Contact intensity and extended hydrodynamics in the BCS-BEC crossover

TL;DR

This paper investigates the contact intensity in the BCS-BEC crossover of a superfluid Fermi gas and introduces an extended hydrodynamics framework to analyze collective excitations and response functions.

Contribution

It provides a comprehensive calculation of contact intensity across the crossover and develops an extended hydrodynamics theory linked to conformal invariance.

Findings

Calculated contact $C$ in the full BCS-BEC crossover.

Derived analytical formulas for $C$ in harmonic traps.

Analyzed nonlinear sound waves and response functions using extended hydrodynamics.

Abstract

In the first part of this chapter we analyze the contact intensity $C$, which has been introduced by Tan [Ann. Phys. 323, 2952 (2008)] and appears in several physical observables of the strongly correlated two-component Fermi gas. We calculate the contact $C$ in the full BCS-BEC crossover for a uniform superfluid Fermi gas by using an efficient parametetrization of the ground-state energy. In the case of harmonic confinement, within the Thomas-Fermi approximation, we derive analytical formulas of $C$ in the three relevant limits of the crossover. In the second part of this chapter we discuss the extended superfluid hydrodynamics we have recently proposed to describe static and dynamical collective properties of the Fermi gas in the BCS-BEC crossover. In particular we show the relation with the effective theory for the Goldstone field derived by Son and Wingate [Ann. Phys. 321, 197 (2006)] on the basis of conformal invariance. By using our equations of extended hydrodynamics we determine nonlinear sound waves, static response function and structure factor of a generic superfluid at zero temperature.