Bose and Fermi Systems

Piotr Garbaczewski

Recently an exact spectral solution was constructed by Sudarshan and Tata for the (NΘ) Fermi version of the Lee model. We demonstrate that it provides a partial solution for the related pure Bose spectral problems. Moreover, the (NΘ) Bose (Bolsterli–Nelson) version of the Lee model is shown to possess Fermi partners, both exhibiting the partial solubility interplay: finding solutions in the Fermi case would presumably be easier than in the original Bose model. Fermi states of the underlying Bose systems in three space dimensions are explicitly identified.

M. Iskin, C. A. R. Sá de Melo

The ground-state phase diagram of Fermi-Fermi mixtures in optical lattices is analyzed as a function of interaction strength, population imbalance, filling fraction, and tunneling parameters. It is shown that population imbalanced Fermi-Fermi mixtures reduce to strongly interacting Bose-Fermi mixtures in the molecular limit, in sharp contrast to homogeneous or harmonically trapped systems, where the resulting Bose-Fermi mixture is weakly interacting. Furthermore, insulating phases are found in optical lattices of Fermi-Fermi mixtures in addition to the standard phase-separated or coexisting superfluid--excess-fermion phases found in homogeneous systems. The insulating states can be a molecular Bose-Mott insulator (BMI), a Fermi-Pauli insulator (FPI), a phase-separated BMI-FPI mixture, or a Bose-Fermi checkerboard.

T. Suzuki

We study the role of the Bose–Fermi (BF) pair correlations in the cold BF-mixture of atomic gases. After summarizing the previous results on the formation of composite BF-pairs in the uniform BF mixture, we present an exactly solvable model where bosons and fermions are distributed over finite number of orbits and interact via attractive pairing-type interaction. We show that, as the interaction strength increases, BF pairs with different quantum numbers are gradually created in the ground state through a series of level crossings, until finally the system becomes a Fermi sea of BF-pairs.

Willi-Hans Steeb, Yorick Hardy