Work

Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

Year: 2020

Type: article

Abstract: We study the effect of the boundary on a system of weakly interacting bosons in one dimension.It strongly influences the boson density, which is completely suppressed at the boundary position.Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level.Quantum fluctuations modify the density profile considerably.The local density approaches the average one as an inverse square of the distance from the boundary.We calculate an analytic expression for the density profile at arbitrary separations from the boundary.We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density.At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization.The quantum contribution to the boson density gives rise to small corrections of the bound-state energy levels.However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

Source: Physical Review Research

DOI: 10.1103/physrevresearch.2.043104

Authors: Aleksandra Petković, Benjamin Reichert, Zoran Ristivojevic

Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Laboratoire de Physique Théorique, Université de Toulouse

Language: English

Topic: Cold Atom Physics and Bose-Einstein Condensates

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Agence Nationale de la Recherche