Variational study of a dilute Bose condensate in a harmonic trap

Abstract

A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting through a repulsive two-body scattering length $a>0$. The dimensionless parameter ${\mathcal{N}}_0\equiv N_{0}a/d_0$ characterizes the effect of the interparticle interactions, with ${\mathcal{N}}_0\ll 1$ for an ideal gas and ${\mathcal{N}}_0\gg 1$ for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of ${\mathcal{N}}_0$, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.

14 pages, RevTeX, submitted to Journal of Low Temperature Physics

References in corpus (4)

• Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas
• Bosons in anisotropic traps: ground state and vortices
• Order Parameter at the Boundary of a Trapped Bose Gas
• Aspect ratio analysis for ground states of bosons in anisotropic traps

Cited by in corpus (21)

• Theory of Bose-Einstein condensation in trapped gases
• Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
• Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate
• Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates
• Quantum Corrections to the Ground State of a Trapped Bose-Einstein Condensate
• Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas
• Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation
• Faraday waves in collisionally inhomogeneous Bose-Einstein condensates
• The inverse problem for the Gross - Pitaevskii equation
• Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms
• A Variational Sum-Rule Approach to Collective Excitations of a Trapped Bose-Einstein Condensate
• Nonlinear dynamics of Bose-condensed gases by means of a low- to high-density variational approach
• Tunnelling induced collapse of an atomic Bose-Einstein condensate in a double-well potential
• Bose-Einstein condensation in variable dimensionality
• Bose-Einstein condensation in harmonic double wells
• Elementary excitations of trapped Bose gas in the large-gas-parameter regime
• On the kinetic energy of unitary Fermi gas in a harmonic trap
• Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates
• Bosonic enhancement of spontaneous emission near an interface
• General energy bounds for systems of bosons with soft cores
• Generalized wave-packet model for studying coherence of matter-wave interferometers