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arXiv:1909.03578 · Physical Review A

Role of the confinement-induced effective range in the thermodynamics of a strongly correlated Fermi gas in two dimensions

Brendan C. Mulkerin, Hui Hu, Xia-Ji Liu

Published Jan 8, 2020• 7 citations
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Abstract

We theoretically investigate the thermodynamic properties of a strongly correlated two-dimensional Fermi gas with a confinement-induced negative effective range of interactions, which is described by a two-channel model Hamiltonian. By extending the many-body $T$-matrix approach by Nozi\`eres and Schmitt-Rink to the two-channel model, we calculate the equation of state in the normal phase and present several thermodynamic quantities as functions of temperature, interaction strength, and effective range. We find that there is a nontrivial dependence of thermodynamics on the effective range. In the experiment, where the effective range is set by the tight axial confinement, the contribution of the effective range becomes nonnegligible as the temperature decreases down to the degenerate temperature. We compare our finite-range results with recent measurements on the density equation of state, and show that the effective range has to be taken into account for the purpose of a quantitative understanding of the experimental data.

DOI
10.1103/physreva.101.013605

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We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its zero-temperature equation of state and breathing mode frequency based on existing auxiliary-field quantum Monte Carlo data. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, to quantitatively explain recent experimental measurements with ultracold 2D fermions. We resolve in a satisfactory way the puzzling experimental observations of the smaller than expected equations of state and breathing mode frequency. Our establishment of the minimal model for 2D fermions is crucial to understand the Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.
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We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using the fixed-node diffusion Monte Carlo method, we calculate the equation of state and density profiles for the full fermionic system, which allows us to address the importance of finite-range corrections arising from the internal fermionic structure of the dimers. We interpret the results in terms of a molecular Bose gas in quasi-two-dimensional confinement and compare them with theoretical predictions for a weakly interacting two-dimensional Bose gas, identifying the range of validity of mean-field and beyond-mean-field descriptions. We also develop an analytical theory for the transverse density profile, capturing its broadening with increasing interaction strength. This work provides a benchmark for an effective bosonic description of strongly bound fermionic dimers and offers insights into confinement-induced dimensional effects.