Functional renormalization for the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover

Area of Science:

• Quantum physics
• Condensed matter physics
• Ultracold atomic gases

Background:

• The Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover describes the transition between fermionic superfluidity and bosonic condensation.
• Ultracold atomic gases provide a tunable platform to study quantum phenomena like the BCS-BEC crossover.

Purpose of the Study:

• To review the functional renormalization group (RG) approach for investigating the BCS-BEC crossover in ultracold fermionic gases.
• To highlight the non-perturbative capabilities of functional RG in describing the crossover physics.

Main Methods:

• The study focuses on the functional renormalization group (RG) method, formulated with a scale-dependent effective action.
• A systematic derivative expansion is employed to analyze the many-body and few-body physics.

Main Results:

• The functional RG approach provides a continuous interpolation between atomic/molecular microphysics and macroscopic physics.
• The method accurately describes the phase diagram as a function of scattering length and temperature.
• It captures both universal features of many-body physics and accurate accounts of few-body physics in the BEC and BCS limits.

Conclusions:

• The functional RG is a powerful, non-perturbative tool for studying the BCS-BEC crossover in ultracold atomic gases.
• This approach offers a unified description of the crossover phenomena across various scales and physical regimes.