Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction

Eiermann, B.; Anker, Thomas; Albiez, M.; Taglieber, M.; Treutlein, Philipp; Marzlin, Karl‐Peter; Oberthaler, Markus K.

doi:10.1103/physrevlett.92.230401

Cited by 681 publications

(557 citation statements)

References 20 publications

Supporting

Mentioning

537

Contrasting

Unclassified

Order By: Relevance

“…In the present case, the effect of the coupling is more complex. Given µ belongs to a bandgap in the present model if µ falls into one of the gaps in both equations (4) and (5). Further consideration demonstrates that, depending on the values of κ and OL strength ε, each gap originating from the ME spectrum either shrinks (or, sometimes, completely closes up), similar to the situation in the above-mentioned model of linearly coupled Bragg gratings, or splits into pairs of subgaps.…”

Section: Linear Spectrummentioning

confidence: 91%

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

Gubeskys

Malomed

2007

Phys. Rev. A

View full text Add to dashboard Cite

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.

show abstract

Section: Linear Spectrummentioning

confidence: 91%

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

Gubeskys

Malomed

2007

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…In this case, it is possible (as, e.g., in the experiment of Ref. [44]) to tune ω z so that it provides only a very weak trapping along the z-direction; this way, the shift in the potential trapping energies over the wells where the BEC is confined can be made practically negligible. In such a case, the potential in Eq.…”

mentioning

confidence: 99%

“…Importantly, they have also been observed in many elegant experiments using various relevant techniques. These include, among others, phase engineering of the condensates in order to create vortices [28,29] or dark matterwave solitons in them [30][31][32][33][34], the stirring (or rotation) of the condensates providing angular momentum creating vortices [35,36] and vortex-lattices [37][38][39], the change of scattering length (from repulsive to attractive via Feshbach resonances) to produce bright matter-wave solitons and soliton trains [40][41][42][43] in attractive condensates, or set into motion a repulsive BEC trapped in a periodic optical potential referred to as optical lattice to create gap matter-wave solitons [44]. As far as vortices and vortex lattices are concerned, it should be noted that their description and connection to phenomena as rich and profound as superconductivity and superfluidity, were one of the themes of the Nobel prize in Physics in 2003.…”

mentioning

confidence: 99%

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

2008

View full text Add to dashboard Cite

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...

show abstract

“…Many intriguing phenomena that are hardly observed in conventional solid-state systems have already been reported: Bloch oscillations, Landau-Zener tunneling, [1][2][3] resonantly enhanced tunneling, 4 and solitons at the edge of the Brillouin zone. 5 A series of experiments have further demonstrated that a Bose-Einstein condensate (BEC) in a periodic potential has a critical momentum where the superfluidity becomes unstable by measuring the center-of-mass oscillations of a BEC or the decay of superfluid flows in a moving lattice. [6][7][8][9][10][11][12] As has been indicated theoretically, [13][14][15][16][17][18][19][20] this phenomenon is identified as the dynamical instability that occurs in the presence of lattice potential, and also without any energy dissipation in contrast to the well-known Landau instability of a superfluid.…”

Section: Introductionmentioning

confidence: 99%

Density Modulations Associated with the Dynamical Instability in the Bose–Hubbard Model

et al. 2014

View full text Add to dashboard Cite

We analyze the non-equilibrium quantum dynamics of a Bose-Einstein condensate that flows in an optical lattice on the basis of the Bose-Hubbard model. The time evolution of a condensate calculated by the dynamical Gutzwiller approximation has clarified that density modulations appear as a precursor phenomenon of the dynamical instability. Furthermore, the principal mode of modulations strongly depends on both the interparticle interaction strength and the rate of momentum acceleration. We show that these features of density modulations are well explained by the stability phase diagram obtained on the basis of the Bogoliubov theory.

show abstract

Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction

Cited by 681 publications

References 20 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

Density Modulations Associated with the Dynamical Instability in the Bose–Hubbard Model

Contact Info

Product

Resources

About