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 ₐ₅=2/|₂ (0) |-|ₒ (0) |, where the charge and spin dressed energies ₂, ₒ (0) are precisely given by the thermodynamical BA equations. While we further find a persistent revival dynamics of the impurity with a larger periodicity ₋=L/v₂ (Q-k^*) -vₒ (k^*) than ₐ₅, manifesting a quantum reflection induced by the periodic boundary conditions of a finite length L, here v₂, ₒ 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.