Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

Louis, Pearl J. Y.; Ostrovskaya, Elena A.; Savage, C. M.; Kivshar, Yuri S.

doi:10.1103/physreva.67.013602

Cited by 256 publications

(221 citation statements)

References 33 publications

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“…Bound states of π-out-of-phase fundamental solitons, which also feature the odd parity, but include peaks separated by an empty lattice site, have been found too, in the AA and RR systems alike (in the singlecomponent GPE with the repulsive nonlinearity, the presence of an empty site between the peaks is a necessary condition for the existence of a stable bound state of two out-of-phase fundamental gap solitons [27,29]). Families of the bound states of this type are shown in Fig.…”

Section: Twisted Solitons and Bound Statesmentioning

confidence: 99%

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Gubeskys

Malomed

2007

Phys. Rev. A

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We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, ∆, between the OLs in the two cores is also studied. It is concluded that ∆ = π/2 only mildly deforms the picture, while ∆ = π changes it drastically, replacing the symmetry-breaking bifurcations by pseudo-bifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.

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Section: Twisted Solitons and Bound Statesmentioning

confidence: 99%

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Gubeskys

Malomed

2007

Phys. Rev. A

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“…The concept of Bloch waves can also be extended in the nonlinear case (g = 0) [163][164][165][166][167][168][169][170]. In particular, when the coupling constant is small, the nonlinear bandgap spectrum and the nonlinear Bloch waves are similar to the ones in the linear case [166].…”

Section: Reduced Mean-field Models For Becs In Optical Latticesmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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“…We consider a cigar-shaped quasi-1D BEC with inhomogeneous atomic interaction described by wave function u(x,t) satisfying the following dimensionless 1D GP equation [27,28] i ∂u ∂t = − 1 2…”

Section: Analytical Consideration Of Localizationmentioning

confidence: 99%

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

Cheng

Adhikari

2011

Phys. Rev. A

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By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.

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Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

Cited by 256 publications

References 33 publications

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

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