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Fermions in Two Dimensions: Scattering and Many-Body Properties

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Abstract

Ultracold atomic Fermi gases in two dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T = 0 ab initio diffusion Monte Carlo calculations. The many-body dynamics are largely dependent on the two-body interactions; therefore, we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then, we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.

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Acknowledgements

The authors would like to thank G. E. Astrakharchik, T. Enss, J. Thywissen, and E. Vitali for helpful discussions. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canada Foundation for Innovation (CFI), the Early Researcher Award (ERA) program of the Ontario Ministry of Research, Innovation and Science, the US Department of Energy, Office of Nuclear Physics, under Contract DE-AC52-06NA25396, and the LANL LDRD program. Computational resources were provided by SHARCNET, NERSC, and Los Alamos Open Supercomputing. The authors would like to acknowledge the ECT* for its warm hospitality during the “Superfluidity and Pairing Phenomena” workshop in March 2017, where part of this work was carried out.

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Authors and Affiliations

  1. Department of Physics, University of Guelph, Guelph, ON, N1G 2W1, Canada

    Alexander Galea, Tash Zielinski & Alexandros Gezerlis

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Stefano Gandolfi

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  1. Alexander Galea
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  2. Tash Zielinski
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  3. Stefano Gandolfi
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  4. Alexandros Gezerlis
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Correspondence to Alexandros Gezerlis.

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Galea, A., Zielinski, T., Gandolfi, S. et al. Fermions in Two Dimensions: Scattering and Many-Body Properties. J Low Temp Phys 189, 451–469 (2017). https://doi.org/10.1007/s10909-017-1803-1

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  • DOI: https://doi.org/10.1007/s10909-017-1803-1

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