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Physical Review

Coherent Resonance Fluorescence Excited by Short Light Pulses

David C. Burnham, R. Y. Chiao

Published Dec 10, 1969• 251 citations
Publisher

Abstract

Assuming infinite relaxation times and negligible pulse attenuation, we calculate the ringing produced when a resonant light pulse passes through a medium. These assumptions imply that each atom of the medium is excited identically and will therefore radiate coherently. Two models are used for the atoms of the medium: the classical harmonic oscillator and the two-level quantum-mechanical atom. The validity of the various approximations is discussed in detail.

DOI
10.1103/physrev.188.667

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Assuming infinite relaxation times and negligible pulse attenuation, we calculate the ringing produced when a resonant light pulse passes through a medium. These assumptions imply that each atom of the medium is excited identically and will therefore radiate coherently. Two models are used for the atoms of the medium: the classical harmonic oscillator and the two-level quantum-mechanical atom. The validity of the various approximations is discussed in detail.
Fluorescence has been detected from Rb atoms following narrow-line excitation by a short coherent optical pulse. The fluorescence oscillates as a function of the pulse area AAA with maxima for $A=\ensuremath{\pi},3\ensuremath{\pi},5\ensuremath{\pi},\dots{}$ and minima for $A=0,2\ensuremath{\pi},4\ensuremath{\pi},\dots{}$. In addition to demonstrating one of the simplest coherent optical effects, this experiment dramatizes the potential of the technique for determining dipole moments, pulse areas, relaxation times, and lifetimes. The details of the experimental apparatus are described. Results of a computer simulation of the experiment including the actuai excitation pulse shape, absorption frequency width, finite absorption (5-10% of pulse), and loss to a third level are given.
The resonance fluorescence of a two-level atom interacting with a laser pulse is studied, following the short-pulse approximation. The authors demonstrate that an explicit expression of the energy spectrum in terms of atomic-state amplitudes holds also for an off-resonance excitation. Some analytically solvable cases are studied in detail, showing that the main spectral properties of the fluorescence emitted under adiabatic and non-adiabatic pulsed excitation can be easily described. For the first time the continuous dependence of the fluorescence spectrum on laser detuning is reported for a smooth pulse.
A Green's function formulation of the problem of resonance fluorescence from a system of identical two level atoms is presented. The general formulation is suitable for the investigation of a variety of nonlinear phenomena, e.g., propagation of electromagnetic waves inside the medium, fluorescence from a finite medium, optical bistability, atomic correlations, and additional side bands. Translational motion, collisions, Coulomb dipole–dipole interaction, excitation transfer, and local field corrections are also included in the basic equations. The effect of atom–atom correlations in the relaxation mechanism (radiative or collisional) is also taken into account. Finally, the results are also presented in the "generalized dressed atom" (GDA) representation. Applications of the general theory will be given in a future paper.
The approximation of nonoverlapping lines is used to calculate spectra of resonance fluorescence and Raman scattering when two- and three-level atoms are pumped by a smooth pulse of duration comparable with the excited-state lifetime. The difference between the quasienergy terms, that determines the satellite frequency, depends on time and has the same value twice, at the pulse leading and trailing edges, so that interference may occur between the radiation produced in the appropriate parts of the pulse. However, the interference pattern is blurred since radiative broadening destroys the coherence. Relationships are obtained between the parameters for which interference may be observed. An analysis is made of the change to short pulses when allowance can be made for the scattered field using the first order of perturbation theory.
A simple theoretical model is formulated which describes dynamical features of the interaction of two-level atoms with a continuum of radiation oscillators. In particular, this paper is concerned with resonance scattering by single atoms in the presence of an external classical field, and spontaneous emission by a system of identical atoms. In the case of resonance scattering, the response of an atom to rapid changes of the amplitude of the external field is studied. The model for spontaneous emission by a system of atoms is based on the assumptions that all atoms have the same resonance frequency, and that the atoms are contained in a volume whose extension is small compared with the wavelength of the emitted radiation. The complete evolution of a system of mmm atoms is determined by a set of coupled first-order linear differential equations, and explicit solutions are presented for the values m=1,2,3,4,and8m=1,2,3,4, \mathrm{and} 8m=1,2,3,4,and8. Pair correlations of the atoms and photon-number fluctuations are discussed. An approximation for resonance fluorescence by a system of atoms with a broad distribution of resonance frequencies is included in an Appendix.