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arXiv:1607.08760 · SciPost Physics

Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

T. Congy, A. M. Kamchatnov, Nicolas Pavloff

Published Oct 25, 2016• 38 citations
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Abstract

We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context.

DOI
10.21468/scipostphys.1.1.006

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We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context.
Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.
Periodic waves in a two-component Bose-Einstein condensate are considered with allowance for mixing of components admitted by the interaction between atoms. The possibility of relative motion of the components leads to significant variability of the system dynamics as compared to the case of a single-component condensate. In particular, it was experimentally established that, if one component flows relative to another, waves with counterphase oscillations of the components can be excited in the two-component condensate. A theory of one-phase periodic waves is developed for the case of weak mixing of the components, in which the condensate dynamics is described with sufficiently good precision by a system of Gross-Pitaevskii equations with equal constants of nonlinear interaction between atoms both of the same and different kinds. Both condensates with repulsive and attractive interactions between atoms are considered. The limiting case of waves with constant amplitude is studied in detail. The structure of soliton analogs in these systems is considered. The possibility of applying the proposed theory to description of experimentally observed wavy periodic structures in two-component Bose-Einstein condensate is discussed.
We investigate the localized nonlinear matter waves in the two-component Bose-Einstein condensates with time- and space-modulated nonlinearities analytically and numerically. The similarity transformations are developed to solve the coupled Gross-Pitaevskii equations and two families of explicitly exact solutions are derived. Our results show that not only the attractive spatiotemporal inhomogeneous interactions but the repulsive ones support novel localized nonlinear matter waves in two-component Bose-Einstein condensates. The dynamics of these matter waves, including the breathing solitons, quasibreathing solitons, resonant solitons, and moving solitons, is discussed. We confirm the stability of the exact solutions by adding various initial stochastic noise and study the general cases of the interaction parameters numerically. We also provide the experimental parameters to produce these phenomena in future experiments.
We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.