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

Abstract

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 in 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 can be expressed in a universal way. Our treatment allows to describe 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. In the realizations of the discussed quench protocol in a cold atom experiment, these different velocities are accessible through different measurement procedures.

51 pages (preprint style), 10 figures; updated version with detailed analysis of the internal dynamics of the profiles emerging after the quench

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• Equilibration in one-dimensional quantum hydrodynamic systems
• Some connections between the Classical Calogero-Moser model and the Log Gas
• Interplay of Solitons and Radiation in One-Dimensional Bose Gases
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Orthogonality catastrophe and fractional exclusion statistics
• From locality to irregularity: Introducing local quenches in massive scalar field theory
• Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions
• Duality in a hyperbolic interaction model integrable even in a strong confinement: Multi-soliton solutions and field theory
• Provable bounds for the Korteweg-de Vries reduction in multi-component Nonlinear Schrodinger Equation