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Physical Review A

Correlations in light emitted by three-level atoms

David Thomas Pegg, R. Loudon, P. L. Knight

Published Jun 1, 1986• 134 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.33.4085

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Physical Review A•Mar 1, 1996•34 citations
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.
We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density p[0{p}_{[0}p[0​,t)(t1{\mathrm{t}}_{1}t1​,t2{t}_{2}t2​,..., tn{t}_{n}tn​) which gives us the probability density that exactly n photons are emitted at times t1{t}_{1}t1​,t2{t}_{2}t2​,...,tn{t}_{n}tn​ by the atom in the time interval [0,t). We show that p[0{p}_{[0}p[0​,t) essentially factorizes into products of conditional densities c\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\tau}) that, given a photon is emitted at time zero, the next photon emission occurs at time \ensuremath{\tau}. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ``quantum jumps.''
Expressions are derived for the intensity correlations or degrees of second-order coherence within and between two light beams of different frequency generated by cascade emission from a three-level atom. The atoms are assumed to be excited by two monochromatic coherent light beams in resonance with the upper and lower pairs of levels that constitute the triplet. The two emitted beams individually show photon antibunching and the correlation between the beams shows another complementary kind of non-classical effect. It is suggested that measurements on the system described here would provide more detailed information on quantum effects in cascade emission than previous observations with direct excitation to the uppermost atomic level by electron bombardment.
We investigate the two-time intensity correlation functions of the fluorescence field emitted from a VVV-type three-level atom. We are particularly interested in the manner in which the atom emits photons in the presence of quantum interference. We show that under strong-field excitation quantum interference leads to anticorrelations of photons emitted from the atomic excited levels which can exist for extremely long times. This indicates that the excited atomic levels are not the preferred radiative states. We find that the atom spends most of its time in a superposition of the excited atomic levels from which it emits strongly correlated photons. The strong correlations are present only for a nonzero splitting between the excited levels, and for degenerate levels the correlations reduce to that of a two-level atom. Moreover, we find that the transition from the ground level to the symmetric superposition of the excited levels does not saturate even for a strong driving field. We also calculate the correlation functions for a weak driving field, and find that in this case the photon correlations are not significantly affected by quantum interference, but the atom can emit a strongly correlated pair of photons produced by a three-wave mixing process. Under appropriate conditions, with near-maximal quantum interference, it is possible to make the maximum value of the correlation function extremely large, in marked contrast with the corresponding case with no quantum interference.
The phenomenon of antibunching provides important support for the physical principle of the collapse of the wave function following a detection of a photon. In this paper we show that interrupted fluorescence in a three-level, V-configuration atom, with one transition strongly driven and one weakly driven, can be regarded as evidence supporting the complementary principle of ``collapse by nondetection.'' Use of this principle leads to the immediate deduction of remarkably simple general expressions for the average bright and dark periods, which allows these quantities to be calculated for both coherent and incoherent excitation without the need to solve the density-matrix equations, or even to find their long-term steady-state solutions. Thus the concept of collapse by nondetection appears to be not only valid but is also useful for predicting physically observable phenomena.
We examine the intensity correlation functions of the two fluorescent fields that are emitted from the top and middle states of a doubly driven three-level atom in the cascade configuration. Novel interference effects are shown. (i) Both of the fluorescent fields have anticorrelations which can exist for long times when the applied fields are on the two-photon resonance and far off one-photon resonances. (ii) Both of the fluorescent fields have strong correlations when the applied fields are far off one- and two-photon resonances. In particular, the extremely strong correlation occurs for the photons emitted from the top state. The above phenomena are traced to the multiple interference mechanisms.
We examine the various two-time fluorescence intensity correlations emitted by a driven three-level atom in a cascade configuration. For a strongly driven atom, the two intensity autocorrelation functions, one from the upper transition, the other from the lower transition, exhibit different behaviors. In addition to the an oscillation similar to the two-level intensity correlation we find an additional oscillation for the upper transition only. This is shown to be due to the spontaneous decay between the lower transition levels. \textcopyright{} 1996 The American Physical Society.