Exactly solvable model of the BCS-BEC crossover

Area of Science:

• Condensed Matter Physics
• Quantum Gases
• Many-Body Physics

Background:

• Superfluidity in one dimension is complex, with distinct Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes.
• Bridging these regimes requires models that capture the transition from fermionic to bosonic behavior.

Purpose of the Study:

• To introduce and analyze an integrable model describing the complete crossover from BCS-like to Bose-like superfluidity in one-dimensional interacting fermions.
• To establish a theoretical framework connecting the Gaudin-Yang model (attractive fermions) and the Lieb-Liniger model (repulsive bosons).

Main Methods:

• Utilizing a geometric resonance in the one-dimensional scattering length to tune the system across the BCS-BEC crossover.
• Investigating the evolution of the inverse coupling constant from -infinity to +infinity.
• Analyzing ground state energy, elementary density and spin excitations, and correlation functions.

Main Results:

• The model successfully describes the continuous evolution from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers.
• Key thermodynamic and dynamic properties were studied across the crossover.
• The theoretical framework provides a complete description of the superfluid crossover.

Conclusions:

• The proposed integrable model offers a powerful tool for understanding one-dimensional quantum gases and their phase transitions.
• Experimental realization with cold atoms is feasible, providing a platform to explore this fundamental quantum phenomenon.
• This work unifies distinct models of interacting quantum systems in one dimension.