Bose-Einstein condensation on curved manifolds
Open Access
- 1 June 2020
- journal article
- research article
- Published by IOP Publishing in New Journal of Physics
- Vol. 22 (6), 063059
- https://doi.org/10.1088/1367-2630/ab91fb
Abstract
Here we describe a weakly interacting Bose gas on a curved smooth manifold, which is embedded in the three-dimensional Euclidean space. To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the three-dimensional Bose gas in the vicinity of its surface. Following the notion of dimensional reduction as outlined in [L Salasnichet al, Phys. Rev. A65, 043614 (2002)], we assume a large enough trap frequency so that the normal degree of freedom of the condensate wave function can be approximately integrated out. In this way we obtain an effective condensate wave function on the quasi-two-dimensional surface of the curved manifold, where the thickness of the cloud is determined self-consistently. For the particular case when the manifold is a sphere, our equilibrium results show how the chemical potential and the thickness of the cloud increase with the interaction strength. Furthermore, we determine within a linear stability analysis the low-lying collective excitations together with their eigenfrequencies, which turn out to reveal an instability for attractive interactions.Funding Information
- Fundação de Amparo à Pesquisa do Estado de São Paulo (2013/07276-1)
- Deutsche Forschungsgemeinschaft (277625399)
- Deutscher Akademischer Austauschdienst (88881.143936/2017-01)
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (88881.143936/2017-01)
- Conselho Nacional de Desenvolvimento Científico e Tecnológico (305586/2017-3)
This publication has 33 references indexed in Scilit:
- Bose-Einstein Condensation in MicrogravityScience, 2010
- Emergence of Turbulence in an Oscillating Bose-Einstein CondensatePhysical Review Letters, 2009
- Dynamics of condensate shells: Collective modes and expansionPhysical Review A, 2007
- Ultracold atoms confined in rf-induced two-dimensional trapping potentialsEurophysics Letters, 2004
- Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentialsPhysical Review A, 2004
- Two-Dimensional Atom Trapping in Field-Induced Adiabatic PotentialsPhysical Review Letters, 2001
- Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equationsPhysical Review A, 1997
- Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational AnalysisPhysical Review Letters, 1996
- Theory of vortices and monopoles on a spherePhysical Review D, 1991
- On the Third Fundamental Form of a SurfaceAmerican Journal of Mathematics, 1953