Microscopic origin of the quantum supersonic phenomenon in one dimension

Using the Bethe ansatz (BA), we rigorously obtain nonequilibrium dynamics of an impurity with a large initial momentum $Q$ in the one-dimensional interacting bosonic medium. We show that magnonlike and excitonlike states obtained from the BA equations drastically determine the oscillation nature of the quantum flutter with the periodicity given by ${\tau }_{\mathrm{QF}}=2\pi /\left[\right|{\varepsilon }_c\left(0\right)|-|{\varepsilon }_s\left(0\right)\left|\right]$, where the charge and spin dressed energies ${\varepsilon }_{c,s}\left(0\right)$ are precisely given by the thermodynamical BA equations. While we further find a persistent revival dynamics of the impurity with a larger periodicity ${\tau }_L=L/[v_c(Q-k^{*})-v_s\left(k^{*}\right)]$ than ${\tau }_{\mathrm{QF}}$, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length $L$, here $v_{c,s}$ 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.