BCS–BEC crossover in one-dimensional integrable model

Jean-Noël Fuchs, RECATI A, W. Zwerger

Zhou Li, Chenyu Xu, Yong-li Ma

We propose an eigenfunction expansion method to solve the integral equations raised by one-dimensional δ-interaction integrable models. Based on this method, the crossover from BCS superfluid of singlet pairs to BEC of molecules is exactly analyzed in both ground and excited states in terms of the momentum distributions. In the exact one-dimensional model, we derive the expressions and calculate the dependence of several physical quantities on the inverse of the dimensionless coupling parameter γ. These physical quantities include the ground state energy, chemical potential, momentum cutoff, charge velocity, excitation energy, excitation momentum, spin gap and spin velocity. Our exact results agree well with previous numerical results. In the practical quasi-one-dimensional model, we apply the method to the ground state and the results give a clear BCS–BEC crossover picture.

Germán Sierra

Jean-Noël Fuchs, Alessio Recati, W. Zwerger

We discuss an integrable model of interacting fermions in one dimension that allows a complete 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 -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau 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.

Zhaochuan Shen

This dissertation presents the theoretical study of two-component fermionic gases. It firstly studies the BCS-BEC crossover for the system of the two-component fermionic gas in optical lattices. If the system were loaded into deep three-dimensional optical lattices, a tight-binding model with the lowest band is applicable. If the band is more than half-filled and by increasing the attractive interactions, then there exists a novel crossover, from a paired BCS superfluid to a BEC of holes, back to the BCS superfluid, and finally to a conventional BEC regime of diatomic molecules. If the band is less than half-filled, the crossover is similar to that without optical lattices. If the band is fully filled, a quantum phase transition from band insulator to BCS-BEC superfluid occurs. Then, this dissertation studies a model describing the one-dimensional Feshbach resonance. Because this model satisfies the Yang-Baxter equations, it was assumed that the Bethe Ansatz could solve this model. However, this dissertation demonstrates that it is not integrable by calculating the chemical potential from the Bethe Ansatz, and by studying the scattering between the bosons. To the researcher's knowledge, this model is the first continuum model that satisfies the Yang-Baxter equations, but is not integrable. After that, this dissertation studies the quenches in the system of paired fermionic superfluids. If the system is slightly driven from its equilibrium state, the asymptotic behaviors of this small oscillation are calculated with both s- and p-wave interactions, and in both the BCS and the BEC regimes, under the mean field collisionless approximation.

Nguyen Dinh Dang, Nguyễn Quang Hưng, Peter Schuck