We thus split a circular BEC by a radial potential barrier, see Fig. 1a for an illustration. This would lead to two concentric clouds, unlike the above-discussed common way of splitting a BEC and, as we shall see below, enrich the physics of BEC splitting.By analyzing the many-body time-independent and time-dependent wavefunctions of the system, we construct both static and dynamic phase diagrams of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We therefore demonstrate the dynamical fragmentation of a BEC, despite its ground state being fully condensed. The results imply that a large manifold of fragmented excited states can significantly impact the dynamics of 2D BECs.We consider a repulsive BEC with N = 100 bosons in the 2D circular trap shown in Fig. 1a. Throughout this work dimensionless units are used, such that the single-particle kinetic-energy operator readsT (r) = − 1 2 ∇ 2 r [22]. The explicit form of the one-body potential is given by V (r) = V trap (r) + V barrier (r). Here V trap (r) = {200e −(r−rc) 4 /2 , r ≤ r c = 9; 200, r > r c } is a flat trap which has the shape of "a crater" and V barrier (r) = 200e ...

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Two trapped particles interacting by a finite-range two-body potential in two spatial dimensions

Cited by 52 publications

References 60 publications

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

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