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E. Díaz(1), Ch. Gaul(2), R. P. A. Lima(1), C. A. Müller(2) and F. Domínguez-Adame(1)
(1) GISC, Departamento de Fisica de Materiales, Universidad Complutense, E-28040 Madrid, Spain (2) Physikalisches Institut Universität Bayreuth 95440 Bayreuth, Germany At the end of the nineties ultracold gases came up as a very promising scenario to perform quantum transport experiments in lattices. In particular, due to the possibility to create perfect periodic potential where scattering by defects is negligible, long living Bloch oscillations (BO) are expected to occur [1] much easier than in other systems even in the case of interacting Bose- Einstein condensates(BEC) [2]. However these interactions may induce nonlinear instabilities in the system which destroy the coherence necessary for BO to arise [3,4]. Some efforts were already carried out to avoid this damped oscillations [5]. In this sense, we study analytically and numerically the existence of BO within an optical lattice considering a time oscillating interaction of the atoms. This interaction seems to counteract the effect of the instabilities allowing for persistent BO for specific ratios of the two relevant frequencies involved in the dynamics, the Bloch and the driving frequency. Our starting point is the discrete Gross-Pitaevskii equation within the tight binding approximation. We solve it numerically and by means of a collective-coordinates ansatz. In addition, a stability analysis of Bogoliubov excitations based on the Floquet theory [6] is proposed. Thus we accurately predict the suitable parameters of the oscillating interaction to avoid the destruction of BO. References 1. M. Ben Dhan, E. Peik, J. Reichel, Y. Castin and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996). 2. R. Sharf and A. R. Bishop, Phys. Rev. A. 43, 6535 (1991). 3. V. V. Konotop and M. Salerno, Phys. Rev. A 65, 021602 (2002). 4. L. Fallani et al. Phys. Rev. Lett. 90, 110404 (2004). 5. M. Salerno, V. V. Konotop and Yu. V. Bludov, Phys. Rev. Lette. 101, 030405 (2008). 6. Garald Teschl "Ordinary differential equations an dynamical systems" Publisher: Faculty of Mathematics, University of Vienna (2008). |
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