Bose-Einstein condensation on curved manifolds

• Published in: New journal of physics Vol. 22; no. 6; pp. 63059 - 63081
• Main Authors: Móller, Natália S, dos Santos, F Ednilson A, Bagnato, Vanderlei S, Pelster, Axel
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2020
• Subjects: bubble trap; Chemical potential; Condensates; curved manifolds; Euclidean geometry; Euclidean space; Manifolds (mathematics); Physics; quantum gases; Resonant frequencies; Stability analysis; Thickness; Wave functions
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ab91fb

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 Salasnich et al, Phys. Rev. A 65, 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.