Bose polaron in spherical trap potentials: Spatial structure and quantum depletion

Abstract

We investigate how the presence of a localized impurity in a Bose-Einstein condensate of trapped cold atoms that interact with each other weakly and repulsively affects the profile of the condensed and excited components at zero temperature. By solving the Gross-Pitaevskii and Bogoliubovde Gennes equations, we find that an impurity-boson contact attraction (repulsion) causes both components to change in spatial structure in such a way as to be enhanced (suppressed) around the impurity, while slightly declining (growing) in a far region from the impurity. Such behavior of the quantum depletion of the condensate can be understood by decomposing the impurity-induced change in the profile of the excited component with respect to the radial and azimuthal quantum number. A significant role of the centrifugal potential and the "hole" excitation level is thus clarified.

Theory of a resonantly interacting impurity in a Bose-Einstein condensate

“…Even then, the use of the Bogoliubov approximation misses cubic and quartic interaction terms, which are a crucial part of the boson repulsion required to balance the local attraction and prevent an unlimited growth of local density, as pointed out in [5,38]. Alternatively, Gross-Pitaevskii theory fully incorporates boson repulsion but does not describe bound states with a local interaction in Born approximation [40][41][42].…”

“…If both potentials are weak, the Born approximation may be applied to V IB as well, hence it works when the two interaction length scales are of the same order [41,42]. Here, however, we are interested in large IB coupling and need to look for a theory that takes into account the interaction potential shapes in more detail.…”

Pattern formation in one-dimensional polaron systems and temporal orthogonality catastrophe

“…Recently, the properties of the Gross-Pitaevskii type Eq. ( 6) have been intensively studied [55][56][57][58][59][60][61][62] in one and three spatial dimensions. Below we will briefly review the implications of the 1D solution Eq.…”

“…Accordingly, these systems have recently been a topic of intense theoretical study in the ultracold community especially regarding their stationary properties . Lately, it has been argued that the ground state of the Bose polaron can be well-described in terms of a simple Gross-Pitaevskii mean-field type variational approach [55][56][57][58][59][60][61][62][63], herewith referred to as the Gross Ansatz (GA) 1 . The latter neglects all correlations except for the two-body bath-impurity ones.…”

“…To avoid confusion, since within the common Gross-Pitaevskii equation for an ideal BEC all correlations are neglected, here we will instead adopt the term Gross Ansatz (GA)[3] when referring to the technique employed in Ref [55][56][57][58][59][60][61][62][63]…”