  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.
