Journal
NEW JOURNAL OF PHYSICS
Volume 22, Issue 6, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/ab91fb
Keywords
quantum gases; bubble trap; curved manifolds
Categories
Funding
- CAPES (CoordenacAo de Aperfeicoamento de Pessoal de Nivel Superior, Improvement Coordination of Higher Level Personnel) [488/2018, 88881.143936/2017-01]
- DAAD (Deutscher Akademischer Austauschdienst, German Academic Exchange Service) [488/2018, 88881.143936/2017-01]
- CAPES-Brazilian Federal Agency for Support and Evaluation of Graduate Education within the Ministry of Education of Brazil
- CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, National Council for Scientific and Technological Development) [305586/2017-3]
- CEPID / CEPOF-FAPESP programme [2013/07276-1]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via the Collaborative Research Centres SFB/TR185 [277625399]
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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.
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