Light cone dynamics in excitonic states of two-component Bose and Fermi gases

TL;DR

This paper investigates the non-equilibrium light cone dynamics of excitonic states in one-dimensional two-component Bose and Fermi gases, revealing how interactions and excitations influence information propagation.

Contribution

It introduces a method to study large quantum gases with localized excitons by leveraging integrability and superposition of eigenstates, enabling analysis of systems with up to 100 particles.

Findings

Light cone behavior varies with interaction strength and density.

Scaling collapse of light cones observed in both Bose and Fermi gases.

Gapped roton-like excitations in Bose gases lead to secondary light cones.

Abstract

We consider the non-equilibrium dynamics of two-component one dimensional quantum gases in the limit of extreme population imbalance where the minority species has but a single particle. We consider the situation where the gas is prepared in a state with a single spatially localized exciton: the single particle of the minority species is spatially localized while the density of the majority species in the vicinity of the minority particle sees a depression. Remarkably, we are able to consider cases where the gas contains on the order of $N=100$ particles, comparable to that studied in experiments on cold atomic gases. We are able to do by exploiting the integrability of the gas together with the observation that the excitonic state can be constructed through a simple superposition of exact eigenstates of the gas. The number of states in this superposition, rather than being exponentially large in the number of particles, scales linearly with $N$. We study the evolution of such spatially localized states in both strongly interacting Bose and Fermi gases. The behavior of the light cones when the interaction strength and density of the gas is varied can be understood from exact results for the spin excitation spectrum in these systems. We argue that the light cone in both cases exhibits scaling collapse. However unique to the Bose gas, we show that the presence of gapped finite-momentum roton-like excitations provide the Bose gas dynamics with secondary light cones.