Critical Temperature for Bose-Einstein condensation in quartic potentials

TL;DR

This paper calculates the critical temperature for Bose-Einstein condensation in quartic potentials, highlighting how finite particle number effects differ from quadratic potentials, with implications for quantum phase transition observations.

Contribution

It provides the first detailed calculation of the critical temperature in quartic potentials and analyzes finite particle number effects, revealing contrasting behaviors compared to quadratic traps.

Findings

Finite temperature $T_c$ is computed for quartic potentials.

Finite particle number effects on $T_c$ are larger for $N<10^5$ in quartic traps.

Behavior reverses for $N extgreater 10^5$, with smaller effects.

Abstract

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature $T_c$ of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on $T_c$ and find that $\Delta T_c/T_c$ is larger in quartic potential as compared to quadratic potential for number of particles $ < 10^5$. Interestingly, the situation is reversed if the number of particles is $\gtrsim10^5$.