arXiv:cond-mat/0011303 · Physical Review A

Low-lying excitations of a trapped rotating Bose-Einstein condensate

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

Published Apr 18, 2001• 12 citations

Abstract

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.

DOI: 10.1103/physreva.63.055602

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arXiv:cond-mat/0011303 · Physical Review A

Low-lying excitations of a trapped rotating Bose-Einstein condensate

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

Published Apr 18, 2001• 12 citations

arXiv HTML PDF

Abstract

\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.

DOI: 10.1103/physreva.63.055602

Related papers

Weakly interacting Bose-Einstein condensates under rotation

G. M. Kavoulakis, Ben R. Mottelson, C. J. Pethick

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\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.

(|m|=2)

surface modes. For

L/N=1,

a vortexlike state is formed and all the atoms occupy the

m=1

state. For small negative values of $L/N\ensuremath{-}1,$ the states with

m=0

and

m=2

become populated, and for small positive values of $L/N\ensuremath{-}1,$ 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 $L/N\ensuremath{-}1,$ as well as the energy of the low-lying excited states.

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-

N

expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.

N

in the condensate on a low-lying single-particle excitation, which is describable within mean-field theory. Our analysis shows deviations between the many-body and mean-field results which clearly persist when

N

is increased up to the experimentally relevant regime, typically ranging from several thousand up to a million bosons in size. Implications are briefly discussed.

{R}^{6}

, where

R

is the condensate radius measured in units of the oscillator length. The lowest dipole modes are constructed explicitly in the Bogoliubov approximation.