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Chinese journal of atomic and molecular physics

Quantum fluctuation dynamics in momentum spread of cold atoms

WANGZhong-jie, WangQin-Mou, HuangWan-Xia

Published Jan 1, 2003• 0 citations
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Abstract

Dynamics of the quantum system that consists of a cold atom in a modulated standing wave of light is analyzed using the time-dependent variational principle formulation based on squeezed coherent states. A group of ordinary differential equations describing evolution of two pairs of canonically conjugate variables (q(t), p(t); G(t), Π(t)) are derived where G(t) and Π(t) describe the quantum fluctuations of the system. It has been shown that a transition from the regular motion to the chaotic motion in G(t), Π(t) phase space. Quantum system seems to be capable to show the classical-like chaotic structure.

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Dynamics of the quantum system that consists of a cold atom in a modulated standing wave of light is analyzed using the time-dependent variational principle formulation based on squeezed coherent states. A group of ordinary differential equations describing evolution of two pairs of canonically conjugate variables (q(t), p(t); G(t), Π(t)) are derived where G(t) and Π(t) describe the quantum fluctuations of the system. It has been shown that a transition from the regular motion to the chaotic motion in G(t), Π(t) phase space. Quantum system seems to be capable to show the classical-like chaotic structure.
We investigate the classical and quantum dynamics of atoms moving in a phase-modulated standing light field. In both cases the width of the momentum distribution exhibits characteristic oscillations as a function of the modulation amplitude. We argue that at the maxima of these oscillations the system is chaotic, whereas in the valleys it is almost regular. Quantum localization appears only in the chaotic regime. We connect our analysis with a recent experiment [F. Moore et al., Phys. Rev. Lett. 73, 2974 (1994)].
In this paper the model of two level atomic momentum spread in amplitude and phase modulated standing light wave was investigated. this is a nonlinear quantum pendulum driven by a time dependent perterbation with two frequencies. This system shows chaotic behaviour in the classical limit. The system exists the characteristic of dynamical localization for the same parameters as that in the classical model correspoinding to it. Localization length of the system with two incommensurate perturbing frequency is much larger than that of the system with one perturbing frequency.
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.
Cold rubidium atoms are subjected to an amplitude-modulated far-detuned standing wave of light to form a quantum-driven pendulum. Here we discuss the dynamics of these atoms. Phase space resonances and chaotic transients of the system exhibit dynamics which can be useful in many atom optics applications as they can be utilized as means for phase space state preparation. We explain the occurrence of distinct peaks in the atomic momentum distribution, analyse them in detail and give evidence for the importance of the system for quantum chaos and decoherence studies.