Nambu-Goldstone mode in a rotating dilute Bose-Einstein condensate

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Masahito Ueda¹ and Tatsuya Nakajima²
¹Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan and ERATO, Japan Science and Technology Corporation (JST), Saitama 332-0012, Japan
²Physics Department, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan

Received 14 November 2003; revised 28 December 2005; published 7 April 2006

TheNambu-Goldstone mode (NGM), associated with vortex nucleation in a harmonicallyconfined, two-dimensional dilute Bose-Einstein condensate is studied. We argue, basedon exact diagonalization calculations, that the NGM manifests in thelowest-lying envelope of the quasidegenerate spectrum that emerges as thevortex is about to enter the condensate. The quasidegenerate statesconstitute a series of octupole-mode branches that originate primarily frompairwise repulsive interactions between octupole excitations and are distinguished bythe number of admixed quadrupolar excitations. As the vortex approachesthe center of the condensate and the system's axisymmetry isrestored, the NGM becomes massive due to its coupling tohigher rotational bands. We clarify the mechanism of this massacquisition by using a newly developed projection-operator method.

URL:	http://link.aps.org/doi/10.1103/PhysRevA.73.043603
DOI:	10.1103/PhysRevA.73.043603
PACS:	03.75.Kk; 05.30.Jp; 67.40.Db 03.75.Kk Dynamic properties of Bose-Einstein condensates; collective and hydrodynamic excitations, superfluid flow 05.30.Jp Boson systems (quantum statistical mechanics) 67.40.Db Quantum statistical theory; ground state, elementary excitations (liquid ⁴He) YEAR: 2006
KEYWORDS:	Bose-Einstein condensation, vortices, nucleation

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In a previous paper [T. Nakajima and M. Ueda, Phys. Rev. Lett. 91, 140401 (2003)], we reported the results of similar exact diagonalization calculations for N=25. However, this size is too small to reveal the structure of a quasi-degenerate spectrum on the order of g, and thus we could not distinguish the NGM from the yrast line. However, if we restrict L to LN, we can perform exact diagonalization calculations for a much larger N, say, N=10 000, though we are then not able to cover L up to L/N~0.1, which is necessary to investigate how the NGM becomes massive with increasing L.
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