Superfluid flow past an obstacle in annular Bose–Einstein condensates

M Syafwan,P Kevrekidis,H Susanto,L Hackermüller,I Lesanovsky,P Krüger,A Paris-Mandoki

doi:10.1088/0953-4075/49/23/235301

Abstract

We investigate the flow of a one-dimensional nonlinear Schrödinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose–Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.

Highlights

Persistent flow is a remarkable property of macroscopic quantum systems
A characteristic feature associated with superfluidity is the existence of a critical velocity above which its breakdown leads to the creation of excitations
In experiments with Bose–Einstein condensates (BECs), evidence for a critical velocity was obtained by moving an obstacle, i.e. a tightly focused laser beam, through a BEC [12, 13]

Summary

Introduction

Persistent flow is a remarkable property of macroscopic quantum systems. Bose–Einstein condensates (BECs) in a ring geometry [1,2,3,4,5,6] have been shown recently to support circulating superfluid flow [5, 7, 8]. As a final step in this theme of comparisons, we would like to mention recent work, which has explored the case of a rotating weak link as a function not of the potential/domain parameters considered here (such as the barrier strength or the domain length), but rather as a function of the interaction strength [43] This elaborate task requires different approaches in the weakly interacting limit (treated by means of a GP equation) and in the strongly interacting limit (treated by means of a Luttinger liquid approach and in the case of a Tonks gas by a Bose–Fermi mapping to the case of noninteracting fermions). Intermediate regimes were treated by density-matrix renormalization group computations which, revealed an unexpected optimality in the observed persistent currents at some intermediate interaction strengths between the above limits

Theoretical setup

R2 yqq ky

Numerical results and connections to theory

Discussion and future challenges