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arXiv:physics/0405046 · Physical Review Letters

Atoms in Double- δ -Kicked Periodic Potentials: Chaos with Long-Range Correlations

Philip H. Jones, M. M. A. Stocklin, G. Hur, T. S. Monteiro

Published Nov 22, 2004• 49 citations
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Abstract

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.

DOI
10.1103/physrevlett.93.223002

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We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it may also be an innate property of certain isolated, periodically driven quantum systems. Here, we experimentally realize the simplest such system, consisting of two coupled, kicked quantum rotors, by subjecting a coherent atomic matter wave to two periodically pulsed, incommensurate optical lattices. Momentum transport in this system is found to be radically different from that in a single kicked rotor, with a breakdown of dynamical localization and the emergence of classical diffusion. Our observation, which confirms a long-standing prediction for many-dimensional quantum-chaotic systems, sheds new light on the quantum-classical correspondence.
We discuss recent experimental and theoretical investigations of quantum dynamics in periodically kicked chaotic systems. These investigations are centred on a modified version of the classic δ-kicked rotor, as realized using laser-cooled caesium atoms. Dramatic phenomena, principally quantum accelerator modes, have been observed and these have inspired novel theoretical approaches to quantum chaos. The latter work has, in turn, prompted further experiments and the combined experimental and theoretical effort continues to lead to exciting advances in this field.
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.
Summary form only given. Dynamical localization is one of the signatures of quantum chaos most intensely studied in recent years. These studies rely on the experimental realization of a kicked rotor by placing cold atoms in a far detuned, periodically driven, stationary wave. For a set of parameters such that the classical limit of such a system shows a chaotic diffusive motion in the momentum space, quantum interferences have been shown to suppress the chaotic diffusion in the quantum case. The momentum distribution then presents a characteristic double exponential form. We have performed an experiment in which dynamical localization is studied in the presence of a stationary wave driven by two series of pulses that can have commensurable or incommensurable frequencies, which can be shown to be formally equivalent to perform the experiment in two dimensions. We have thus shown that localization is still observed when the two frequencies are commensurable, but that the classical diffusion in momentum space persists for a much longer time if the frequencies are incommensurable.
Contrary to a driven classical system that exhibits chaos phenomena and diffusive energy growth, a driven quantum system can exhibit dynamical localization that features energy saturation. However, the evolution of the dynamically localized state in the presence of many-body interactions has long remained an open question. Here we experimentally study an interacting 1D ultracold gas periodically kicked by a pulsed optical lattice, and observe the interaction-driven emergence of dynamical delocalization and many-body quantum chaos. The observed dynamics feature a sub-diffusive energy growth manifest over a broad parameter range of interaction and kick strengths, and shed light on an area where theoretical approaches are extremely challenging.
The central theme of this thesis is the directed transport of cold atoms in optical lattices. Several methods for producing such an outcome are proposed, experimentally realised and characterised, in both dissipative and non-dissipative regimes. Accordingly, this thesis may be thought to be composed of two parts. The first section reports results of directed transport in non-dissipative optical lattices, where we used the atom optics realisation of the delta-kicked rotor (DKR) as a model system. Initial experiments performed on this system showed evidence of dynamical localisation, the signature of quantum chaos, and we exploited the presence of the momentum boundary (a barrier to diffusion arising from the approximation of delta-kicks with finite width impulses) to produce asymmetric momentum diffusion. Breaking the DKR system symmetries produced directed diffusion due to chaotic dynamics alone. We observed directed transport in a spatially symmetric system whenever temporal symmetry was broken, and also when the spatial and temporal symmetry of the DKR were simultaneously broken. We also report the first experimental evidence for a 'double-DKR', where experiments performed using a kick sequence composed of closely spaced pairs of kicks instead of single kicks caused significant alterations in the observed behaviour of the kicked rotor system. The origin of this new behaviour was explained in the framework of kick-to-kick correlations and our results were found to be in excellent agreement with numerical simulations. The second part of this thesis describes the realisation of a Brownian ratchet in a 3D dissipative lattice, where fluctuations between different potential surfaces acted as the source of noise. These fluctuations were rectified by the application of a periodic, bi-harmonic driving force, which broke the temporal symmetry of the system. Both current reversal and stochastic resonance behaviour characteristic of a Brownian ratchet were observed.