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Physical Review A

Intensity correlations between the components of the resonance fluorescence triplet

C. A. Schrama, Gerard Nienhuis, H.A. Dijkerman, C. Steijsiger, H G M Heideman

Published Jun 1, 1992• 83 citations
Publisher

Abstract

We present a theoretical analysis of the intensity correlations between the spectral components of the resonance fluorescence triplet while allowing for detection time differences that are smaller than the inverse frequency width of the frequency filter. Explicit expressions are derived for the intensity correlation functions that are valid for all times. Furthermore, we present the results of measurements on these correlation functions for the $^{1}$${\mathit{S}}_{0}$${\mathrm{\ensuremath{\leftrightarrows}}}^{1}$${\mathit{P}}_{1}$ resonance transition of natural barium. In general, the results confirm the theoretical predictions.

DOI
10.1103/physreva.45.8045

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We present a theoretical analysis of the intensity correlations between the spectral components of the resonance fluorescence triplet while allowing for detection time differences that are smaller than the inverse frequency width of the frequency filter. Explicit expressions are derived for the intensity correlation functions that are valid for all times. Furthermore, we present the results of measurements on these correlation functions for the ^{1}$${\mathit{S}}_{0}$${\mathrm{\ensuremath{\leftrightarrows}}}^{1}$${\mathit{P}}_{1} resonance transition of natural barium. In general, the results confirm the theoretical predictions.
We study the photon correlations between the output of two spectral filters set within the fluorescence triplet of a two-state atom. The time uncertainty arising from the spectral resolution of the filters implies a possible interference between opposite orders of emission, contributing to the same detection order. Furthermore, the fluorescent emission is a quantum-mechanical process, and successive emissions in different components do not commute. The correlation functions are affected both by the memory time of the filters and by the noncommutativity of successive emissions. When the two filter bandwidths are larger than the widths of the components, this only modifies the short-time behavior of the correlation functions between two photons from different spectral components. For narrow filters, the entire correlation function is dominated by memory-time effects. Positive (bunching) correlations arise when the two filters are set at the same frequency, and also when they are positioned symmetrically at opposite sides of the driving frequency.
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.
In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields that pass through Fabry-Perot interferometers. Our general expression is then applied to study correlation signals in the limit of well separated spectral lines of the resonance fluorescence spectrum. In particular, we study the normalized second-order temporal intensity correlation functions in the case of the interferometers tuned to the components of the spectrum and obtain interferential corrections to the approximate results derived in the secular limit. In addition, we explore purely spectral correlations and show that they can fully be understood in terms of the two-photon cascades down the dressed state ladder.
Atomic inversion revivals are the first evidence of the quantum character of the radiation, predicted by the Jaynes–Cummings model, that are experimentally measurable in cavity quantum electrodynamics.1 We propose another test by studying the two time photon correlations between spectrally resolved components of resonance fluorescence spectrum of the coherent Jaynes–Cummings model. The spectrum raises from spontaneous emission between adjacent energy many folds, whose splitting is given by the Rabi frequency for every Fock state. This originates sideband discreteness that can be observed when the filter bandwidth is smaller than the sideband width (atom-cavity coupling). There is photon correlation only if these photons are from consecutive emissions in the dresssed lader, producing a frequency offset. Also, a photon from a sideband is more likely to be emitted before a photon from the other sideband when detuning is finite, in a fashion analogous to that studied by Aspect et al.2 for free space rf. Moreover, the decay is due solely to the filter bandwidth, reflecting lack of cavity losses. These correlations could be observed in presence of mixed fields, therefore are less dependant on the coherence of the experimental cavity fields than the revivals are.