Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench

TL;DR

This paper demonstrates that a local quench in a quantum system can create a unique GGE deviation causing negative absorption, which can be detected through optical measurements, revealing non-equilibrium quantum states.

Contribution

It identifies a specific GGE deviation caused by a local potential quench that results in negative absorption, linking theoretical predictions with observable optical effects.

Findings

GGE deviation can produce negative absorption peaks.

A local attractive potential induces a bound state below the continuum.

Negative absorption signals GGE presence in fermionic systems.

Abstract

When a parameter quench is performed in an isolated quantum system with a complete set of constants of motion, its out of equilibrium dynamics is considered to be well captured by the Generalized Gibbs Ensemble (GGE), characterized by a set $\{\lambda_\alpha\}$ of coefficients related to the constants of motion. We determine the most elementary GGE deviation from the equilibrium distribution that leads to detectable effects. By quenching a suitable local attractive potential in a one-dimensional electron system, the resulting GGE differs from equilibrium by only one single $\lambda_{\alpha}$, corresponding to the emergence of an only partially occupied bound state lying below a fully occupied continuum of states. The effect is shown to induce optical gain, i.e., a negative peak in the absorption spectrum, indicating the stimulated emission of radiation, enabling one to identify GGE signatures in fermionic systems through optical measurements. We discuss the implementation in realistic setups.