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Physical Review A

Correlation measurements in resonance fluorescence with spectral resolution and atomic inversion via detection of a spectrally filtered photon

Vyacheslav Shatokhin, S. Ya. Kilin

Published Jan 4, 2001• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.63.023803

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Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
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.
Spectrally resolved detection of single atom resonance fluorescence in the limit of well-separated spectral lines is considered. By using a special type of correlation measurements over the fluorescent field, in which a filtered photon detection is followed by an unfiltered photon detection, we obtain a conditioned atomic state following the filtered photon detection. The properties of the atomic state following detection of the reflected photon are studied and interpreted on the basis of quantum interference between the dressed states. Measurement operators associated with the detection of the passed and reflected photons are derived and used to construct the master equation for the atomic density matrix subjected to continuous spectral detection, the filter tuning being arbitrary.
Frequency-resolved quantum correlation of resonance fluorescence is investigated in a two-atom radiating system. In this quantum radiating system, only one atom is driven by a laser field, and the spontaneous transition of the undriven atom resonates with one of the Rabi sidebands of the driven atom. A single-mode empty cavity is applied to serve as a Lorentzian filter to output the superbunched fluorescent photon pairs when its frequency is tuned to halfway between the central peak and one of the side peaks. In the case of large filter width, two-photon correlation signal and its physical correspondence can be bridged analytically in our approach. It reveals that this superbunching effect turns out to be the constructive quantum interference between a pair of coupled two-photon cascaded transitions. Ulteriorly, it is the consequence of the modulations of the unfiltered dressed-state transition amplitudes by the filter. Our analytical formalism also shows that, although the dipole-dipole interaction is usually weak, the interatomic coherence caused by this weak perturbation can also play a crucial role in breaking through the superbunching limit obtained from a single two-level atom in the same parameter regime. In addition to being a treasurable quantum pump to probe into the target quantum system, it is also found in our investigation that this superbunched fluorescence can serve as a promising quantum response in detecting this weak perturbation in the interior of the quantum source. A general case is also considered when the two-atom radiating system is monitored by two filter-detector monitoring systems. It is found that this filtered strong quantum correlation can be maintained even though the two photons are spatially separated.
Summary form only given. Spectral detection of resonance fluorescence allows to regard atomic spectra as a sequence of elementary scattering events accompanied by emissions of photons with different frequencies. What the reduced atomic state (RAS) is after such a photon detection represents fundamental interest and appears important in understanding some correlation experiments. We report about derivation of analytic expression for the RAS for the important particular case of the well separated spectral lines of the resonance fluorescence spectrum.
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.
Abstract Frequency-resolved photon statistics of resonance fluorescence generated from a two-level system driven by a strong laser field and a weak laser field with equal frequencies are studied. The frequency resolution of fluorescent radiation is described by quantum filtering dynamics, which is simulated theoretically by two single-mode quantum optical cavities with tunable frequencies to scan the incident fluorescent radiation. By calculating the two-photon intensity–intensity correlation functions in terms of the cavity modes, we demonstrate that two-color strong correlations of resonance fluorescence can be generated not only between the opposite sidebands, but also between the central band and one of the sidebands: although both sidebands are broadened due to the perturbation of the weak laser field on the strong-field dressed atom. We emphasize that these properties are in contrast to the conventional case of the standard single-atom Mollow triplet. Moreover, if the resonance frequencies of the two filtering cavities are tuned appropriately, broadband two-color strong correlations are predicted, and the physical origin is revealed from the perspective of quantum interference of photon emission dynamics. This can be considered as a feasible scheme for the design of broadband non-classical light sources, and may be beneficial to the quantum precise detection of atomic and molecular dynamics via quantum optical spectroscopy.
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.