Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

S K Adhikari

doi:10.1038/s41598-017-16106-w

Abstract

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential or (b) a 1D Gaussian potential, both along the z axis and no potential along the x and y axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well (z > 0), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and a numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

Highlights

The topic of spontaneous symmetry breaking (SSB) in localized quantum states obeying Schrödinger dynamics has drawn much attention lately both in experimental[1] and theoretical[2,3,4,5,6,7] fronts
Motivated by the above consideration, in this paper we study SSB, Josephson oscillation[17,18,19,20] and self trapping in a 3D self-bound attractive matter-wave quantum ball[26,27,28] placed in a parity-symmetric (a) 1D double-well potential or (b) a 1D Gaussian potential along the z axis
The effect of this loss rate is expected to be considerable in a large high-density trapped attractive Bose-Einstein condensate (BEC) and will be negligible for the small-time dynamics of untrapped quantum balls presented in this paper, as was demonstrated in ref.[26], and is not considered here

Summary

Introduction

The topic of spontaneous symmetry breaking (SSB) in localized quantum states obeying Schrödinger dynamics has drawn much attention lately both in experimental[1] and theoretical[2,3,4,5,6,7] fronts. Motivated by the above consideration, in this paper we study SSB, Josephson oscillation[17,18,19,20] and self trapping in a 3D self-bound attractive matter-wave quantum ball[26,27,28] placed in a parity-symmetric (a) 1D double-well potential or (b) a 1D Gaussian potential along the z axis. These 1D potentials are necessary for SSB; these potentials act in 1D and have no effect on the localization of the 3D quantum ball. Collapse has been stopped by a three-body repulsion and an adequate two-body attraction

Methods

Results

Conclusion