Parametric instability in periodically driven Luttinger liquids

TL;DR

This paper investigates how periodic modulation of interactions in a Luttinger liquid causes parametric instabilities, leading to exponential density perturbation growth and distinctive momentum distribution features, with implications for driven quantum systems.

Contribution

It reveals the universal development of parametric resonance instabilities in periodically driven Luttinger liquids and identifies long-lived metastable states at specific driving regimes.

Findings

Instability causes exponential amplification of density perturbations.

Momentum distribution forms a terrace structure due to absorption of driving quanta.

Long-lived metastable states occur at slow and fast driving regimes.

Abstract

We analyze the properties of a Luttinger liquid under the influence of a periodic driving of the interaction strength. Irrespective of the details the driven system develops an instability due to a parametric resonance. For slow and fast driving, however, we identify intermediate long-lived meta-stable states at constant time-averaged internal energies. Due to the instability perturbations in the fermionic density are amplified exponentially leading to the buildup of a superlattice. The momentum distribution develops a terrace structure due to scattering processes that can be associated with the absorption of quanta of the driving frequency.