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An exactly solvable model of the BCS-BEC crossover

J. N. Fuchs·A. Recati·W. Zwerger
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Abstract

We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.

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J. N. Fuchs, A. Recati, W. Zwerger. 2004-03-11. An exactly solvable model of the BCS-BEC crossover. https://doi.org/10.1103/physrevlett.93.090408

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