Correlations between the emission of photons from an excited three-level atom with one transition more strongly driven than the other are studied. Antibunching, anticorrelation, and superbunching are exhibited in the four possible configurations: ``vee'' (V), ``lambda'' (\ensuremath{\Lambda}), and two cascades with the upper or lower transition strongly driven. We pay particular attention to the projection of the atom into particular states by the measurement of fluorescence, and its significance for detecting quantum jumps in the weak transition by observing the fluorescence from the strong transition. For incoherent excitation we find that cross antibunching (the anticorrelation between emissions of different types of photons) manifests itself as prolonged periods of darkness. For the V and the cascade configuration with a strongly driven lower transition, these periods herald the emission of a weak-transition photon; for the other cascade and the \ensuremath{\Lambda} configuration the periods are heralded by the emission of a weak-transition photon. For on-resonance coherent excitation, dark periods are extremely infrequent for the former two configurations, and are extremely long or infinite for the latter two.
Measurements on non-classical effects fall into two categories depending on whether the two intensities or photon counts to be correlated refer to a single light beam or to two different beams. The main experimental work in the single-beam case is on resonance fluorescence; the relevant theory is reviewed in some detail, with particular emphasis on the simpler aspects of the calculations. Alternative proposals for generating non-classical single beams by non-linear optical experiments are reviewed more briefly. A similar coverage of double-beam experiments is given, with a detailed account of the theory of non-classical correlations between the light beams generated in two-photon cascade emission, and a briefer survey of corresponding non-linear optical experiments.
Two-time correlations in the emissions of photons by a single atom of sodium in the presence of a coherent exciting field near resonance have been investigated. In the experiment sodium atoms in an atomic beam are excited by a perpendicular light beam from a tunable dye laser, and they are prepared by optical pumping to behave as two-level quantum systems. The fluorescent light is collected by a microscope objective in a direction that is approximately orthogonal to both beams and imaged on two photomultipliers. Photoelectric pulse correlations are measured in the presence of exciting fields of various strengths and for various detunings from the atomic resonance, and are found to exhibit significant nonclassical features. The results show clearly that the emitted photons exhibit antibunching, in good quantitative agreement with the predictions of quantum electrodynamics.
We present a theory of cascade emission from an array of
N fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is
J=0, that of the intermediate state is
J=1, and that of the upper state is
J=0. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of
N atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.
A scheme for the generation of nonclassical pairs of photons in atomic vapors is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows antibunching, unlike the case of the three-level cascade emission, which shows bunching. The Cauchy-Schwarz inequality, which is the ratio of the cross-correlation to the autocorrelation function, in this case is estimated to be
103−−106 for controllable time delay, and is one to four orders of magnitude larger compared to previous experiments. The choice of Doppler-free geometry, in addition to the fact that at three-photon resonance the excitation and deexcitation processes occur in a very narrow frequency band, ensures cleaner signals.
The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.