Proposal for a Chaotic Ratchet Using Cold Atoms in Optical Lattices

Abstract

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 t r . We conclude that the cold atom ratchets require Db= h 1, where b is a small deviation from period-one pulses. DOI: 10.1103/PhysRevLett.89.194102 PACS numbers: 05.45.Mt, 05.40.Jc, 05.60.-k, 32.80.Pj Cold atoms in optical lattices provide an excellent experimental demonstration of the phenomenon of dynamical localization [1,2]. Dynamical localization (DL) has been described as the so-called ''quantum suppression of classical chaos.'' In the usual realizations, a periodically driven or kicked system makes a transition to chaotic classical dynamics for sufficiently strong perturbation. The classical energy is unbounded and grows diffusively with time. For the corresponding quantum system, in contrast, the diffusion is suppressed after an h-dependent time scale, the ''break time'' t . The final quantum momentum distribution is localized with a characteristic exponential profile. The formal analogy established with Anderson localization [2] forms a key analysis of this phenomenon. A series of recent experiments on cesium atoms in pulsed optical lattices [3] gave a classic demonstration of this effect.The possibility of experiments with asymmetric lattices, in particular, with asymmetric double wells [4,5], leads us to investigate the possibility of constructing a ''clean'' atomic ratchet, where the transport results purely from the chaotic Hamiltonian dynamics, with no Brownian or dissipative ingredients. Ratchets are spatially periodic systems which, by means of a suitable spatialtemporal asymmetry, can generate a current even in the absence of a net force. There is already an extensive body of work on Brownian and deterministic ratchets with dissipation [6,7], driven by the need to understand biophysical systems such as molecular motors and certain mesoscopic systems. Some of this work encompasses the quantum dynamics [8]. For a full review see [9]. However, to date there has been very little work on Hamiltonian ratchets. One notable exception is the work by Flach et al.[10] where the general form of the spatial and temporal desymmetrization required to generate transport was investigated. The only substantial study of quantum Hamiltonian ratchets, however, is the work of Dittrich et al. [11] which showed how transport can occur in mixed phase spaces. They demonstrated that transport is zero if starting conditions cover all regions of phase space uniformly. A key result was a sum rule showing transport in the chaotic manifold is balanced by transport in the adjoining regular manifolds (stable islands/tori). Very recently [12], it was shown that a kicked map with a ''rocking'' linea...

Kicked-rotor quantum resonances in position space

“…The experimental realization of the QKR has triggered in the last decade an impressive number of studies involving dynamical localization [5,6,7,8,9,10,11], quantum transport [12,13,14,15], ratchets [16,17,18], chaosassisted tunneling [19,20], classical and quantum resonances [21,22,23,24]. Quantum resonances have been used in studies of fundamental aspects of quantum chaos such as quantum stabilization [25] or measurements of the gravitation [26].…”

Directed Motion for Delta-Kicked Atoms with Broken Symmetries: Comparison between Theory and Experiment

“…0. In contrast, for the quantum dynamics, a new and modified form of localization, asymmetric dynamical localization (ADL), was found in [5,6] to arrest the diffusion and ''freeze'' the asymmetry. Hence the relative asymmetry I R t !…”

“…Previous studies of chaotic Hamiltonian ratchets [4] indicated that directed motion arises if certain symmetries are broken, but persists only in the presence of mixed phase-space dynamics (e.g., a bounded classical phase space with a mixture of regular tori and chaotic regions). The quantitative analysis of the directed current then relies on the details of the classical phase space [2].In [5,6] an alternative theoretical proposal for chaotic but asymmetric momentum diffusion, aimed at a realization with cold atoms in far-detuned pulsed optical lattices, was presented. Experiments with cold atoms in neardetuned, driven optical lattices had already been shown to provide realizations of classical Brownian and dissipative ratchets [7].…”

“…In [5,6] an alternative theoretical proposal for chaotic but asymmetric momentum diffusion, aimed at a realization with cold atoms in far-detuned pulsed optical lattices, was presented. Experiments with cold atoms in neardetuned, driven optical lattices had already been shown to provide realizations of classical Brownian and dissipative ratchets [7].…”

Controlling the momentum current of an off-resonant ratchet

“…It has revealed a wide variety of interesting effects including: dynamical localization [2], quantum resonances (QR) [2][3][4], quantum accelerator modes [5,6], and quantum ratchets [7][8][9][10][11][12][13][14][15]. The latter are quantum mechanical systems that display directed motion of particles in the absence of unbalanced forces.…”