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Physical Review

Interference Effects in the Resonance Fluorescence of "Crossed" Excited Atomic States

P. A. Franken

Published Jan 15, 1961• 331 citations
Publisher

Abstract

The recent spectroscopic method developed by Colegrove, Franken, Lewis, and Sands exploits interference effects which occur in the resonance fluorescence of atoms exhibiting pairs of "crossed" excited states. Some of the theoretical features of the technique are discussed in terms of the formalism developed by Breit from which the salient features of the observed lineshapes can be readily deduced. Alternative derivations of the Breit formula are given together with a discussion of the nature and representation of the requisite resonance radiation.

DOI
10.1103/physrev.121.508

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The recent spectroscopic method developed by Colegrove, Franken, Lewis, and Sands exploits interference effects which occur in the resonance fluorescence of atoms exhibiting pairs of "crossed" excited states. Some of the theoretical features of the technique are discussed in terms of the formalism developed by Breit from which the salient features of the observed lineshapes can be readily deduced. Alternative derivations of the Breit formula are given together with a discussion of the nature and representation of the requisite resonance radiation.
An interaction Hamiltonian analogous to that in a coupled Lee model is used to calculate the transition matrix appropriate for the description of the anticrossing effect in optical resonance fluorescence. The transition matrix is found to contain two terms (in addition to those for resonance scattering through each of the coupled states) which exist in the amplitude only because the damping matrix in the coupled representation is not diagonal. This matrix is diagonal when the uncoupled states have equal radiative widths, and the resonance scattering intensity is then given by the Breit formula. This result justifies the application by Eck, Foldy, and Wieder of the Breit equation to their initial discovery of the anticrossing effect even though this formula would not be expected to apply to the general anticrossing situation. The crossing effect can also be discussed as a special case of the approach presented.
In the context of laser spectroscopy we consider the effects of interference between the spontaneous emission to a common lower level from neighbouring, closely spaced, excited-state levels. In particular the effects on the fluorescence spectrum and on the measured positions of the line centres are described. A formalism, based upon the atomic density matrix, is developed quantitatively to describe these effects within complex hyperfine systems such as the sodium D-lines. Where possible, we have tried to simplify the resultant equations, defining the magnitude of the various fluorescent components and establish a general result for the phase of each component. Finally, the formalism is applied to the particular case of the sodium D1-line, where very different results are obtained depending on whether optical pumping into unobserved states is included, or omitted, from the calculation.
The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when two Zeeman levels of an atom are brought into coincidence ("crossed") by the application of an external magnetic field. "Anticrossing" refers to the case where the two levels involved are coupled by a small static interaction. In this paper the general expression for an anticrossing signal is given and its predictions compared with signals observed in the 22P2 ^{2}P22P term of Li. It is shown that anticrossings produce signals in many experimental situations for which there would be no signal from a normal level crossing.
The effect of the laser linewidth on the resonance fluorescence spectrum of a two-level atom is revisited. The novel spectral features, such as hole-burning and dispersive profiles at line centre of the fluorescence spectrum are predicted when the laser linewidth is much greater than its intensity. The unique features result from quantum interference between different dressed-state transition channels. c # 1999 Elsevier Science B.V. PACS : 42.50.Hz; 32.80.-t Keywords: Resonance fluorescence; Laser linewidth; Quantum interference The study of resonance fluorescence spectra has provided much fundamental insight into the subject of atom1light interactions. It is well known that for weak laser field excitation, the spectrum exhibits a Lorentzian lineshape, whereas it develops into the Mollow triplet for strong field excitation [1]. The latter is a direct signature of stimulated emissions and absorptions of the atom during the time interval for one spontaneous decay. Recently, considera...
In a recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)], polarization-sensitive measurements of the fluorescence from two four-level ions driven by a linearly polarized laser were made. Depending on the polarization chosen, different degrees of interference were observed. We carry out a theoretical and numerical study of this system, showing that the results can largely be understood by treating the atoms as independent radiators which are synchronized by the phase of the incident laser field. The interference and its loss may be described in terms of the difference between coherent and incoherent driving of the various atomic transitions in the steady state. In the numerical simulations, which are carried out using the Monte Carlo wave-function method, we remove the assumption that the atoms radiate independently and consider the photodetection process in detail. This allows us to see the total interference pattern build up from individual photodetections and also to see the effects of superfluorescence, which become important when the atomic separation is comparable to an optical wavelength. The results of the calculations are compared with the experiment. We also carry out simulations in the non-steady-state regime and discuss the relationship between the visibility of the interference pattern and which-path considerations.