Weakly interacting Bose-Einstein condensates under rotation

Abstract

We investigate the ground and low excited states of a rotating, weakly interacting Bose-Einstein condensed gas in a harmonic trap for a given angular momentum. Analytical results in various limits, as well as numerical results are presented, and these are compared with those of previous studies. Within the mean-field approximation and for repulsive interaction between the atoms, we find that for very low values of the total angular momentum per particle, L/N → 0, where Lh is the angular momentum and N is the total number of particles, the angular momentum is carried by quadrupolar (|m| = 2) surface modes. For L/N = 1 a vortex-like state is formed and all the atoms occupy the m = 1 state. For small negative values of L/N − 1 the states with m = 0 and m = 2 become populated, and for small positive values of L/N − 1 atoms in the states with m = 5 and m = 6 carry the additional angular momentum. In the whole region 0 ≤ L/N ≤ 1 we have strong analytic and numerical evidence that the interaction energy drops linearly as a function of L/N . We have also found that an array of singly quantized vortices is formed as L/N increases. Finally we have gone beyond the mean-field approximation and have calculated the energy of the lowest state up to order N for small negative values of L/N − 1, as well as the energy of the low-lying excited states.

Vortices in a trapped dilute Bose-Einstein condensate

“…Figure 9 shows the angular momentum versus the angular velocity for the first several states. Reference [91] has carried out more detailed studies of the states for relatively small values of the angular momentum per particle l 2.…”

Multiply quantized vortices in trapped Bose-Einstein condensates

“…In condensed Bose gases confined in harmonic-oscillator potentials, it has been found both analytically [9], numerically [10,11] and variationally [11] that multiply quantized vortices are not energetically favorable, and no quantum numbers larger than unity have been observed in experiment [3,4]. However, none of these studies has considered whether altering the power law of the confining potential can open up for the existence of multiply quantized vortices.…”

“…We shall now show how the analysis of Ref. [9] works when the trapping power n in Eq. (3) is larger than two.…”

“…[9] showed why multiply quantized vortices are never the minimum-energy state in a system which is harmonically confined in the x-y plane. We will here extend the same analysis to the case when the confinement is steeper than harmonic.…”

“…Following Ref. [9], we now consider perturbatively the interaction energy. The perturbation for a given wave function ψ is, from Eq.…”