Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases

We discuss the hydrodynamic approach to the study of the time evolution-induced by a quench-of local excitations in one dimension. We focus on interaction quenches: the considered protocol consists of creating a stable localized excitation propagating through the system, and then operating a sudden change of the interaction between the particles. To highlight the effect of the quench, we take the initial excitation to be a soliton. The quench splits the excitation into two packets moving in opposite directions, whose characteristics for short times can be expressed in a universal way. Our treatment allows for the description of the internal dynamics of these two packets in terms of the different velocities of their components. We confirm our analytical predictions through numerical simulations performed with the Gross-Pitaevskii equation and with the Calogero model (as an example of long range interactions and solvable with a parabolic confinement). Through the Calogero model we also discuss the effect of an external trapping on the protocol. The hydrodynamic approach shows that there is a difference between the bulk velocities of the propagating packets and the velocities of their peaks: it is possible to discriminate the two quantities, as we show through the comparison between numerical simulations and analytical estimates. We show that our analytical results capture with remarkable precision the findings of the numerical simulations also for intermediate times and we provide predictions for the time at which the two packets becomes distinguishable. In the realizations of the discussed quench protocol in a cold atom experiment, these different velocities are accessible through different measurement procedures.