Two-component Bose-Einstein condensates in periodic potential

Kostov, N. A.; Enolskii, V. Z.; Gerdjikov, Vladimir S.; Konotop, V. V.; Salerno, Mario

doi:10.1103/physreve.70.056617

Cited by 59 publications

(43 citation statements)

References 26 publications

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“…Recently a great progress was achieved for analysis of linear stability of periodic solutions of type (3.1), (3.2) (see e.g. [15,24,25,18,26] and references therein). Nevertheless the stability analysis is known only for solutions of type (5.1)-(5.6) and solutions with nontrivial phase of type (6.3) and (6.4).…”

Section: Linear Stability Preliminary Resultsmentioning

confidence: 99%

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Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

Kostov

Gerdjikov

Valchev

2007

SIGMA

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Abstract. We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a quasi-one dimensional quantum degenerate BoseFermi mixture trapped in optical lattice. In the limit k → 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.

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Section: Linear Stability Preliminary Resultsmentioning

confidence: 99%

“…These results were generalized to the n-component CNLS in [18]. For 2-component CNLS explicit stationary solutions are derived in [26].…”

Section: Basic Equationsmentioning

confidence: 99%

Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

Kostov

Gerdjikov

Valchev

2007

SIGMA

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“…This leads to the possibility of their coherent control. We then consider this system in an optical lattice [32,33,34], where a superfluid phase is found to exist under general conditions.In the case of two species condensate with a wave function ψ i (x, t) for the species i, the coupled quasi-1D GP equation in the presence of an external potential V i , can be written as,and i ψ 2 = − 2 2m ψ ′′ 2 + V 2 (x, t)ψ 2 + [g 21 |ψ 1 | 2 + g 2 |ψ 2 | 2 − ν 2 ]ψ 2 .The strength of the intra-species interactions is g i and ν j is the chemical potential. We assume the interspecies…”

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confidence: 99%

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

et al. 2009

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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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“…Equation (1) has been applied in various physical fields, such as plasma physics [12], nonlinear optics [13,14], condense matter physics [15,16], geophysics fluid dynamics [17], etc. In the context of nonlinear optics, p and q in (1) describe the envelopes of the waves with mutually orthogonal linear polarization, x and t correspond to normalized distance and time, respectively.…”

Section: Introductionmentioning

confidence: 99%