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arXiv:1308.2288 · Europhysics Letters (EPL)

Periodic waves in two-component Bose-Einstein condensates with repulsive interactions between atoms

A. M. Kamchatnov

Published Sep 1, 2013• 4 citations
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Abstract

We consider periodic waves in miscible two-component Bose-Einstein condensates with repulsive nonlinear interaction constants. Exact one-phase solution is found for the case when all these constants are equal to each other ( i.e. , for the Manakov limit). New types of nonlinear polarization waves are considered in detail. The connection of the solutions found with experimentally observed periodic structures in two-component condensates is discussed.

DOI
10.1209/0295-5075/103/60003

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We consider periodic waves in miscible two-component Bose-Einstein condensates with repulsive nonlinear interaction constants. Exact one-phase solution is found for the case when all these constants are equal to each other ( i.e. , for the Manakov limit). New types of nonlinear polarization waves are considered in detail. The connection of the solutions found with experimentally observed periodic structures in two-component condensates is discussed.
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.
Traveling waves in two-component Bose-Einstein condensates whose dynamics is described by the Manakov limit of the Gross-Pitaevskii equations are considered in a general situation with relative motion of the components when their chemical potentials are not equal to each other. It is shown that in this case the solution is reduced to the form known in the ``Kowalevski top'' theory of motion. Typical situations are illustrated by the particular cases when the general solution can be represented in terms of elliptic functions and their limits. Depending on the parameters of the wave, both density waves (with in-phase motions of the components) and polarization waves (with counterphase motions) are considered.
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.
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.
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.
Coupled nonlinear Schrödinger (CNLS) equations with an external elliptic function potential model with high accuracy a quasi-one-dimensional interacting two-component Bose-Einstein condensate (BEC) trapped in a standing wave generated by a few laser beams. The construction of stationary solutions of the two-component CNLS equation with a periodic potential is detailed and their stability properties are studied by direct numerical simulations. Some of these solutions allow reduction to the Manakov system. From a physical point of view the trivial phase solutions can be interpreted as exact Bloch states at the edge of the Brillouin zone. Some of them are stable while others are found to be unstable against weak modulations of long wavelength. By numerical simulations it is shown that the modulationally unstable solutions lead to the formation of localized ground states of the coupled BEC system.