Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice

Mayteevarunyoo, Thawatchai; Malomed, Boris A.

doi:10.1103/physreva.74.033616

Cited by 64 publications

(77 citation statements)

References 47 publications

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“…Twisted (alias odd) solitons, which feature two out-of-phase amplitude peaks in one period of the underlying lattice, were found and shown to be stable in the single-component GPE with attractive nonlinearity [26] (unlike formally similar subfundamental gap solitons in the model with self-repulsion, which are unstable [27]). …”

Section: Twisted Solitons and Bound Statesmentioning

confidence: 99%

“…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%

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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%

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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“…refs. [25], [26], and [27], where both loosely and tightly bound GSs were investigated in BEC models). We demonstrate that this is the case indeed, except when the chemical potential is very close to edges of the bandgap (in that case, GSs start to develop wavy tails, signalizing a transition to delocalized states in the Bloch bands).…”

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confidence: 99%

Tightly bound gap solitons in a Fermi gas

Adhikari

Malomed

2007

Europhys. Lett.

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Abstract. -Within the framework of the mean-field-hydrodynamic model of a degenerate Fermi gas (DFG), we study, by means of numerical methods and variational approximation (VA), the formation of fundamental gap solitons (FGSs) in a DFG (or in a BCS superfluid generated by weak interaction between spin-up and spin-down fermions), which is trapped in a periodic opticallattice (OL) potential. An effectively one-dimensional (1D) configuration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG (which amounts to the known quintic equation for the Tonks-Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL-induced spectrum ( unless they are very close to edges of the gaps) feature a (tightly-bound) shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly-bound subfundamental solitons (SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of ∼ 10 4 − 10 5 atoms, can be created by available experimental techniques in the DFG of 6 Li atoms.Introduction: Matter-wave solitons were created as localized nonlinear excitations in Bose-Einstein condensates (BECs) of attractively interacting 7 Li [1] and 85 Rb [2] atoms loaded in a cigar-shaped trap. In both cases, the interaction was switched from repulsion to attraction by applying magnetic field near the Feshbach resonance [3,4]). In the absence of axial confinement, the solitons can propagate freely in the axial direction. This was followed by the creation of gap solitons, GSs (formed by a few hundred atoms of 87 Rb) in a self-repulsive BEC loaded in a cigar-shaped trapped combined with an optical lattice (OL) [5], which was created as the interference pattern by counter-propagating laser beams (see also review [6]). Theoretical description of the dilute BEC relies upon the Gross-Pitaevskii equation (GPE), which provides for a remarkably accurate description of various matter-wave patterns, including solitons [7]. In particular, GSs exist at values of the chemical potential that fall in finite gaps of the band spectrum of the linear problem, induced by the periodic OL potential. In that case, the system possesses a negative effective mass, which allows the formation of solitons in balance with the repulsive nonlinearity [8].

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“…The observed resonances in these experiments were explained by the generation of parametric amplification of Bogoliubov states and the subsequent nonlinear dynamics, which leads to the broadening of the momentum distribution [13,14]. Parametric resonances of trapped condensates under the action of periodic modulation of the trap's strength have been studied earlier [15][16][17][18]. Various dynamical effects in periodically timemodulated optical lattice potentials were studied in [16].…”

Section: Introductionmentioning

confidence: 99%

“…Parametric resonances of trapped condensates under the action of periodic modulation of the trap's strength have been studied earlier [15][16][17][18]. Various dynamical effects in periodically timemodulated optical lattice potentials were studied in [16]. In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

2012

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Abstract:In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice. PACS

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Stability limits for gap solitons in a Bose-Einstein condensate trapped in a time-modulated optical lattice

Cited by 64 publications

References 47 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

Tightly bound gap solitons in a Fermi gas

Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

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