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

Abstract

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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