Abstract
In this chapter we discuss the BCS–BEC crossover in one-dimensional Fermi gases. We present exact results using the Bethe Ansatz as well as numerical calculations of the correlation functions and the complete phase diagram. In a balanced gas, a continuous crossover occurs from a BCS-type fermionic superfluid to a BEC of pairs that are described by the Lieb-Liniger model. In the case of a finite imbalance, superfluidity persists in the form of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with finite-momentum pairs on the weak coupling side. For strong attractive interactions, it is replaced by a Bose-Fermi mixture. The perspectives to observe an FFLO-state with ultracold fermions in a harmonic trap are discussed.
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Acknowledgments
F.H.-M. and W.Z. acknowledge support from the Deutsche Forschungsgemeinschaft through FOR801. A.E.F. acknowledges support from the NSF through grant DMR-0955707. We thank R. Hulet for very fruitful discussions.
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Feiguin, A.E., Heidrich-Meisner, F., Orso, G., Zwerger, W. (2012). BCS–BEC Crossover and Unconventional Superfluid Order in One Dimension. 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_14
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