Quantum Enhancement of Momentum Diffusion in the Delta-Kicked Rotor

d’Arcy, M. B.; Godun, R. M.; Oberthaler, M. K.; Cassettari, Donatella; Summy, Gil

doi:10.1103/physrevlett.87.074102

Cited by 132 publications

(107 citation statements)

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“…2(c [14,15]. These corrections have even been measured experimentally with cold cesium atoms in pulsed optical lattices [16,17]. For example, the 2J 2 K term originates from two-kick correlations of the form C 2 2hV 0 x i V 0 x i 2 i.…”

Section: Volume 89 Number 19 P H Y S I C a L R E V I E W L E T T E Rmentioning

confidence: 87%

Proposal for a Chaotic Ratchet Using Cold Atoms in Optical Lattices

et al. 2002

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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...

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Section: Volume 89 Number 19 P H Y S I C a L R E V I E W L E T T E Rmentioning

confidence: 87%

Proposal for a Chaotic Ratchet Using Cold Atoms in Optical Lattices

et al. 2002

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“…It is characterized by a diffusion rate D 0 , i.e., hp 2 i D 0 t. However, in the quantum case this process is suppressed on the time scale of the so-called ''break time'' t D 0 = h 2 [6]. The series of ground-breaking experiments in [3] was followed by other experiments with optical lattices probing a wide range of quantum chaos phenomena including dynamical tunneling [7], the effect of quantum loss of coherence on dynamical localization [8], and quantum accelerator modes [9].Here we show that a straightforward modification of the quantum chaos experiments can form the basis for a device to control the traffic of cold atoms moving along a channel in, say, an atom chip by selecting a specified velocity. In these experiments the atoms experience a periodically pulsed or driven standing wave of light.…”

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confidence: 99%

Chaotic Filtering of Moving Atoms in Pulsed Optical Lattices by Control of Dynamical Localization

2003

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We propose a mechanism for a velocity-selective device which would allow packets of cold atoms traveling in one direction through a pulsed optical lattice to pass undisturbed, while dispersing atoms traveling in the opposite direction. The mechanism is generic and straightforward: for a simple quantum kicked rotor pulsed with unequal periods, the quantum suppression of momentum diffusion (dynamical localization) yields momentum localization lengths L which are no longer isotropic, as in the standard case, but vary smoothly and controllably with initial momentum. DOI: 10.1103/PhysRevLett.91.253003 PACS numbers: 32.80.Pj, 05.45.Mt, 05.60.-k There is much current interest in the development of new techniques to manipulate cold atoms. Recent work in atom optics has resulted in new devices termed ''atom chips'' [1,2] where cold atoms may be trapped and guided by fields above a solid substrate. Within such an atom chip, techniques to split, transport, and otherwise control the traffic of atoms can play an important role.In addition, cold atoms in pulsed or driven optical lattices have become a paradigm in the field of quantum chaos: experiments on sodium and cesium atoms [3] provided a textbook demonstration of dynamical localization (DL) [4,5], the quantum suppression of classical chaotic diffusion. The corresponding classical motion is fully chaotic for sufficiently strong driving. The energy of the system grows diffusively with each consecutive pulse or ''kick'': in the absence of phase-space barriers, which are present only in the regular regime, the average energy hp 2 i of the particles is unbounded and this diffusive increase in energy continues indefinitely. It is characterized by a diffusion rate D 0 , i.e., hp 2 i D 0 t. However, in the quantum case this process is suppressed on the time scale of the so-called ''break time'' t D 0 = h 2 [6]. The series of ground-breaking experiments in [3] was followed by other experiments with optical lattices probing a wide range of quantum chaos phenomena including dynamical tunneling [7], the effect of quantum loss of coherence on dynamical localization [8], and quantum accelerator modes [9].Here we show that a straightforward modification of the quantum chaos experiments can form the basis for a device to control the traffic of cold atoms moving along a channel in, say, an atom chip by selecting a specified velocity. In these experiments the atoms experience a periodically pulsed or driven standing wave of light. By pulsing the usual sinusoidal lattice with slightly different periods we show that the diffusion rate is not only momentum dependent, i.e., D Dp, but takes a particular smooth and controllable form. We investigated the quantum dynamics and found that they are associated with a corresponding local break time t p Dp= h 2 . Since these break times vary by 2 orders of magnitude, this represents a strong effect. By simply varying the pulsing periods, we can specify a value of p, so that for particles moving in one direction D p 0, which means they absorb littl...

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“…Measuring p 2 (t) accurately can, however, still be complicated by problems with spurious tails in the momentum distribution, nevertheless, these problems can likely be overcome especially since the predicted effects do not require the experiments to be run for long times (see Ref. [31] for a recent measurement of the behavior near the quantum resonances including decoherence effects).…”

Section: Figmentioning

confidence: 99%