Dipole Orientation Induced Effects in Dipolar Bose-Einstein Condensates

Abstract

Ultracold quantum gases have thrived as an interdisciplinary field of condensed matter physics, quantum optics, atomic and molecular physics. It boasts set-ups with precisely controllable and highly tuneable interaction parameters. Research in this area has sparked after the realisation of Bose-Einstein condensation in alkali atoms in 1995. The goal is to continuously seek quantum gas systems where more and more complex interactions may be embedded. Bose-Einstein condensation were, later, achieved in atoms like Cr, Er, and Dy which have significant dipole moments, bringing anisotropic interactions to the quantum gas systems. In the last 15 years, dipolar Bose-Einstein condensates have consistently been found at the forefront of ultracold atomic research. Our goal is to explore the tunability of the dipole-dipole interaction. The simplest way is via an external field which can easily tune the polarisation direction of the dipole moment. Effectively it tunes the dipole-dipole interaction between the atoms, potentially from repulsive to attractive. The effect of this on the collective behaviour of dipolar Bose- Einstein condensates are dramatic. Below our findings have been outlined for reference. We begin by reviewing the advent of the theory of Bose gas and the general short-range two-body interactions in Chapter 1. We introduce dipolar interactions and prescribe the available methods for tuning these interactions. Theoretically these systems are addressed using mean-field theory. We list the conditions under which mean-field theory is applicable and show a glimpse of beyond the mean-field theory, which becomes crucial in the final chapter. In Chapter 2, we review the stability of both homogeneous and trapped Bose-Einstein condensates by studying the elementary excitations in the system. The theoretical methodologies for calculating Bogoliubov excitations and the low-lying modes of the condensates have been explained along with important discoveries from the experimental counterpart. The last section in Chapter 2 contains the theory of parametric modulation, a technique that has become widely popular in ultracold systems due to availability of precise tuning of interactions parameters. In Chapter 3, the effect of tilting of dipole moment have been explored in dipolar Bose-Einstein condensates in the quasi-2D. We emphasize on the effect of trapping geometry on the stability followed by characterizing various stable and unstable domains with the help of phase diagrams in experimentally relevant parameter space. Post instability dynamics under different instabilities reveal markedly different features, capturing the essence of anisotropic nature of dipole-dipole interactions. Anisotropic solitons, new kind of self-trapped solutions and their respective stabilities have been analysed in detail and succinctly put as a phase diagram. In the end, we propose experimental preparation of the so far elusive quasi-2D soliton via adiabatic tuning of tilting of dipole moment. Chapter 4 consists of an ongoing work on dipolar Bose-Einstein condensation in quasi- 1D. We consider multiple cigar-shaped condensates under parametric modulation. Consequently, some non-intuitive yet interesting phenomena have come to light. In homogeneous systems, we show emergence and transfer of Faraday patterns from layer to layer when only one layer is modulated. The selection of pattern relies on the Bogoliubov spectrum, which can be changed dramatically by tuning the dipole moment. We also show the transfer of mode-locking phenomenon in trapped bilayer condensates. Interestingly, this excitation transfer may be enhanced or suppressed again by tuning the dipole moment polarisation direction. We also find that the center of mass motion and the widths oscillations in multilayer dipolar systems are coupled, giving rise to energy transfer between them as well. In the final chapter, we introduce doubly-dipolar BECs with purely 3D calculations. The system has magnetic and electric dipole-dipole interaction and the polarisation angle between the two dipole moments is now the most important tuneable parameter. In the context of beyond-mean-field effects, we show the presence of self-bound droplet solutions in doubly-dipolar BECs. Most interestingly, the droplet is shown to undergo a shape transition from the traditional cigar-shaped to a new pancake-shape by tuning the polarisation angle. Further we prove that not only a structural transition, but also it is a dimensional crossover instigated purely by internal interactions in the absence of any external trapping geometry.

This thesis is a detailed work on the effects of tilting angle of the dipole moment in dipolar BECs in quasi-2D, quasi-1D and 3D geometries. We present the stability analysis and instability dynamics and consequent emergence of some novel solutions. Recent experimental results in tuning the strength of dipole-dipole interaction as well as the polarisation angle will provide a much necessary boost for future explorations of this topic.