Stability of the density-wave state of a dipolar condensate in a pancake trap

TL;DR

This paper investigates the stability of a density-wave state in a dipolar boson-fermion mixture confined in a pancake-shaped trap, identifying the transition point from a Gaussian to a hexagonal density-wave state using variational analysis.

Contribution

It extends previous studies by analyzing the stability of density-wave states in a dipolar mixture within a pancake geometry, focusing on fermion-induced interactions.

Findings

Transition point from Gaussian to density-wave state identified

Fermion-induced interactions significantly affect stability

Variational analysis confirms stability conditions

Abstract

We study a dipolar boson-fermion mixture in a pancake geometry at absolute zero temperature, generalizing our previous work on the stability of polar condensates and the formation of a density-wave state in cylindrical traps. After examining the dependence of the polar condensate stability on the strength of the fermion-induced interaction, we determine the transition point from a ground-state Gaussian to a hexagonal density-wave state. We use a variational principle to analyze the stability properties of those density-wave state.