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Physical Review A

Dissipative nonlinear quantum dynamics in atomic optics

Sigurd Dyrting, Gerard J Milburn

Published Apr 1, 1995• 19 citations
Publisher

Abstract

It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom's internal state, a band structure, and a time-dependent dissipative process.

DOI
10.1103/physreva.51.3136

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It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom's internal state, a band structure, and a time-dependent dissipative process.
Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck’s constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 ° out of phase with the initial state.
A new effect of chaotic motion of the center of mass of a cold atom in the coherent field of a standing light wave in a high-finesse Fabry-Pérot cavity is theoretically predicted and numerically implemented in the absence of any random fluctuations due to spontaneous emission. Numerical experiments demonstrate that the Hamiltonian chaos arises near resonance in the range of parameters characteristic of the strong coupling regime that was implemented in recent experiments. The effect is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
In this manuscript I present an experimental investigation of the dynamics of an ultracold gas of bosonic ytterbium loaded into optical lattices and exposed to resonant light. The interaction between atoms and light makes it possible to study the coherence properties of the gas. The resonant driving is performed on the relevant optical transitions featured by ytterbium. On the one hand, I demonstrate the coherent driving of the internal state of the atoms on the clock transition, the excited state of which is metastable and can not spontaneously decay, thus preserving the coherence of the gas. The temporal internal dynamics in a deep lattice allows me to measure the collisional properties at low temperature for both clock states. On the other hand, I use the spontaneously emitted photons of the intercombination transition excited level to induce a coupling to the atomic external degrees of freedom. I present the momentum diffusion of a superfluid excited on this transition. Strong interactions between atoms slow down the decoherence and lead to an anomalous sub-diffusive relaxation. A simple model comprising atomic motion, interactions and dissipation accounts for our observations. A theoretical study of the dissipative dynamics in optical lattices sheds light on complementary phenomena such as induced dipole-dipole interactions or collective effects in spontaneous emission.
The nonlinear dynamical effects of synchronization and bifurcations of Rabi oscillations and oscillations of the center of mass of an atom moving in the field of a standing light wave are theoretically and numerically examined. After completion of a transient process, synchronized oscillations, stable with respect to small noise, are established both upon ballistic motion of the atom and upon its oscillations in the optical potential well. The bifurcations of limit cycle generation with different periods (tripling of the period is most pronounced) and the passage to a chaotic strange attractor through an intermittency are obtained.
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.