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Conference on Lasers and Electro-Optics

Atomic inversion after a photon detection

Vyacheslav Shatokhin, S. Kilm

Published Aug 29, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.2000.908073

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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.
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.
We have studied the statistics of fluorescent photons emitted by a two-state atom in a laser beam in the limit where either the detuning or the Rabi frequency is large. For this case, the spectrum of resonance fluorescence has three separated lines. We have obtained closed form expressions for the conditional probability density for the emission of the nth photon and for the probability for emission of n photons in a time interval [0,T]. Our solutions are complementary to the known solutions for the case of perfect resonance.
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.
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.
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.