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arXiv:1308.1194 · Physical Review Letters

Oblique Breathers Generated by a Flow of Two-Component Bose-Einstein Condensates Past a Polarized Obstacle

A. M. Kamchatnov, Yaroslav V. Kartashov

Published Oct 3, 2013• 15 citations
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Abstract

We predict that oblique breathers can be generated by a flow of two-component Bose-Einstein condensates past a polarized obstacle that attracts one component of the condensate and repels the other one. The breather exists if intraspecies interaction constants differ from the interspecies interaction constant, and it corresponds to the nonlinear excitation of the so-called polarization mode with domination of the relative motion of the components. Analytical theory is developed for the case of small-amplitude breathers that is in reasonable agreement with the numerical results.

DOI
10.1103/physrevlett.111.140402

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We predict that oblique breathers can be generated by a flow of two-component Bose-Einstein condensates past a polarized obstacle that attracts one component of the condensate and repels the other one. The breather exists if intraspecies interaction constants differ from the interspecies interaction constant, and it corresponds to the nonlinear excitation of the so-called polarization mode with domination of the relative motion of the components. Analytical theory is developed for the case of small-amplitude breathers that is in reasonable agreement with the numerical results.
It is shown that a spin-orbit interaction leads to drastic changes in wave patterns generated by a flow of a two-component Bose-Einstein condensate (BEC) past an obstacle. The combined Rashba and Dresselhaus spin-orbit interaction affects in different ways two types of excitations —density and polarization waves— which can propagate in a two-component BEC. We show that the density and polarization "ship wave" patterns rotate in opposite directions around the axis located at the obstacle position and the angle of rotation depends on the strength of the spin-orbit interaction. This rotation is accompanied by a narrowing of the Mach cone. The influence of the spin-orbit coupling on density solitons and polarization breathers is studied numerically.
We consider a spin-1 Bose—Einstein condensate trapped in a harmonic potential with different nonlinearity coefficients. We illustrate the dynamics of soliton breathers in two-component and three-component states by numerically solving the one-dimensional time-dependent coupled Gross—Pitaecskii equations (GPEs). We present that two condensates with repulsive interspecies interactions make elastic collision and novel soliton breathers are created in two-component state. We also demonstrate novel soliton breathers in three-component state with attractive coupling constants. Furthermore, possible reasons for creating soliton breathers are discussed.
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.
We investigate two vector-soliton–like matter waves collisions in two-component Bose-Einstein condensates with attractive interactions and Gaussian barrier. We present a detailed numerical analysis of the roles of atomic interactions, barrier, relative velocity, and relative phase in collisional dynamics. We show that the interspecies interactions are crucial to make the wave packet propagate as a “breather”. We find that the collision-induced trajectory shifts of waves are mainly determined by the intraspecies interactions and proportional to them in the weak nonlinearity regime. Moreover, we explore the meeting time of colliding waves and find it depends on the competition between barrier potential and atomic interactions. Particularly, we study the collisions of two waves with a slight velocity asymmetry (or with different relative phases) and the waves merging and split are demonstrated. The underlying inelastic mechanism closely related to energy exchange is briefly discussed as well.
This paper is concerned with two-component Bose–Einstein condensates with both attractive intraspecies and interspecies interactions passing an obstacle in a plane, which can be described by the ground states of the nonlinear Schrödinger system defined in an exterior domain Ω=R2\ω, with ω⊂R2 being a bounded smooth convex domain. Under the assumption that the trapping potentials Vi(x) for i = 1, 2 attain their global minima only on the whole boundary ∂Ω, the existence, non-existence, and limiting behavior of ground states for the system are studied. When intraspecies interactions a1 and a2 satisfy 0 < a1, a2 < a* and interspecies interaction β satisfies 0 < β < β* by the delicate energy analysis, an optimal blow-up rate for ground states is also given as β ↗ β*, where β*=a*+(a*−a1)(a*−a2), a*≔‖Q‖22, and Q is the unique positive solution of ΔQ − Q + Q3 = 0 in R2.