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arXiv:cond-mat/0407702 · Physical Review Letters

Quantum Ratchets in Dissipative Chaotic Systems

Gabriel G. Carlo, Giuliano Benenti, Giulio Casati, Dima L. Shepelyansky

Published Apr 26, 2005• 79 citations
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Abstract

Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.

DOI
10.1103/physrevlett.94.164101

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Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.
We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.
We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate DDD is asymmetric in momentum up to a finite time trt_rtr​. The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time t∗>trt^* > t_rt∗>tr​. We conclude that the cold atom ratchets require Db/ℏ∼1Db/ \hbar \sim 1Db/ℏ∼1 where b is a small deviation from period-one pulses.
We report on the successful experimental realization of a quantum ratchet for ultracold atoms in a driven spatially asymmetric optical lattice. Ratchets are usually considered as a tool, which rectify an otherwise undirected, for instance oscillating or fluctuating, motion of particles or objects. In order to observe a directed transport of atoms one has to break the space-time symmetry of the system. Here, we report on the realization of a quantum ratchet in the absence of dissipative processes (Hamiltonian regime) within the interaction time.
Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.