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Physical Review A

Spectral correlations in resonance fluorescence

Gerard Nienhuis

Published Jan 1, 1993• 84 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.47.510

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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.
Frequency-resolved correlation (FRC) is investigated in fluorescent emission radiated from a $\mathrm{\ensuremath{\Lambda}}$-type atomic system by employing weak coupling regime between quantum emitter and cavities, in which each cavity substituting a Lorentzian filter is assumed to pass through only one fluorescent photon at a time so that the analytical discussions for time orderings can be carried out in a truncated Hilbert space with single-excitation state for each cavity mode. In the limit of bad cavity (large passband width of filter) and short delay, the conditional time ordering amplitudes are introduced with the help of conditioned dressed atom-photon states prepared by preselection to probe into the effect of preferential screening for time orderings of filter-detector systems. Meanwhile, the past quantum state formalism is also applied in FRC to further excavate their collective monitoring effect. Based on the obtained two-mode correlation signals, it is found that, in nonresonant two-photon cascaded processes, bunching and antibunching can appear in two opposite detection orderings, respectively, and can be switched. The physical origin is explored that the two different transition amplitudes of emitted photons from a common spectral band of resonance fluorescence are responsible for opposite time orderings, thus, the imbalance between two complementary time orderings can be enhanced, which is impossible to achieve in resonance fluorescence of two-level atoms. This mechanism is embodied in the conditional time ordering amplitudes produced by this detection theory of cavity modes.
We study the two-time correlation function of spectrally filtered light from a quantum mechanical light source. The bunching and anti-bunching properties of the photo-statistics of a field display the quantum nature of the source. We study whether these properties are affected by the presence of filters that are modelled by dielectric slabs. We quantize the radiation field in the presence of the filters and express the correlation function in terms of source operators. As a quantum source we take the resonance fluorescence of a driven two-level atom. We find that the spectral correlations depend on the linewidth of the filters. When the pass time of the filter is much longer than the time scale on which the source evolves, the presence of the filter can conceal the quantum nature of the source. However, quantum mechanical correlations between opposite side bands survive even for very narrow filters.
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^{1}1S0{\mathit{S}}_{0}S0​${\mathrm{\ensuremath{\leftrightarrows}}}^{1}$P1{\mathit{P}}_{1}P1​ resonance transition of natural barium. In general, the results confirm the theoretical predictions.
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.