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Physical Review A

Multiatom and transit-time effects on photon-correlation measurements in resonance fluorescence

Harry J. Kimble, M. Dagenais, L. Mandeļ

Published Jul 1, 1978• 226 citations
Publisher

Abstract

An expression is derived for the expected number of photon pairs separated by a time interval $\ensuremath{\tau}$ that are detected in photoelectric correlation measurements of an atomic beam, when due account is taken of the fluctuations of the number of radiating atoms and of the effect of their finite transit time through the field of view. The theoretical expression is checked against some recent measurements and good agreement is obtained.

DOI
10.1103/physreva.18.201

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An expression is derived for the expected number of photon pairs separated by a time interval \ensuremathτ\ensuremath{\tau}\ensuremathτ that are detected in photoelectric correlation measurements of an atomic beam, when due account is taken of the fluctuations of the number of radiating atoms and of the effect of their finite transit time through the field of view. The theoretical expression is checked against some recent measurements and good agreement is obtained.
The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.
Photoelectron counting sequences for single-atom resonance fluorescence are studied. The distribution of waiting times between photoelectric counts is calculated, and its dependence on driving-field intensity and detection efficiency is discussed. The photoelectron-counting distribution is derived from the waiting-time distribution. The relationship between photoelectron counting sequences and photon emission sequences is discussed and used to obtain an expression for the reduced state of the atom during the waiting times between photoelectric counts. The roles of irreversibility and the observer in atomic state reduction are delineated.
We consider a special kind of correlation measurements in single-atom resonance fluorescence, which includes detection of a spectrally filtered photon followed by detection of an unfiltered photon. We relate the stationary normalized intensity correlation function measured in such a scheme to the reduced atomic state following detection of the filtered photon. In the limit of well separated spectral lines of the resonance fluorescence spectrum, we obtain the analytic expression for the reduced atomic state. We show that at resonance excitation, this state is inverted when the filter is tuned in between the central line and any of the sidebands. This effect is interpreted as a result of quantum interference between the complementary atomic radiative transitions giving rise to the detected photon. We propose to observe this effect in measuring the equal-time field correlation function of the filtered and unfiltered photons as a function of the filter resonance frequency.
Extending the concept of the time-dependent physical spectrum introduced by Eberly and Wodkiewicz (1977) the authors present a formula for the n-fold time-resolved correlation spectrum depending on n time and n frequency arguments. The corresponding measuring device consists of n coupled photodetectors with frequency resolving equipment in front of each. As an application the authors consider the resonance fluorescence radiation of a two-level atom irradiated monochromatically. Under certain conditions the authors derive a simple expression for the n-fold detection probability of photons at time t i (i=1, . . ., n) with frequencies belonging to the central peak or to one of the sidebands of the fluorescence triplet.