Matter waves and quantum tunneling engineered by time-dependent interactions

Yu. V. Bludov, V. V. Konotop, and M. Salerno

Phys. Rev. A 81, 053614 – Published 17 May 2010

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.

Received 1 April 2010

DOI:https://doi.org/10.1103/PhysRevA.81.053614

Authors & Affiliations

Yu. V. Bludov¹, V. V. Konotop^2,3, and M. Salerno⁴

¹Centro de Física, Universidade do Minho, Campus de Gualtar, Braga 4710-057, Portugal
²Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal
³Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Piso 6, Lisboa 1749-016, Portugal
⁴Dipartimento di Fisica “E.R. Caianiello,” CNISM and INFN–Gruppo Collegato di Salerno, Università di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy

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Vol. 81, Iss. 5 — May 2010

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Images

Figure 1
(a),(c),(e) Dependencies $g (t)$ , which satisfy the condition (4), for OL amplitude $v = 3$ , initial Bloch wavenumber $Q (0) = 0$ , when external force is described by Eq. (6) with $Γ = - 0.001$ (a), and by Eq. (7) with $Γ_{1} = - 0.001$ , $Γ_{2} = 0.001$ (c) or $Γ_{2} = - 0.002$ (e). (b),(d),(f) Spatiotemporal evolution of a soliton in a BEC with time-varying nonlinearity, depicted in (a), (c), and (f), respectively. (g) Spatiotemporal evolution of a soliton in a BEC with the same parameters as those of (f), except for constant nonlinearity $g (t) = - 1$ . The initial condition in (b), (d), (f), and (g) is the stationary gap soliton with $E = - 0.938$ .Reuse & Permissions
Figure 2
(a) Dependency $g (t)$ , which satisfies the condition (8), for tunneling between first and second bands ( $n = 1$ ) of the OL with amplitude $v = 3$ and tunneling time $T_{tun} = 85.0$ . (b) Long-living Rabi oscillations of soliton in the momentum space $| c_{2} (q) |^{2}$ [ $c_{n} (q, t) = \int_{- \infty}^{\infty} ψ (x, t) \bar{φ_{n, q} (x)} dx$ ] under the action of an external force with strength $ν = - 0.05$ and frequency $Ω = 2.89$ in a BEC with time-varying nonlinearity, depicted in (a). (c) Decaying Rabi oscillations of a soliton in a BEC with constant nonlinearity $g (t) = 1$ . The external force parameters are the same as in (b). In (b) and (c) Rabi oscillations start from the stationary state near the lower edge of the gap with chemical potential $E = - 0.7324$ .Reuse & Permissions
Figure 3
(a) Soliton chemical potential $E (t)$ (solid lines) and nonlinearity $g (t)$ (dashed lines), which allows the soliton steering to the top of the second band of the OL with amplitude $v = 3$ by an external force (10). The initial condition is the stationary soliton near the lower edge of the first band with chemical potential $E = - 0.9375$ . (b)–(d) show the solitonic shapes (solid lines) at corresponding points in (a). Also in (b)–(d) the solitonic shapes are compared to stationary solutions (dashed lines) near the upper edge of the first band (b), lower (c) and upper (d) edges of the second band. These stationary solutions correspond to the same number of particles as the initial conditions ( $N = 0.0427$ ).Reuse & Permissions
Figure 4
(a) Soliton chemical potential $E (t)$ (solid lines) and nonlinearity $g (t)$ (dashed lines), which allows the soliton steering to the top of the second band (as in Fig. 3) and back. The OL parameters and initial condition are the same as those in Fig. 3. (b) shows the solitonic shape (solid line) at correspondent point in panel (a) as well as initial soliton (dashed line).Reuse & Permissions

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