Trapped Bose-Einstein condensate in the weakly interacting limit

David A. W. Hutchinson, R. J. Dodd, Nick P. Proukakis +4 more

Andrew David Jackson, G. M. Kavoulakis

We examine the problem of a repulsive, weakly interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per particle is between zero and one and find that the interaction energy decreases linearly as a function of the angular momentum in agreement with previous numerical and limiting analytical studies.

Mircea Marinescu, Anthony F. Starace

An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.

C. G. Townsend, N. J. van Druten, Michael R. Andrews +4 more

Jacob Dunningham, Matthew J. Collett, Daniel F. Walls

G. M. Kavoulakis, Ben R. Mottelson, S. M. Reimann

We investigate the low-lying excitations of a weakly interacting, harmonically trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum L of the system is much less than the number of the atoms N in the trap. We show that in the asymptotic limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ the excitation energy, measured from the energy of the lowest state, is given by ${27N}_{3}{(N}_{3}\ensuremath{-}{1)v}_{0}/68,$ where ${N}_{3}$ is the number of octupole excitations, and ${v}_{0}$ is the unit of the interaction energy.