The Boson-Fermion correspondence

M. Iskin, C. A. R. Sá de Melo

The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.

V. A. Yatsun

J. Sakamoto, Y. Heike

We study a massive Thirring-like model in 2-dimensional space-time, which contains two different species of fermions. This model is a field theoretical version of the quantum mechanical model originally proposed by Glöckle, Nogami and Fukui, where different fermions interact with each other through δ-function potentials. We derive a corresponding boson model by the bosonization technique in the path integral formulation. This is a simple but non-trivial extension of the freedom of the bosonization technique. Operator correspondences between fermion and boson fields are given. One of these could not be realistically expected from the naive correspondence of the original single-species models. It is essential for this point that in our model fermions of the same kind do not interact with each other directly. We find that for a specific value of the coupling constant, one boson field becomes free while the other is a Sine-Gordon field. For this case, therefore, our two-species model is equivalent to the ordinary Sine-Gordon model of a single boson field.

Michelangelo Sambataro

The correspondence between the $\mathrm{SD}$ fermion and $\mathrm{sd}$ boson spaces is studied. A procedure is discussed to derive boson images of fermion operators. Spectra in the two spaces are compared. $E2$ operators are also studied.

Arnout Jozef Ceulemans