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Doklady Physics

Resonance fluorescence statistics of a two-level atom in feedback loop

V. A. Tomilin, Leonid V. Il'ichov

Published Oct 1, 2013• 5 citations
Publisher

Abstract

Statistics of photoemission events into the components of a triplet of resonance fluorescence of a two-level atom in a classical optical field, the phase of which changes by π upon the detection of spontaneous photon, is compared with the case when the feedback is absent. In contrast to the known problem on the statistics of resonance fluorescence of a two-level atom, a grouping of photocounts should be observed in each separate side component of the triplet. Anticorrelation of photoemission into side components is also predicted, and the type of correlations between the emission into the central component of the triplet and into any of the side ones can be controlled by varying the detuning of the radiation frequency from the resonant value.

DOI
10.1134/s1028335813100042

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Statistics of photoemission events into the components of a triplet of resonance fluorescence of a two-level atom in a classical optical field, the phase of which changes by π upon the detection of spontaneous photon, is compared with the case when the feedback is absent. In contrast to the known problem on the statistics of resonance fluorescence of a two-level atom, a grouping of photocounts should be observed in each separate side component of the triplet. Anticorrelation of photoemission into side components is also predicted, and the type of correlations between the emission into the central component of the triplet and into any of the side ones can be controlled by varying the detuning of the radiation frequency from the resonant value.
A theoretical analysis of the resonance fluorescence of a two‐level atom in a classical monochromatic field with feedback phase switching depending on the fluorescence triplet component which the last spontaneously emitted photon belongs to is presented. The considered feedback loop is a hybrid quantum‐classical system. Statistics of photoemissions into the triplet components is investigated as well as correlations between the components. In contrast to the well‐known resonance fluorescence of a two‐level atom without feedback phase switching, a bunching of photocounts is predicted in each side‐band, and successive photoemissions into different side‐bands manifest antibunching. The type of the statistics can efficiently be controlled by the frequency detuning of the external field. In many points the considered feedback scheme provides drastically different statistical features of fluorescence when compared with the scheme of frequency‐unselective feedback phase switching. image
The statistics of photoemission events of a pair of closely spaced two-level atoms is calculated in a classical light field whose phase is changed by π after the detection of each spontaneous photon. This statistics is compared with the statistics in the case when the feedback is missing. In both cases, one can observe noticeable antibunching of photons in the range of parameters where no antibunching is observed in a single-atom system. The feedback substantially increases the antibunching. This effect manifests itself more strongly in relatively weak fields and for considerable frequency detunings.
The resonance fluorescence spectrum of a two-level atom in a classical light field, whose phase is changed by a feedback system by π after the detection of each spontaneous photon, has been calculated. The spectrum resembles the well-known Rautian-Mollow triplet. However, the sidebands become sharply asymmetric at a nonzero frequency detuning of the light field from the atomic resonance transition. In addition, the spectrum retains the pronounced triplet shape even beyond the secular approximation, when the sidebands of the Rautian-Mollow structure become unresolved in the absence of the feedback.
The problem of the statistics of photoemission events in a specified direction and with a given polarization is solved for a resonantly fluorescing atom with degenerate levels. The degeneracy of the levels is taken into account within the semiclassical approach to the description of the atomic angular momentum. Relationships for the probability distribution of photoemission events in a specified solid angle and with a given helicity are derived for all components of the resonance fluorescence triplet. The results obtained make it possible to elucidate the influence of the polarization of a pump field on the statistics and correlations of photoemission events of different types.
Abstract We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach to this type of problem by considering a Kolmogorov equation for the probability distribution of the atomic state, which takes into account first the deterministic evolution of this state under the effect of the incoming laser beam and second the random emission of photons during the spontaneous decay of the excited state(s) to the ground state. This approach yields solvable equations in the two level atom case. For the three level atom case we set the problem and clearly define its frame. The results obtained are valid in both opposite limits of rare and frequent spontaneous decay, compared to the period of the optical Rabi oscillations due to the interaction between resonant excitation and atomic levels. Our analysis gives access to various statistical properties of the fluorescence light, including one showing that its fluctuations in time are not invariants under time reversal. This result makes evident the fundamentally irreversible character of quantum measurements, represented here by the emission of photons of fluorescence.