BCS-BEC crossover and unconventional superfluid Order in one dimension

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. © 2012 Springer-Verlag Berlin Heidelberg.