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Physical Review A

Dynamical localization of atomic-beam deflection by a modulated standing light wave

R. Graham, Martin Schlautmann, P. Zoller

Published Jan 1, 1992• 227 citations
Publisher

Abstract

The deflection of an atomic beam passing a standing-wave laser field in front of an oscillating mirror occurs by chaotic diffusive momentum transfer in a classical description and, as we show, is limited by dynamical localization quantum mechanically. An experiment to observe this quantum effect in an atomic beam is proposed.
DOI
10.1103/physreva.45.r19

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We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.
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 have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.
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.