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Optics Express

Higher energy collective excitations in trapped Bose condensates

Li You, R. L. Walsworth, William Hoston

Published Nov 10, 1997• 4 citations
Publisher

Abstract

We investigate theoretically the collective excitations of trapped Bose condensates with energies of the order of the chemical potential of the system. For the MIT sodium Bose condensate in a Cloverleaf trap, we find interesting level crossing behavior for high energy excitations and calculate the spatial magnetic dipole moments for selective creation of condensate excitations.

DOI
10.1364/oe.1.000293

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We investigate theoretically the collective excitations of trapped Bose condensates with energies of the order of the chemical potential of the system. For the MIT sodium Bose condensate in a Cloverleaf trap, we find interesting level crossing behavior for high energy excitations and calculate the spatial magnetic dipole moments for selective creation of condensate excitations.
Collective excitations of a dilute Bose condensate have been observed. These excitations are analogous to phonons in superfluid helium. Bose condensates were created by evaporatively cooling magnetically trapped sodium atoms. Excitations were induced by a modulation of the trapping potential, and detected as shape oscillations in the freely expanding condensates. The frequencies of the lowest modes agreed well with theoretical predictions based on mean-field theory. Before the onset of Bose-Einstein condensation, we observed sound waves in a dense ultracold gas.
In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results also apply to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential; these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and one-dimensional traps.
We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground-state density profile of 23{}^{23}23Na atoms and the Bogoliubov spectrum of the elementary excitations as a function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.
Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.
We calculate the angular momentum and energy of a vortex dipole in a trapped atomic Bose-Einstein condensate. Fully analytic expressions are obtained. We apply the results to understand an interesting phenomenon in the MIT group experiment [Raman et al., Phys. Rev. Lett. 87, 210402 (2001)], an excellent agreement is achieved, and further experimental investigation is proposed to confirm this vortex dipole mechanism. We then suggest an effective generation and detection of vortex dipole for experimental realization. Application of the sum rule to calculate collective mode frequency splitting is also discussed.