Phase separation of multi-component Bose–Einstein condensates in optical lattices

Kuo, Yuen Cheng; Shieh, Shih Feng

doi:10.1016/j.jmaa.2008.06.044

Cited by 4 publications

(3 citation statements)

References 35 publications

(41 reference statements)

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“…Among the various lines of investigation, the theoretical study of the stationary states [30], dynamical instabilities [31,32] and the collective excitations [33,34] of TBECs are noteworthy. Furthermore, in optical lattices TBECs have also been observed in recent experiments [35,36].Theoretical studies of TBECs in optical lattices [37][38][39][40] and, in particular, phase-separation [41][42][43] and dynamical instabilities [44] have also been carried out. Despite all these theoretical and experimental advancements, the study of collective excitations of TBECs in optical lattices is yet to be explored.…”

Section: Introductionmentioning

confidence: 88%

Fluctuation-driven topological transition of binary condensates in optical lattices

2015

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We examine the role of thermal fluctuations in two-species Bose-Einstein condensates confined in quasi-twodimensional (quasi-2D) optical lattices using the Hartree-Fock-Bogoliubov theory with the Popov approximation. The method, in particular, is ideal to probe the evolution of quasiparticle modes at finite temperatures. Our studies show that the quasiparticle spectrum in the phase-separated domain of the two-species Bose-Einstein condensate has a discontinuity at some critical value of the temperature. Furthermore, the low-lying modes like the slosh mode becomes degenerate at this critical temperature, and this is associated with the transition from the immiscible side-by-side density profile to the miscible phase. Hence, the rotational symmetry of the condensate density profiles are restored, and so is the degeneracy of quasiparticle modes.

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Section: Introductionmentioning

confidence: 88%

Fluctuation-driven topological transition of binary condensates in optical lattices

2015

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“…Nonetheless, we will keep our main motivation as non-equilibrium dynamics in Bose mixtures [2]. In the context of cold atoms, vector nonlinear Schrödinger equation (VNLS) (aka multi-component Gross-Pitaevskii equation) appears in multiple coupled species of bosons [35][36][37][38][39][40][41][42][43][44][45][46] or bosons with hyperfine degrees of freedom (spinor BECs [47][48][49][50][51][52][53][54][55]). The nonlinearities or interactions one sees are of inter-species and intra-species type.…”

Section: Introductionmentioning

confidence: 99%

Provable bounds for the Korteweg–de Vries reduction in multi-component nonlinear Schrödinger equation

Swarup¹,

Vasan²,

Kulkarni³

2020

J. Phys. A: Math. Theor.

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We study the dynamics of multi-component Bose gas described by the Vector Nonlinear Schrödinger Equation (VNLS), aka the Vector Gross-Pitaevskii Equation (VGPE) . Through a Madelung transformation, the VNLS can be reduced to coupled hydrodynamic equations in terms of multiple density and velocity fields. Using a multi-scaling and a perturbation method along with the Fredholm alternative, we reduce the problem to a Korteweg de-Vries (KdV) system. This is of great importance to study more transparently, the obscure features hidden in VNLS. This ensures that hydrodynamic effects such as dispersion and nonlinearity are captured at an equal footing. Importantly, before studying the KdV connection, we provide a rigorous analysis of the linear problem. We write down a set of theorems along with proofs and associated corollaries that shine light on the conditions of existence and nature of eigenvalues and eigenvectors of the linear problem. This rigorous analysis is paramount for understanding the nonlinear problem and the KdV connection. We provide strong evidence of agreement between VNLS systems and KdV equations by using soliton solutions as a platform for comparison. Our results are expected to be relevant not only for cold atomic gases, but also for nonlinear optics and other branches where VNLS equations play a defining role.I.

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“…. Recently, it is reported in Ref 12. that the phase separation of the ground state solutions of the CDNLS equation in higher-dimensional lattices occurs as the coupling constants ␤ ij are sufficiently large.…”

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confidence: 99%

Horseshoes for coupled discrete nonlinear Schrödinger equations

Shieh

2009

Journal of Mathematical Physics

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In this paper, we study the spatial disorder of coupled discrete nonlinear Schrödinger ͑CDNLS͒ equations with piecewise-monotone nonlinearities. By the construction of horseshoes, we show that the CDNLS equation possesses a hyperbolic invariant Cantor set on which it is topological conjugate to the full shift on N symbols. The CDNLS equation exhibits spatial disorder, resulting from the strong amplitudes and stiffness of the nonlinearities in the system. The complexity of the disorder is determined by the oscillations of the nonlinearities. We then apply our results to CDNLS equations with Kerr-like nonlinearity. We shall also show some patterns of the localized solutions of the CDNLS equation.Systems of CNLS equations arise in many fields of physics, including condensed matter, hydrodynamics, optics, plasmas, and Bose-Einstein condensates ͑BECs͒ ͑see e.g., Refs. 1, 4, 8, and 15͒. The coupling constants ␤ ij are the interaction between the ith and the jth component of the system. The interaction is attractive if ␤ ij Ͻ 0 and repulsive if ␤ ij Ͼ 0. In the presence of strong periodic trapped potentials, a CNLS equation can be approximated by a CDNLS equation. Equation ͑1.1͒ a͒ Electronic

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Phase separation of multi-component Bose–Einstein condensates in optical lattices

Cited by 4 publications

References 35 publications

Fluctuation-driven topological transition of binary condensates in optical lattices

Fluctuation-driven topological transition of binary condensates in optical lattices

Provable bounds for the Korteweg–de Vries reduction in multi-component nonlinear Schrödinger equation

Horseshoes for coupled discrete nonlinear Schrödinger equations

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