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Journal of Modern Optics

Two-photon Correlations in the Interference of a Resonance Fluorescence and a Classical Field

Th. Richter

Published Jan 1, 1991• 1 citation
Publisher

Abstract

The joint probability P 12 of detecting two photons at two different positions in the interference of a classical field with the resonance fluorescence field from a coherently driven two-level atom is investigated. We find that P 12 shows a stronger modulation with detector separation than is predicted by a classical wave theory. Under stationary conditions and if the driving field is strong enough to saturate the atomic transition, the relative modulation amplitude a of the P 12 pattern reaches its maximum possible value a = 1 for E → 0 (where E is the classical field amplitude), but simultaneously the whole phenomena vanishes, P 12 → 0. For equal intensities of the classical and the resonance fluorescent field we have a = ⅔. Compared with this, a classical wave theory predicts a possible maximum value of a = ½.

DOI
10.1080/09500349114550071

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The joint probability P 12 of detecting two photons at two different positions in the interference of a classical field with the resonance fluorescence field from a coherently driven two-level atom is investigated. We find that P 12 shows a stronger modulation with detector separation than is predicted by a classical wave theory. Under stationary conditions and if the driving field is strong enough to saturate the atomic transition, the relative modulation amplitude a of the P 12 pattern reaches its maximum possible value a = 1 for E → 0 (where E is the classical field amplitude), but simultaneously the whole phenomena vanishes, P 12 → 0. For equal intensities of the classical and the resonance fluorescent field we have a = ⅔. Compared with this, a classical wave theory predicts a possible maximum value of a = ½.
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 joint probability of simultaneously detecting four photons at at least two different points in the superposition field of two independent plane waves with random phases is calculated and compared with the results of a classical wave theory. There are important differences when the number of photons is small. In particular, if there is one photon in one beam and three photons in the other one, two two-photon detectors can be placed at positions such that they never both respond at the same time, even though the intensity of one beam is three times stronger than that of the other. This conclusion has no classical analogue.
Abstract Frequency-resolved photon statistics of resonance fluorescence generated from a two-level system driven by a strong laser field and a weak laser field with equal frequencies are studied. The frequency resolution of fluorescent radiation is described by quantum filtering dynamics, which is simulated theoretically by two single-mode quantum optical cavities with tunable frequencies to scan the incident fluorescent radiation. By calculating the two-photon intensity–intensity correlation functions in terms of the cavity modes, we demonstrate that two-color strong correlations of resonance fluorescence can be generated not only between the opposite sidebands, but also between the central band and one of the sidebands: although both sidebands are broadened due to the perturbation of the weak laser field on the strong-field dressed atom. We emphasize that these properties are in contrast to the conventional case of the standard single-atom Mollow triplet. Moreover, if the resonance frequencies of the two filtering cavities are tuned appropriately, broadband two-color strong correlations are predicted, and the physical origin is revealed from the perspective of quantum interference of photon emission dynamics. This can be considered as a feasible scheme for the design of broadband non-classical light sources, and may be beneficial to the quantum precise detection of atomic and molecular dynamics via quantum optical spectroscopy.
Frequency-resolved quantum correlation of resonance fluorescence is investigated in a two-atom radiating system. In this quantum radiating system, only one atom is driven by a laser field, and the spontaneous transition of the undriven atom resonates with one of the Rabi sidebands of the driven atom. A single-mode empty cavity is applied to serve as a Lorentzian filter to output the superbunched fluorescent photon pairs when its frequency is tuned to halfway between the central peak and one of the side peaks. In the case of large filter width, two-photon correlation signal and its physical correspondence can be bridged analytically in our approach. It reveals that this superbunching effect turns out to be the constructive quantum interference between a pair of coupled two-photon cascaded transitions. Ulteriorly, it is the consequence of the modulations of the unfiltered dressed-state transition amplitudes by the filter. Our analytical formalism also shows that, although the dipole-dipole interaction is usually weak, the interatomic coherence caused by this weak perturbation can also play a crucial role in breaking through the superbunching limit obtained from a single two-level atom in the same parameter regime. In addition to being a treasurable quantum pump to probe into the target quantum system, it is also found in our investigation that this superbunched fluorescence can serve as a promising quantum response in detecting this weak perturbation in the interior of the quantum source. A general case is also considered when the two-atom radiating system is monitored by two filter-detector monitoring systems. It is found that this filtered strong quantum correlation can be maintained even though the two photons are spatially separated.
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 discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.