Crossover from adiabatic to sudden interaction quench in a Luttinger liquid

TL;DR

This paper investigates how Luttinger liquids transition from adiabatic to sudden interaction quenches, revealing different regimes in fermionic properties and providing insights relevant for cold atom experiments.

Contribution

It introduces a comprehensive analysis of interaction quenches in Luttinger liquids, identifying distinct regimes and their signatures in fermionic correlations and momentum distributions.

Findings

Identification of multiple regimes: Fermi liquid, sudden quench LL, adiabatic LL, and time-dependent exponent LL.

Observation that these regimes can be distinguished through fermionic momentum distributions.

Results applicable to arbitrary quench protocols, aiding experimental analysis.

Abstract

Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LL), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regimes, and a LL regime with time dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.