Natural orbitals and Bose-Einstein condensates in traps: A diffusion Monte Carlo analysis

Abstract

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, na 3 < 10 −5 , where n = N/V and a is the hard core diameter, the condensate is localized at the center of the trap. As na 3 increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At na 3 ≤ 10 −4 the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At na 3 ≈ 10 −3 corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At na 3 > ∼ 10 −2 , mean field theory fails. At na 3 > ∼ 0.1, the Bosons behave more like a liquid 4 He droplet than a trapped Boson gas.

Localization of Bose–Einstein Condensation by Disorder

“…At na 3 = 0.09, the condensate is found chiefly outside the trough, on each side of the trough where the number density is lower. Similarly for alkali gases in harmonic traps at high density (high na 3 ), the condensate is found at the edges of the trap where boson density is lowest 16,17 . This is also similar to helium droplets where the condensate fraction is large at the surface of the droplet where the density is low.…”

“…As na 3 increases, f 0 decreases, especially for na 3 ≥ 0.1. In non-uniform systems, f 0 is low in regions of large attractive external potential where the density na 3 is high 16,17 . In an otherwise uniform cell we have introduced an attractive potential trough which separates the cell into two parts.…”

Bose-Einstein-condensed gases with arbitrary strong interactions

“…For this region of γ, our n 0 is in good agreement with the Monte Carlo calculations. Monte Carlo techniques have also been used for studying the condensate fraction of trapped atoms [37][38][39]. But the latter results cannot be directly compared with n 0 in a homogeneous gas, since in traps, the condensate fraction is a function of spatial variables as well as of the trap shape [37][38][39][40][41].…”

Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

“…, N − 1, all other occupations being zero [13,14,23]. Although natural orbitals are much-used in quantum chemistry, the first application to degenerate gases is due to Dubois and Glyde [30].…”