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arXiv:0710.1339 · New Journal of Physics

Resonant ratcheting of a Bose–Einstein condensate

L. Morales-Molina, Sergej Flach A

Published Jan 14, 2008• 35 citations
arXivHTMLPDF

Abstract

We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion even in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Denisov et al 2007 Europhys. Lett. 79 10007; Denisov et al 2007 Phys. Rev. A 75 063424). Here, we study the fate of these resonances within a Gross–Pitaevskii equation which describes a mean field interaction between many particles. We find that the resonance (i) is not destroyed by interactions, (ii) shifts its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles.

DOI
10.1088/1367-2630/10/1/013008

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We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion even in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Denisov et al 2007 Europhys. Lett. 79 10007; Denisov et al 2007 Phys. Rev. A 75 063424). Here, we study the fate of these resonances within a Gross–Pitaevskii equation which describes a mean field interaction between many particles. We find that the resonance (i) is not destroyed by interactions, (ii) shifts its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles.
The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose-Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport.
We investigate the effect of the nonlinear interaction on the quantum resonance ratchet for the periodically kicked Bose-Einstein condensate that is realized on a ring. In the noninteracting case, the wave packet spreads asymmetrically in momentum space, leading to a directed current. We show that for the weak nonlinear interaction, the probability density distribution in momentum space has two peaks which linearly shift to ward positive and negative momentum, respectively. The force periodically acting on each peak is a constant with time evolution. The competition between the motions of the two parts of cold atoms leads to the reduce or the revival of the momentum current. For the strong nonlinearity, the momentum distribution has only one peak which does not shift with time. The force on this peak is almost zero with time evolution, thus the directed current varnishes.
The dynamical evolution of a periodically kicked Bose-Einstein condensate was investigated by simulation. Emphasis was placed on the influence of the nonlinear interaction between atoms on the quantum-resonance ratchet effect. It was found that weak nonlinear interaction reduces the ratchet effect while the strong nonlinear interaction causes the ratchet current to disappear or even reversed. The ratchet effect under high-order quantum resonance conditions was further studied. The ratchet effect is not obvious in this case and can be easily destroyed by the noise of the kicking potential period.
We investigate the Gross–Pitaevskii equation which describes an atomic Bose–Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded into chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states in the phase-continuing region could be prepared from the uniformly initial states by slow growth of the external potential. 1.
The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales.