PATH INTEGRAL MONTE CARLO STUDIES OF ULTRACOLD FEW-ATOM SYSTEMS

Yangqian Yan

Motivated by the fact that ultracold atomic systems can nowadays be realized exper- imentally with varying number of particles, this thesis explores the transition from few- to many-body physics in ultracold matter via the path-integral Monte Carlo (PIMC) technique. The PIMC approach, which accounts for the particle statistics and yields thermodynamic observables, can be applied to both small and large systems. We determine the energy, Tan’s contact, various structural properties, the super- fluid fraction and density, and the condensate fraction of small harmonically trapped bosonic and fermionic systems as functions of the temperature and s-wave scattering length. We find that the superfluid fraction of fermions is negative for certain parameter combinations and develop a microscopic understanding of this, at first sight, surprising behavior. We further illustrate that the superfluid fraction and condensate fraction are distinct quantities by performing finite temperature two-body calculations. A simple model that can be used to extract the ground state energy of N-boson droplets from finite temperature calculations is proposed. This approach, combined with a novel two-body zero-range propagator, is used to explore the generalized Efimov scenario at unitarity. For three bosons, Efimov predicted the existence of an infinite series of geometrically spaced bound states. Whether the N-boson energy is fully determined by three-body physics or dependent on higher-body properties has long been debated in the literature. We find that the N-body ground state energies display a notable model-dependence, suggesting that corrections to Efimov universality become increasingly more important with increasing N. For van der Waals systems, a weaker universality is found. The equation of state (EOS) of spin-balanced equal-mass two-component Fermi gases at unitarity has been determined in cold atom experiments. At high temperature or low density, the virial expansion provides a good description of the EOS. While the second- and third-order virial coefficients have been calculated theoretically and veri- fied experimentally, theory and experiment do not yet agree on the fourth-order virial coefficient. Our ab initio determination of the fourth-order virial coefficient agrees with experiments, thereby settling an ongoing debate in the literature.

PATH INTEGRAL MONTE CARLO STUDIES OF ULTRACOLD FEW-ATOM SYSTEMS

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