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Soviet Journal of Quantum Electronics

Quantum beats in photon correlations of spontaneous emission from two nonidentical atoms

Z. Ficek, R. Tanaś, S. Kielich

Published Jun 30, 1988• 1 citation
Publisher

Abstract

The appearance of quantum beats in a two-time second-order correlation function is discussed for the case of spontaneous emission from two nonidentical atoms. The atoms are separated by distances comparable with the resonance wavelength and have different transition frequencies and natural line widths. It is shown that quantum beats appear for nonidentical and identical atoms. In the latter case the dipole–dipole interaction between the atoms is a necessary condition for the appearance of quantum beats. Two mechanisms lead to quantum beats in the case of nonidentical atoms and such beats may appear even for independent atoms. The effect is similar to that of interference between independent beams.

DOI
10.1070/qe1988v018n06abeh012288

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The appearance of quantum beats in a two-time second-order correlation function is discussed for the case of spontaneous emission from two nonidentical atoms. The atoms are separated by distances comparable with the resonance wavelength and have different transition frequencies and natural line widths. It is shown that quantum beats appear for nonidentical and identical atoms. In the latter case the dipole–dipole interaction between the atoms is a necessary condition for the appearance of quantum beats. Two mechanisms lead to quantum beats in the case of nonidentical atoms and such beats may appear even for independent atoms. The effect is similar to that of interference between independent beams.
The two-time second-order correlation function of the electric field spontaneously emitted by a system of two non-identical two-level atoms with different transition frequencies and different natural linewidths is calculated from the viewpoint of quantum beats and photon anticorrelation effects. Our analytical solution shows that the intensity correlation exhibits quantum beats. The quantum beats are shown to appear even if the two atoms are independent. For identical atoms, beats appear only if dipole–dipole interaction between the atoms is included, and they are then strongly dependent on the direction of observation with respect to the line connecting the two atoms. The anticorrelation effect between the photons emitted in different directions is also discussed. It is shown that for a single-time correlation function the condition for anticorrelation is independent of interatomic interactions. For a two-time correlation function, interatomic interactions reduce the anticorrelation effect.
Spontaneous emission from two non-identical two-level atoms is examined from the viewpoint of quantum beats and super-radiant effects. Our analytical solution, illustrated graphically, shows that the total radiation rate exhibits temporal sinusoidal modulation (beats). The beats result from the fact that the atoms have different transition frequencies and different natural linewidths. For small interatomic separations, the total radiation rate is greater than its initial value. This ‘super-radiant’ property is absent in the case of noninteracting atoms, as well as for two identical atoms. In the case when the atoms are separated by distances much smaller than the resonant wavelength, the population trapping effect can take place in such a system.
The cooperative spontaneous emission from three identical, initially excited two-level atoms separated by distances much smaller than the resonance wavelength is studied taking into account the dipole-dipole near-field interaction. Approximate expressions are obtained for the time evolution of the atomic system, the radiated intensity and the one-time intensity correlation function. As a new result the authors find that the near-field interaction may lead to the occurrence of beats in the intensity. Moreover, the destructive effect of the near-field interaction on the coherence properties of the emitted radiation is discussed.
Spontaneous emission from a multilevel atom is studied from the viewpoint of quantum beats. The master equation describing the atomic dynamics is shown to have some parameters that oscillate at the beat frequencies, and because of this a Pauli type of master equation for the diagonal elements of the density matrix is not obtained. As a result, the transition rates in the atomic system show the characteristic beats. The relation of the rate of change of the energy of the atomic system to the total power radiated in the far zone is also established. The normally and antinormally ordered correlation functions of the spontaneously emitted radiation are calculated under the approximation that the level widths are much smaller than the beat frequencies. The contribution arising from the interference of the free field and the source terms to antinormally ordered correlations is carefully evaluated. The nature of beats present in normally and antinormally ordered correlations is discussed, and their detection from the viewpoint of causing transitions in another atom is considered. The change in the nature of beats due to atomic collective effects is studied. Finally, it is shown that because of quantum effects, intensity correlations do not show any beats.
The time evolution of the populations of the collective states of a two-atom system in a squeezed vacuum can exhibit quantum beats. We show that the effect appears only when the carrier frequency of the squeezed field is detuned from the atomic resonance. Moreover, we find that the quantum beats are not present for the case in which the two-photon correlation strength is the maximum possible for a field with a classical analog. We also show that the population inversion between the excited collective states, found for the resonant squeezed vacuum, is sensitive to the detuning and the two-photon correlations. For large detunings or a field with a classical analog there is no inversion between the collective states. Observation of the quantum beats or the population inversion would confirm the essentially quantum-mechanical nature of the squeezed vacuum.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.