Breaking of Josephson junction oscillations and onset of quantum turbulence in Bose–Einstein condensates

Adam Griffin,Davide Proment,Sergey Nazarenko

doi:10.1088/1751-8121/ab7ad0

Abstract

We analyse the formation and the dynamics of quantum turbulence in a two-dimensional Bose–Einstein condensate with a Josephson junction barrier modeled using the Gross–Pitaevskii equation. We show that a sufficiently high initial superfluid density imbalance leads to randomisation of the dynamics and generation of turbulence, namely, the formation of a quasi-1D dispersive shock consisting of a train of grey solitons that eventually breakup into chains of distinct quantised vortices of alternating vorticity followed by random turbulent flow. The Josephson junction barrier allows us to create two turbulent regimes: acoustic turbulence on one side and vortex turbulence on the other. Throughout the dynamics, a key mechanism for mixing these two regimes is the transmission of vortex dipoles through the barrier: we analyse this scattering process in terms of the barrier parameters, sound emission and vortex annihilation. Finally, we discuss how the vortex turbulence evolves for long times, presenting the optimal configurations for the density imbalance and barrier height in order to create the desired turbulent regimes which last as long as possible.

Highlights

The Josephson junction (JJ) is an experimental set-up designed to showcase the Josephson effect [1]
In similar experimental systems the emergence of a few vortices has recently been witnessed [18], our study differs as we focus on finding specific parameters that produce the largest number of vortices which are sustained for the longest time so that we can observe isotropic vortex turbulence
We have explored the use of a Josephson junction set-up for generating Bose–Einstein condensates (BECs) vortex turbulence

Summary

Introduction

The Josephson junction (JJ) is an experimental set-up designed to showcase the Josephson effect [1]. This quantum mechanical effect, which describes particle tunnelling through a barrier and periodic oscillations, is well studied in the context of Bose–Einstein condensates (BECs) in both theory [2−4] and experiments [5−9]. Current methods to create vortex turbulence include optical spoons [10] and shaking confining traps [11]. These methods require much energy to create a single vortex in fluids with high density. We propose a method to create vortex dipoles with initial imbalance and sustain them by using a Kibble–Zurek [12, 13] like mechanism to prolong the vortex turbulence, that is, create vortices in a region of low density and increase the density in a controlled manner to maintain the topological defects and decrease the relative strength of the acoustic waves

Objectives

Results

Conclusion