How to characterize the dynamics of cold atoms in non-dissipative optical lattices?

Hennequin, Daniel; Verkerk, P.

doi:10.1098/rsta.2010.0027

Cited by 2 publications

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“…The effects of classical and quantum chaos with cold atoms in 2D and 3D OLs have been theoretically and numerically considered recently in [51][52][53][54][55]. Some aspects of classical and quantum chaos with atoms, interacting with electromagnetic fields, have been discussed in [56,57].…”

Section: Cold Atoms In Optical Latticesmentioning

confidence: 99%

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Prants

2017

Phys. Scr.

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This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

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Section: Cold Atoms In Optical Latticesmentioning

confidence: 99%

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Prants

2017

Phys. Scr.

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“…Hennequin & Verkerk (2010) present novel work addressing how to measure such dynamics. Buscarino et al (2010) use chaotic dynamics for programming the trajectories of robots for the same reasons that Metcalfe et al (2010) do for mixing-for better search and discovery within unknown landscapes.…”

Section: Experimental Nonlinear Dynamicsmentioning

confidence: 99%

Experimental nonlinear dynamics

Gluckman

2010

Phil. Trans. R. Soc. A.

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Although it is difficult to point to a definite origin of the field of nonlinear dynamics, it evolved in part from attempts to understand two fundamentally different types of deterministic systems-very simple systems with as few as three variables on the one side that generate erratic non-periodic dynamics, exemplified by the three-body problem; and nearly infinite dimensional systems, such as fluids, that transition from very well-behaved dynamics through a range of increasingly complex space and time-varying dynamics, exemplified by the transitions from laminar to turbulent hydrodynamic flows.By the 1980s, the nonlinear dynamics community fitted roughly into two camps, those looking at and harnessing low-dimensional chaos-the emergence of complex unpredictable behaviour from systems with few degrees of freedom; and those looking at pattern formation-or the emergence of order, or coherentstructured dynamics in space and time-from systems with infinite degrees of freedom. The classic experimental systems for the study of, and application of, chaos were circuits and pendulums, lasers and population dynamics. Pattern formation was studied in fluid flows, crystal growth dynamics, chemical reactions and biology. Often, there was cross-pollination between these camps in developed theoretical tools, computational hardware, data analysis and visualization technology and experimental approach. The objectives overall were to both understand the origins of the phenomena and provide insight into how to harness the origins of complexity, exemplified in the 1990s by the development of chaos control techniques.The current issue is a cross-sectional sampling of the broad experimental applications now addressed in the nonlinear dynamics community. It starts with a solution to a classic hydrodynamic problem in Metcalfe et al. (2010). The challenge addressed is how to optimally mix fluids-critical, for example, in chemical reactors and heat exchangers-with simple laminar, low-energy, flows. Efficient mixing brings arbitrary pairs of fluid particles together. The simplest of such flows does not have the mixture of convergent and divergent points needed to do so. But, as the authors demonstrate, super-positions of such flow patterns, achieved by alternating between boundary conditions, yield highly chaotic fluid trajectories and therefore ideal mixing.The next two articles address issues and applications in chaotic dynamics. In the 1990s, atomic physics was essentially re-born with the perfection of techniques to greatly cool and trap individual, or small numbers of, atoms (Letokhov et al. 1995). Such systems then allow for real experimental systems Networks abound both in nature and in our man-made world. Understanding the underlying structure of such networks, how the individual elements' dynamics determines and is modulated by the group dynamics, how information is processed and transmitted through such networks and how robust they are to changes in connections is currently a major undertaking. Kocarev et al. (2010) address one ...

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How to characterize the dynamics of cold atoms in non-dissipative optical lattices?

Cited by 2 publications

References 26 publications

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Experimental nonlinear dynamics

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