Sinusoidal excitations in two-component Bose-Einstein condensates in a trap

Abstract

The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating wave solutions in quasi one dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates the procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time dependent coupling and the trap variation on the condensate profile are explicated. The TBEC has also been investigated in presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions. PACS numbers: 03.75. Kk, 03.75.Lm, 03.75.Mn Much theoretical work has already gone into studying the ground state solutions of the coupled GrossPitaevskii (GP) equations describing multi-component BECs [1,2,3,4]. TBEC has been observed, where the two hyperfine levels of 87 Rb [5,6] act as the two components. In this case, a fortuitous coincidence in the triplet and singlet scattering lengths has led to the suppression of exoergic spin-exchange collisions, which lead to heating and resultant loss of atoms. A number of interesting features, like the preservations of the total density profile and coherence for a characteristically long time, in the face of the phase-diffusing couplings to the environment and the complex relative motions [7], point to the extremely interesting dynamics of the TBEC. TBEC has been produced in a system comprising of 41 [12,13,14,15]. In the TBEC, a number of investigations, primarily devoted to the study of localized solitons, have been carried out recently [16,17,18,19,20]. The coincidence of singlettriplet coupling in 87 Rb, leads to the well known Manakov system [21] in weak coupling quasi-one dimensional scenario [22,23]. The rich dynamics of solitons in this integrable system has received considerable attention in the literature [24,25,26,27]. The effect of spatial inhomogeneity, three-dimensional geometry, and dissipation on TBEC have been examined. However, the periodic solitary waves have not received much attention in the literature, particularly in the presence of the harmonic trap [28]. Periodic sinusoidal excitations are natural in linear systems. In nonlinear models periodic cnoidal waves can be present. It is worth mentioning that, in nonlinear resonant atomic media, cnoidal excitations have been experimentally generated [29,30], where relaxation naturally led to the atomic level population necessary for the existence of these nonlinear periodic waves [31].Here we analyze the solutions of a generic TBEC model in a quasi-one dimensional geometry for periodic solutions. Interestingly, we find exact sinusoidal wave solutions in this system in the presence of a harmonic trap, which do not occur in the single component case. The presence of two components leads to these waves, whose energy difference are controlled by the cross phase modulation (XPM). In presence of time dependent trap and sc...

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