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The BCS–BEC Crossover and the Unitary Fermi Gas

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The BCS-BEC Crossover and the Unitary Fermi Gas

Part of the book series: Lecture Notes in Physics ((LNP,volume 836))

Abstract

There has been great excitement about the recent experimental and theoretical progress in elucidating the Bardeen-Cooper-Schrieffer (BCS) to Bose Einstein condensation (BEC) crossover in ultracold Fermi gases. Prior to these cold atom experiments, all known, and reasonably well understood, superconductors and superfluids were firmly in one of the two limits. Either they were well described by the celebrated BCS theory of pairing in Fermi systems, or they could be understood in terms of the BEC of bosons, with repulsive interactions. For the first time, the ultracold Fermi gases exhibited behavior that, with the turn of a knob, could be made to span the entire range from BCS to BEC. While such a crossover had been theoretically predicted, its actual realization in the laboratory was a major advance [1, 2], and led to intense investigation of the properties of the very strongly interacting, unitary regime that lies right in the middle of the crossover. We now understand that the unitary Fermi gas has remarkable universal properties, arising from scale invariance, and has connections with fields as diverse as nuclear physics and string theory.

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Notes

  1. 1.

    Within meanfield theory, this occurs when the chemical potential reaches zero. More precise calculations, however, show that the critical coupling strength \(1/(k_Fa)\,{\simeq}\, 0.8\) beyond which fermionic excitations have their minimum at zero momentum appears at \(\mu\,{\,{\simeq}\,}\, -0.54\varepsilon_{\it F}\) [16].

  2. 2.

    A similar result is obtained also in one dimension [30] not, however, in two dimensions, where the repulsive interaction between strongly bound dimers stays finite in the BEC-limit [27, 31].

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Acknowledgments

M.R. would like to thank the US National Science Foundation (NSF-DMR 0706203) and the US Army Research Office (ARO W911NF- 08-1-0338) for support. W.Z. acknowledges support from the Deutsche Forschungsgemeinschaft through FOR801.

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Authors and Affiliations

  1. Department of Physics, Ohio State University, Columbus, OH, 43210, USA

    M. Randeria

  2. Physik Department, Technische Universität München, D-85747, Garching, Germany

    W. Zwerger

  3. Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, MIT, Cambridge, MA, 02139, USA

    M. Zwierlein

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  1. M. Randeria
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  2. W. Zwerger
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  3. M. Zwierlein
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Correspondence to M. Randeria .

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  1. Fakultät für Physik, Physik-Department, Technische Universität München, James-Franck-Straße, Garching, 85747, Germany

    Wilhelm Zwerger

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Randeria, M., Zwerger, W., Zwierlein, M. (2012). The BCS–BEC Crossover and the Unitary Fermi Gas. In: Zwerger, W. (eds) The BCS-BEC Crossover and the Unitary Fermi Gas. Lecture Notes in Physics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21978-8_1

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