Bose-Einstein condensation in trapped bosons: A variational Monte Carlo analysis

Abstract

Several properties of trapped hard sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single particle Gaussian and a hard sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard sphere radius and the number of particles. Special attention is given to diagonalizing the one body density matrix and obtaining the corresponding single particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital with highest occupation. The effect of interaction on other quantities such as the ground state energy, the mean radial displacement, and the momentum distribution are calculated as well. Results are compared with Mean Field theory in the dilute limit.

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

“…This appendix discusses the determination of various observables through the Monte Carlo sampling of the wave function ψ tot . Although our approach follows standard procedures [49,69,75], we find it useful to summarize a few key results in this appendix for completeness.…”

“…The density matrices not only lead to a practical route to determine the momentum distributions associated with the spin-up and spin-down atoms, but also serve to quantify the non-local correlations of the system. For example, for trapped single-species Bose gases, an eigen value of the one-body density matrix of the order of 1 signals a large condensate fraction [49,71,73,74]. The situation is different for two-component fermions [72,73].…”

“…In particular, we propose a measure of the molecular condensate fraction and apply it to few-fermion systems with up to N = 6 atoms. Related analyses have previously been pursued for bosonic gases [49][50][51] and one-dimensional systems [52][53][54], but we are not aware of analogous studies for trapped three-dimensional twocomponent Fermi gases.…”

Bose-Einstein condensation of correlated atoms in a trap

“…The atomic density in the trap is n ≃ 10 12 − 10 14 atoms/cm 3 giving an inter-atomic distance l = V A 1/3 ≃ 10 4Å [18]. In this case, the effective atomic size is small compared both to the trap size and to the inter-atomic distance ensuring the diluteness of the gas.…”

“…Seventy years later, in a remarkable experiment, Anderson et al [9] have cooled magnetically trapped 87 Rb gas to nanokelvin temperatures, and observed the BEC. This discovery has generated a huge amount of theoretical investigations [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”