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Chinese journal of atomic and molecular physics

Dynamical investigation on momentum spread of two-level atom by an amplitude-modulated and phase-modulated standing light wave

Zhong Wang

Published Jan 1, 2001• 0 citations
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Abstract

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.

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Chinese journal of atomic and molecular physics•Jan 1, 2003•0 citations
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.
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)].
We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck's constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation.
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.