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arXiv:0804.3287 · Physical Review A

Double-barrier potentials for matter-wave gap solitons

V. Ahufinger, Boris A. Malomed, G. Birkl, R. Corbalán, Anna Sanpera

Published Jul 7, 2008• 5 citations
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Abstract

We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.

DOI
10.1103/physreva.78.013608

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•Jan 1, 2004•11 citations
We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.
We introduce two- and one-dimensional (1D) models of a binary BEC (Bose-Einstein condensate) in a periodic potential, with repulsive interactions. We chiefly consider the most fundamental case of the interspecies repulsion with zero intraspecies interactions. The same system may also model a mixture of two mutually repulsive fermionic species. Existence and stability regions for gap solitons (GSs) supported by the interplay of the interspecies repulsion and periodic potential are identified. Two-component GSs are constructed by means of the variational approximation (VA) and in a numerical form. The VA provides an accurate description for the GS which is a compound state of two tightly bound components, each essentially trapped in one cell of the periodic potential. GSs of this type dominate in the case of intragap solitons, with both components belonging to the first finite bandgap of the linear spectrum (only this type of solitons is possible in a weak lattice). Intergap solitons, with one component residing in the second bandgap, and intragap solitons which have both components in the second gap, are possible in a deeper periodic potential, with the strength essentially exceeding the recoil energy of the atoms. Intergap solitons are, typically, bound states of one tightly and one loosely bound component. In this case, results are obtained in a numerical form. The number of atoms in experimentally relevant situations is estimated to be $\ensuremath{\sim}5000$ in the 2D intragap soliton, and $\ensuremath{\sim}25\phantom{\rule{0.2em}{0ex}}000$ in its intergap counterpart; in 1D solitons, it may be up to 105{10}^{5}105. For 2D solitons, the stability is identified in direct simulations, while in the 1D case it is done via eigenfrequencies of small perturbations, and then verified by simulations. In the latter case, if the intragap soliton in the first bandgap is weakly unstable, it evolves into a stable breather, while unstable solitons of other types (in particular, intergap solitons) get completely destroyed. The intragap 2D solitons in the first bandgap are less robust, and in some cases they are completely destroyed by the instability. Addition of intraspecies repulsion to the repulsion between the components leads to further stabilization of the GSs.
We present an analytical solution of two solitons of Bose—Einstein condensates trapped in a double-barrier potential by using a multiple-scale method. In the linear case, we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence. For weak nonlinearity, it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties. Especially, in the case of regarding a double-barrier potential as the output source of the solitons, the collision spots between two dark solitons can be controlled by the height of the barrier potential.
Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).
We study the mobility and interaction of gap solitons in a Bose–Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of the discreteness imposed on a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-band-edge gap solitons provide a simple and effective means for generating strongly localized in-gap solitons through soliton fusion.
We study the dynamics of one-dimensional solitons in attractive and repulsive Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is negative . This gives rise to a prediction for the experiment: such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing slow harmonic oscillations, with a period that is estimated to be ∼0.01 s in realistic experimental conditions) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to interaction with the OL. At a later stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide .
Abstract. We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized nearthe-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.