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.
Categories: cond-mat.quant-gas