Bose-Einstein condensate in a rapidly rotating nonsymmetric trap
- Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305-4045 (United States)
A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function {psi}(x,y) is a Gaussian {proportional_to}exp(-r{sup 2}/2), multiplied by an analytic function f(z) of the complex variable z=x+iy. The criterion for a quantum phase transition to a non-superfluid correlated many-body state is usually expressed in terms of the ratio of the number of particles to the number of vortices. Here a similar description applies to a rapidly rotating nonsymmetric two-dimensional trap with arbitrary quadratic anisotropy ({omega}{sub x}{sup 2}<{omega}{sub y}{sup 2}). The corresponding condensate wave function {psi}(x,y) is a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function f(z), where z=x+i{beta}{sub -}y is a stretched complex variable and 0{<=}{beta}{sub -{<=}}1 is a real parameter that depends on the trap anisotropy and the rotation frequency. Both in the mean-field Thomas-Fermi approximation and in the mean-field lowest Landau level approximation with many visible vortices, an anisotropic parabolic density profile minimizes the energy. An elongated condensate grows along the soft trap direction yet ultimately shrinks along the tight trap direction. The criterion for the quantum phase transition to a correlated state is generalized (1) in terms of N/L{sub z}, which suggests that a nonsymmetric trap should make it easier to observe this transition, or (2) in terms of a 'fragmented' correlated state, which suggests that a nonsymmetric trap should make it harder to observe this transition. An alternative scenario involves a crossover to a quasi one-dimensional condensate without visible vortices, as suggested by Aftalion et al., Phys. Rev. A 79, 011603(R) (2009).
- OSTI ID:
- 21408477
- Journal Information:
- Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.033620; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTIC FUNCTIONS
ANISOTROPY
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
COMPLEXES
CONDENSATES
MEAN-FIELD THEORY
PHASE TRANSFORMATIONS
THOMAS-FERMI MODEL
TRAPS
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
ATOMIC MODELS
CALCULATION METHODS
FUNCTIONS
MATHEMATICAL MODELS