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 τQF=2π/[|εc(0)|-|εₛ(0)|], where the charge and spin dressed energies εc,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 τL=L/[vc(Q-k*)-vₛ(k*)] than τQF, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length L, here vc,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.