Critical temperature for Bose-Einstein condensation in quartic potentials

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 Tc 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 Tc and find that ∆Tc/Tc 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 10 5 .

Thermodynamics of a two-dimensional interacting Bose gas trapped in a quartic potential

“…The general form of the quartic oscillator potential, which is used as a confining potential in the present work, is as follows [38] V ext ( r) = λ( r · r) 2 , (1) where λ is an experimental parameter related to the laser beam characteristics [10]. Harmonic traps with such an additional quartic anharmonicity were realized experimentally in 2004 [4,5].…”

“…The transition temperature T 0 for the non-interacting 2D Bose gas in such a quartic trap was calculated in Ref. [10] by using the semiclassical density of states,…”

“…Furthermore, as Gygi et al [8] have pointed out, quartic traps provide a better prerequisite for the experimental observation of quantum phase transitions of ultracold bosonic atoms in optical lattices. Later, the same trap geometry has been considered in the studies of non-interacting systems of lattice bosons [9] and free bosons [10]. Most recently, a comprehensive thermodynamic analysis has been carried out * Corresponding author.…”

“…The others which dealt with the bosons trapped in quartic potentials examined either a non-interacting condensate [10,11] or a weakly interacting condensate at zero temperature [12]. Unlike all these studies, we are interested in a non-rotating condensate trapped in a 2D quartic potential and, for such a system, we study the BEC of weakly interacting bosons at finite temperature.…”

“…Trapping potentials of this form can be achieved experimentally by superimposing the counter propagating laser beams [10]. Quartic potentials are typically considered as a method for stabilizing a Bose-Einstein condensate at fast rotation.…”