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Physical Review A

Matter waves and quantum tunneling engineered by time-dependent interactions

Yu. V. Bludov, V. V. Konotop, Mario Salerno

Published May 17, 2010• 7 citations
Publisher

Abstract

We report the possibility of steering gap solitons in Bose-Einstein condensates loaded in optical lattices by means of time-dependent nonlinearities, which allow one to control in a nondestructive manner both Bloch oscillations and Landau-Zener tunneling (i.e., Rabi oscillations) across band gaps. As an example we show how to move a matter-wave soliton in real and in reciprocal space from a lower to higher bands, avoiding dynamical instabilities. This opens the possibility of experimental access to gap solitons of higher bands and forcing of soliton motion through a lattice via the Feshbach resonance technique.

DOI
10.1103/physreva.81.053614

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We report the possibility of steering gap solitons in Bose-Einstein condensates loaded in optical lattices by means of time-dependent nonlinearities, which allow one to control in a nondestructive manner both Bloch oscillations and Landau-Zener tunneling (i.e., Rabi oscillations) across band gaps. As an example we show how to move a matter-wave soliton in real and in reciprocal space from a lower to higher bands, avoiding dynamical instabilities. This opens the possibility of experimental access to gap solitons of higher bands and forcing of soliton motion through a lattice via the Feshbach resonance technique.
We introduce a new method to achieve long-lived Bloch oscillations and dynamical localization of matter wave gap solitons in optical lattices. The method is based on the time-dependent modulations of the nonlinearity which can be experimentally implemented by means of the Feshbach resonance technique. In particular, we show that the width of the wavepacket is preserved if the time modulations of the nonlinearity are taken proportional to the curvature of the linear band spectrum which for most typical experimental settings are well approximated by harmonic time modulations of proper frequencies.
The nonlinear Landau—Zener tunneling and nonlinear Rabi oscillations of Bose—Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.
We study the pumping of matter-wave solitons formed in Bose-Einstein condensates (BECs) with attractive atomic interactions that are loaded into optical superlattices in which one of the lattices is moving with respect to the other. We find that solitons exhibit the remarkably similar pumping properties in both shallow and deep lattices, and that for exactly the same soliton initially excited, switching between integer (fractional) pumping and trapping can be achieved by simply adjusting the lattice parameters. In addition, we find that the gap solitons, which bifurcate from the lowest energy band in a semi-infinite band gap, also exhibit this lattice-parameter-dependent pumping and trapping. The treatment of solitons as classical particles with effective centre-of-mass equations of motion provides a good description of this parameter-dependent integer (fractional) pumping and trapping of solitons.
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
We show how the chiral properties of Bose-Einstein condensates subject to current-density interactions and loaded in optical lattices can be observed in the realization of nonlinear Bloch states, whose spectrum lacks the usual periodic structure. Chirality is also manifested by spatially localized states, or gap solitons, which are found for positive rotation rates of the lattice at the energy gaps between the linear energy bands, whereas for negative rotations they appear in the semi-infinite gap of the linear spectrum. The stability of extended and localized states is checked through the spectrum of linear excitations and nonlinear time evolution of perturbed states, and the phenomenon of Bloch oscillations is explored. Our results are obtained in quasi-one-dimensional ring geometries with feasible experimental parameters.