Dipolar Bose-Einstein condensates in random potentials

Abstract

Weakly interacting Bose gases in a disorder environment have long been a challenging topic in the field of condensed matter physics due to the intriguing interplay between superfluidity and localization. In this thesis we perform extensive theoretical and numerical studies of dipolar Bose gases in random potentials. To this end we develop a BogoliubovHuang-Meng theory for a weakly interacting Bose-Einstein condensate in a random environment, then specialize it to dipolar interactions and Gaussian correlated disorder. This model provides a reasonable description of weakly interacting Bose gases in random potentials. As a first step, we investigate a three-dimensional dipolar Bose condensed gas in the presence of the three-body interactions with an additional Guassian-correlated disorder potential at both zero and finite temperatures. Importantly, we find that at finite temperature the condensate co-exists with both the Bose-glass and thermal components. Corrections due to quantum, thermal and disorder fluctuations to the condensate depletion, the one-body density correlation function, the equation of state and the ground state energy are properly calculated. We show that the interplay of the disorder, dipole-dipole interaction and threebody interaction play a fundamental role in the physics of the system. Interestingly, we find 10that the three-body interactions release atoms localized in the respective minima of the random potential. Increasing the strength of the three-body interactions leads to decrease the one-body density matrix. Furthermore, we calculated the chemical potential and ultraviolet divergences are removed using an appropriate renormalization method. The combined effects of the dipole-dipole interactions, three-body interactions, and temperature found to crucially affect the chemical potential and the ground state energy. In the absence of the DDI and the three-body interactions, we reproduce the seminal results of Huang and Meng Finally, we consider a dilute Bose-condensed gas of dipolar bosons subjected to Gaussian correlation at zero temperature loaded in a quasi-two-dimensional bilayer setup where dipoles are aligned perpendicularly to the layers and in same /opposite directions in different layers. We calculate analytically and numerically the condensate depletion, the onebody density-matrix, and the superfluid fraction in the framework of the BogoliubovHuang-Meng theory. Our analysis not only provides fascinating new results do not exist in the literature but also shows that the competition between the disorder, the interlayer coupling and the polarization orientation may lead to localize/delocalize the condensed particles results in the transition from the Bose-glass to the superfluid phase and vice versa. For a pure short-range interaction and vanishing interlayer distance, we recover the results found for a single layer system. Our results pave the way for the experimental realization of three-dimensional disordered dipolar Bose gases with pure three-body interactions, and of dirty bosons in a quasi-two-dimensional bilayer configuration