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arXiv:physics/9809010 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Chaotic dynamics of cold atoms in far-off-resonant donut beams

X. M. Liu, Gerard J Milburn

Published Mar 1, 1999• 6 citations
arXivHTMLPDF

Abstract

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the $(x,y)$ plane for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos.

DOI
10.1103/physreve.59.2842

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We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y)(x,y)(x,y) plane for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos.
In this thesis, I study the classical and quantum nonlinear dynamics of two-level atoms in a donut beam, an evanescent beam guiding atoms in a hollow fiber and atoms in an optical standing wave of high-finesse cavity. The laser fields are far-off-resonant beams. The two dimensional classical nonlinear dynamics of atoms in a donut beam and an evanescent-wave in hollow fiber are investigated. Chaotic dynamics exists for classic dynamics of cold atoms in a donut beam and hollow fiber, when the intensity of the beam is periodically modulated. The atoms will accumulate on several annular regions when the system enters a regime of global chaos. The two dimensional quantum nonlinear dynamics of an atom in hollow fiber are investigated. The quantum system of single atom dynamics in cavity QED is investigated. For continuous observation of the nonlinear dynamics of single atom trapped in a high-finesse cavity by a standing wave with intensity modulation, the conditional Hilbert space dynamics of this system, subject to measurement induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. The influence of decoherence due to homodyne measurement is investigated. The evolution of Wigner function shows that the higher order quantum correction terms will play an important role together with potential nonlinearity and measurement strength. The decoherence will result in a remarkable improvement for classical-quantum correspondence.
Summary form only given. One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a dosed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off the beams of light. These beams create the desired spatial pattern, forming an "optical billiard". The system is extremely flexible due to the high level of control of the billiards geometry, the initial atomic sample, and the available measurement techniques. We find an excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new experimental testing ground for classical and quantum chaos.
We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y)(x,y)(x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.
The possibility of experimental observation of chaotic motion of cold atoms in a one-dimensional rigid optical lattice without any modulation of its parameters and additional impact is demonstrated theoretically and numerically. This effect of deterministic chaos arises near the optical resonance due to the nonlinear coupling of electronic and mechanical degrees of freedom in the atom. In a certain range of resonance detunings, at each crossing of the lattice-forming standing wave node by the atom, the atomic dipole moment changes pseudorandomly in a step-like manner, accompanied by an appropriate change in the atom momentum. This leads to the effect of chaotic wandering of atoms, possessing the properties of the classical deterministic chaos, namely, to the exponential sensitivity of atomic trajectories to small variations of the initial conditions and/or the control parameters. With time, part of atoms from the initial cloud changes the direction of their motion to the opposite one, which can be detected in a real experiment. Numerical experiments with lithium atoms with the spontaneous emission taken into account show that by varying the laser radiation intensity (normalised detuning of resonance) in the rigid optical lattice, one can implement the transition from the regular regime of the atomic motion to the chaotic wandering in a real experiment.
Abstract Coherent dynamics of cold atoms in a 2D optical lattice with interfering laser beams is studied with account for internal and external degrees of freedom of an atom. A system of differential equations for coupled degrees of freedom obtained in the semiclassical approximation has regular and chaotic solutions depending on the atomic-field detuning from resonance. The Hamilton chaos is manifested in the form of chaotic Rabi oscillations and random walks of cold atoms in the lattice for relatively small resonance detunings. It is shown that the deterministic chaos appears as a result of jumps in the value of the electric dipole moment of an atom approaching the nodes of a 2D standing wave. This in turn causes a pseudorandom behavior of momenta of atoms and, as a consequence, their random walks in the absolutely rigid 2D optical lattice without any external modulation of its parameters. It is shown in numerical experiments with 106 atoms that their distributions over the lattice for different resonance detunings differ significantly. This fact can be used for detecting the effect of random walks of cold atoms in a real experiment by the absorption image method.