Quenched solitons and shock waves in Bose-Einstein condensates

Abstract

The Bose-Einstein condensate (BEC) formed by ultracold atomic gases provides an ideal platform for studying various quantum phenomena. In this platform, researchers have explored in depth the important equilibrium and steady phenomena including superfluidity, vortices, and solitons, and recently started to study nonequilibrium problems. In a classical system, nonequilibrium problems, such as explosion, usually occur together with shock waves, which is presented when the explosion speed is larger than the local sound speed. For BEC systems which possess quantum properties, how to produce and understand the shock waves becomes a hot research topic. In this work, we systematically discuss the possibility of quantum shock wave and its essential mechanism in a one-dimensional BEC initially containing dark solitons through quenching interactions. When the system is quenched to the limit of non-interaction, we analytically obtain the post-quench dynamics of initially immobile dark solitons, and find the existence of shock wave, which can be explained through the quantum interference effect. When the system is quenched to finite interaction, we find similar phenomena through numerically solving the Gross-Pitaevskii equation, and analyze different situations. When the system is quenched to a finite weaker interaction, the situation is similar to a non-interaction case; when the system is quenched to a stronger interaction, the shock wave is accompanied by the splitting of the initial soliton, and the two objects can synchronously change; specifically when the quenched ratio of strength is an integer squared, the shock wave disappears, and the soliton is split perfectly. We further explore the properties of the shock wave including its amplitude and speed, and obtain the full scenario as the quenched interaction varies. This work provides theoretical guidance for realizing and measuring shock wave in experiment.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose–Einstein condensate

“…While for a 1D BEC in a box trap under the same quench, n−1 grey solitons at each edge can be excited and further move away from the edges, if η ≡ n is an integer. [20] In both situations, if η is not an integer, there will be extra excitations [20][21][22] while the number of excited solitons is the same as that of taking the ceiling of η, i.e., n = η . For a 2D BEC, we find that the condition of the number of excited RDSs is different from that in a 1D BEC.…”

“…The outcome of the interaction quench may be either solitons or Bogoliubov modes, and even shock waves. [21] Specifically, by setting the ratio of the after-and before-quench interaction strength as η 2 , Halperin et al found that, if η is an integer, an initial half black soliton localized at an edge of a box trap will decay into η − 1 moving grey solitons without other excitation. Such a method possesses a solid foundation elaborated by the inverse scattering theory.…”

Generation and modulation of shock waves in two-dimensional polariton condensates

“…8c®3 lfN [32] !1AE [33] !YÅ [34] !p íN [35] ! BEC [36] õ ‡Ôn+•uyÀÂÅ, ¿òÙA^ š [37,38] !ó § [39−42] ! )Ô‰AE +•.…”