Microscopic origin of quantum supersonic phenomenon in one dimension

Using the Bethe ansatz (BA) solution, we rigorously determine non-equilibrium dynamics of quantum flutter and revival of an injected impurity with a large initial momentum $Q$ into the one-dimensional (1D) interacting bosonic medium. We show that two types of BA excited eigenstates drastically dominate the oscillation nature of the quantum flutter with a periodicity which is simply given by the charge and spin dressed energies $\varepsilon_{\rm c,s}(0)$ at zero quasi-momentum $\tau_{\rm QF} = 2\pi/(|\varepsilon_{\rm c}(0)|- |\varepsilon_{\rm s}(0)|)$. While we also determine quantum revival dynamics with a larger periodicity $\tau_{L} = L/\left(v_{\rm c}(Q-k^*)-v_{\rm s}(k^*)\right)$ than $\tau_{\rm QF}$, revealing the quantum reflection of excitations 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 determined by the rapidity of the impurity. Our results reveals a microscopic origin of quantum supersonic phenomenon and shed light on quantum magnon metrology for a measure of the gravitational force.