Microscopic origin of quantum supersonic phenomenon in one dimension

TL;DR

This paper uses Bethe ansatz to analyze the non-equilibrium dynamics of a high-momentum impurity in a 1D bosonic medium, revealing quantum flutter oscillations, revival phenomena, and potential applications in gravity measurement.

Contribution

It provides a rigorous analytical framework for impurity dynamics in 1D systems, linking quantum flutter to magnon and exciton states, and explores quantum reflection effects and practical measurement applications.

Findings

Quantum flutter periodicity determined by charge and spin energies.

Persistent revival dynamics due to boundary conditions.

Impurity as a quantum resource for gravitational force measurement.

Abstract

Using the Bethe ansatz (BA), we rigorously obtain non-equilibrium dynamics of an impurity with a large initial momentum $Q$ in the one-dimensional (1D) interacting bosonic medium. We show that magnon and exciton-like states obtained from the BA equations drastically determine the oscillation nature of the quantum flutter with the periodicity given by $\tau_{\rm QF} = 2\pi/(|\varepsilon_{\rm c}(0)|- |\varepsilon_{\rm s}(0)|)$. Where the charge and spin dressed energies $\varepsilon_{\rm c,s}(0)$ are precisely given by the thermodynamical BA equations. While we further find a persistent revival dynamics of the impurity with a larger periodicity $\tau_{L} = L/\left(v_{\rm c}(Q-k^*)-v_{\rm s}(k^*)\right)$ than $\tau_{\rm QF}$, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length $L$, here $v_{\rm c,s}$ are the sound velocities of charge and spin excitations, respectively, and $k^*$ is a characteristic momentum of the impurity to the Fermi point. Finally, we study the application of such a magnon impurity as a quantum resource for measuring the gravitational force.