Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics

Abstract

While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wave length is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal to noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a non-interacting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase transition like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.

17 pages, 12 figures

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Observation of Bose-Einstein Condensation of Molecules
• Finite Temperature Models of Bose-Einstein Condensation
• Structure, superfluidity, and quantum melting of hydrogen clusters
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Local Superfluidity of Parahydrogen Clusters
• Monte Carlo Simulations of the Unitary Bose Gas
• Persistent currents in one dimension: the other side of Leggett's theorem
• Occupation numbers of the harmonically trapped few-boson system
• Superfluid-Insulator and Roughening Transitions in Domain Walls

Cited by in corpus (3)

• Pairing in a system of a few attractive fermions in a harmonic trap
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Liquid-solid transitions in the three-body hard-core model