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arXiv:1608.01480 · Physical Review A

Correlation functions in resonance fluorescence with spectral resolution: Signal-processing approach

Vyacheslav Shatokhin, S. Ya. Kilin

Published Sep 20, 2016• 14 citations
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Abstract

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.

DOI
10.1103/physreva.94.033835

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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.
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.
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.
The theory of the intensity correlations between photons of different frequencies is re-examined from basic principles and is found to lead to an expression for the correlation function containing operator products which are normally ordered in time. This expression leads to results which are free of certain extra contributions that arise in another version of this theory which contains non-normally ordered products. The analysis presented is based on a description of the frequency-filtering process in terms of Fabry-Perot interferometers. The mirrors of the interferometers are modelled as classical dielectrics. The EM field in the presence of these dielectrics is then quantised and the intensity correlation function defined in terms of these modified field operators. The results are examined in detail for the case of a light field radiated by a two-level atom.
We calculate the second-order correlation function for the atomic fluorescence in the two-photon resonance operation of a driven dissipative Jaynes–Cummings oscillator. We employ a minimal four-level model comprising the driven two-photon transition alongside two intermediate states visited in the dissipative cascaded process, in the spirit of Shamailov et al. (2010). We point to the difference between the output of a JC oscillator exhibiting two-photon blockade and the scattered field of ordinary resonance fluorescence, and discuss the quantum interference effect involving the intermediate states, which is also captured in the axially transmitted light. The spectrum and intensity correlation of atomic emission explicitly reflect the particulars of the cascaded model.
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.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.