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arXiv:physics/0103097 · Journal of Modern Optics

Spectrum of light scattering from an extended atomic wave packet

B. DUBETSKY, P. R. Berman

Published Jan 1, 2002• 1 citation
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Abstract

The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are sensitive to the phase difference between the two components of the wave packet. Using this technique, one can establish the mutual coherence of the two components of the wave packet without recombining them.

DOI
10.1080/09500340110090800

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The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are sensitive to the phase difference between the two components of the wave packet. Using this technique, one can establish the mutual coherence of the two components of the wave packet without recombining them.
The spatial coherence of an atomic wavepacket can be detected in scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, nonoverlapping wavepackets. Spatial coherence manifests itself in the power spectrum of the emitted photons, whose spectral components can exhibit interference fringes as a function of the emission angle. The contrast and the phase of this interference pattern provide information about the quantum state of the center of mass of the scattering atom.
An experiment is described which is an analog of Young's double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other.
The power spectrum of the light scattered by a two-level atom in the presence of a coherent continuous-pulse-train driving field is analyzed. Separate expressions for the coherent and incoherent components of the spectrum are obtained. The coherent part of the spectrum consists of a series of spikes (delta functions) which are displaced from the optical carrier by multiples of the pulse repetition frequency. The incoherent spectrum can have fixed peaks at these same frequencies plus sidebands equally spaced on opposite sides of these fixed peaks. That is, the spectrum consists of a series of triplets. The special case of a two-mode driving field is treated numerically and graphs of spectra are presented.
The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7</=m</=12 for Rb; 5</=m</=7 for K) resonance transitions when a probe pulse is scattered by the wave packet established by the earlier (identical) pump pulse. The spatial and spectral characteristics of the UV emission are well described by axially phase-matched four-wave mixing, and all the prominent frequency components of the wave packets are associated with energy differences between pairs of excited states for which Diota=0 or Diota=2 . These results demonstrate that the wave packet modulates chi((3))of the medium, thus rendering the wave packet detectable.