Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

TL;DR

This study uses diffusion Monte Carlo to analyze Bose-Einstein condensation and natural orbitals of hard core Bosons in traps across various densities, revealing the limits of mean field theories and the transition to liquid-like behavior.

Contribution

It provides a comprehensive quantum Monte Carlo analysis of BEC properties in trapped Bosons over a wide density range, highlighting the limitations of mean field approaches.

Findings

Condensate localization shifts from center to edges with increasing density.

Gross-Pitaevskii theory is accurate at very low densities within 1%.

Mean field theory fails at higher densities, with significant corrections and liquid-like behavior.

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 $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.