Solution of the BEC to BCS Quench in One Dimension

TL;DR

This paper analyzes the non-equilibrium dynamics of a one-dimensional fermionic gas undergoing a sudden BEC-to-BCS coupling quench, revealing an exactly solvable stationary state characterized by bound states and unusual correlation properties.

Contribution

It introduces an exact solution for the stationary state after a BEC-BCS quench in a 1D fermionic system using the Quench Action approach, extending solvable quench models.

Findings

Stationary state dominated by two-particle bound states at strong interactions

Bound state formation inhibited at higher BEC densities

Quasiparticle distribution shows quartic decay, indicating Tan's contact violation

Abstract

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly-bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average inter-particle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the Quench Action approach. We provide an experimentally-accessible characterisation of the stationary state by computing local pair correlation function as well as the quasi-particle distribution functions. We find that the steady state is increasingly dominated by two particle spin singlet bound states for stronger interaction strength but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power law decay suggesting a violation of Tan's contact relations.