Bethe Ansatz integrable models and cold quantum matter: the atomic Fermi gas
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
The experimental realization of optically confined gases of ultracold atoms has highlighted the physical relevance of Bethe Ansatz integrable models 1. Notable examples include the one-dimensional interacting Bose gas and most recently a pair of coupled one-dimensional condensates of interacting atoms. In this talk I will discuss theoretical results for the 1D two-component interacting Fermi atomic gas with an external field 2. Fermi systems are of particular interest because of the subtle role of pairing between different spin components leading to superfluidity and phase separation. For the integrable model with imbalanced spin populations, the phase diagram, critical fields, magnetization and local pairing correlation have been obtained analytically via the thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H < H_c1$. A completely ferromagnetic phase without pairing occurs when the external field $H > H_c2$. In the region $H_c1 < H < H_c2$ there is a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.\\
1) M.T. Batchelor, Physics Today 60 (2007)\\
2) X.W. Guan, M.T. Batchelor, C. Lee and M. Bortz, Phase Transitions and
Pairing Signature in Strongly Attractive Fermi Atomic Gases, cond-mat/0702191