Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis

Víctor M. Pérez-García; H. Michinel; J. I. Cirac; M. Lewenstein; P. Zoller

doi:10.1103/PhysRevLett.77.5320

Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis

Víctor M. Pérez-García, H. Michinel, J. I. Cirac, M. Lewenstein, and P. Zoller

Phys. Rev. Lett. 77, 5320 – Published 30 December 1996

Abstract

We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein condensate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large particle numbers, and agree exactly with the Stringari results in the strong interaction limit. Excellent agreement is obtained with the recent JILA experiment and predictions for the negative scattering length case are also made.

Received 18 July 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.5320

Authors & Affiliations

Víctor M. Pérez-García¹, H. Michinel², J. I. Cirac³, M. Lewenstein⁴, and P. Zoller⁵

¹Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
²Departamento de Física Aplicada, E. U. Óptica e Optometría, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
³Departamento de Física Aplicada, Facultad de CC. Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
⁴Comissariat a l'Energie Atomique, DSM/DRECAM/SPAM, Centre d'Etudes de Saclay, 91191 Gif-sur-Yvette, France
⁵Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria