Lowest-Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r(2) = x(2) + y(2), multiplied by an analytic function P(z) of the single complex variable z = x + iy; the zeros of P (z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega(x)/omega(y) <= 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta proportional to x+i beta_y and 0 <=beta_<= 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.