Interplay between Binary and Three-Body Interactions and Enhancement of Stability in Trapless Dipolar Bose–Einstein Condensates

Sabari Subramaniyan,Kishor Kumar Ramavarmaraja,Boris A Malomed,Radha Ramaswamy

doi:10.3390/app12031135

Abstract

We investigate the nonlocal Gross–Pitaevskii (GP) equation with long-range dipole-dipole and contact interactions (including binary and three-body collisions). We address the impact of the three-body interaction on stabilizing trapless dipolar Bose–Einstein condensates (BECs). It is found that the dipolar BECs exhibit stability not only for the usual combination of attractive binary and repulsive three-body interactions, but also for the case when these terms have opposite signs. The trapless stability of the dipolar BECs may be further enhanced by time-periodic modulation of the three-body interaction imposed by means of Feshbach resonance. The results are produced analytically using the variational approach and confirmed by numerical simulations.

Highlights

The advent of Bose–Einstein condensates (BECs) in 52Cr [1,2], 164Dy [3,4] and 168Er [5]accompanied by long-range dipole-dipole (DD) interactions superimposed on the contact inter-atomic collisions has impacted the investigation of ultracold quantum gases [6]
The theoretical description of a dilute weakly interacting dipolar BECs (DBECs) is based on the Gross– Pitaevskii (GP) equation with the nonlocal DD-interaction term [1,2,23,24,25]
We further show that the introduction of the time-dependent part of the three-body interaction, χ1 may further, enhance the stability of the trapless dipolar repulsive BECs

Summary

Introduction

The advent of Bose–Einstein condensates (BECs) in 52Cr [1,2], 164Dy [3,4] and 168Er [5]. Following the scheme of the stabilization of the inverted (Kapitza) pendulum [30], scenarios for stabilization of two-dimensional (2D) optical [31] and matter-waves [32,33,34] by means of the “nonlinearity management” [35], i.e., the cubic nonlinearity periodically switching between self-attraction and repulsion, have been elaborated. This concept has been subsequently applied to 3D vortex solitons [32,34] and extended to the model containing the three-body interaction [36] and quantum fluctuations [37].

The Model

The Variational Method

N 4 χ21 243π6d4z Ω2

Three-Dimensional Numerical Results

Conclusions