A general theory of flattened dipolar condensates

TL;DR

This paper develops a comprehensive theoretical framework for flattened dipolar Bose-Einstein condensates, analyzing stability, excitations, and various approximation schemes, validated against exact solutions for improved understanding and modeling.

Contribution

It introduces a unified theory for flattened dipolar BECs, including stability analysis, effective interaction parameters, and validation of common approximation methods.

Findings

Benchmark results for condensate and quasiparticle excitations

Validation of approximate schemes against exact theory

Identification of regimes where various models perform well

Abstract

We develop theory for a flattened dipolar Bose-Einstein condensate (BEC) produced by harmonic confinement along one direction. The role of both short-ranged contact interactions and long-ranged dipole-dipole interactions (DDIs) is considered, and the dipoles are allowed to be polarised along an arbitrary direction. We discuss the symmetry properties of the condensate and the part of the excitation spectrum determining stability, and introduce two effective interaction parameters that allow us to provide a general description of the condensate properties, rotons, and stability. We diagonalize the full theory to obtain benchmark results for the condensate and quasiparticle excitations, and characterize the exact mean field stability of the system. We provide a unified formulation for a number of approximate schemes to describe the condensate and quasiparticles, including the standard quasi-two-dimensional (quasi-2D) approximation, two kinds of variational ansatz, and a Thomas-Fermi (TF) approximation. Some of these schemes have been widely used in the literature despite not being substantiated against the exact theory. We provide this validation and establish the regimes where the various theories perform well.