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Journal of Experimental and Theoretical Physics

Statistics of resonance fluorescence of a pair of atoms in a feedback loop

V. A. Tomilin, L. V. Il’ichev

Published Feb 1, 2013• 6 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776113010184

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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.
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 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.
We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.
Photon antibunching in resonance fluorescence - the emission from a single, resonantly driven two-level quantum emitter - is a paradigmatic signature of nonclassical light. Photon entanglement, by contrast, manifests as correlations that can defy any classical description and is typically regarded as a distinct quantum effect. Here, we experimentally extract pairs of narrowband, time-bin-entangled photons from the antibunched resonance fluorescence of a single trapped atom. We verify entanglement via violation of the CHSH Bell inequality and by reconstructing the two-photon density matrix. The observed correlations vanish when the coincidence time window exceeds the antibunching timescale, revealing underlying multimode entanglement in the emitted field. Our results establish a direct link between photon antibunching and photon-photon entanglement, unifying two canonical signatures of nonclassical light.
Conditional homodyne detection (CHD) allows a fresh view of the nonclassicality of optical fields. A balanced homodyne detector replaces a photodetector in the Hanbury-Brown-Twiss setup of photon correlations, thus measuring a quadrature (amplitude) of the field on the cue of a photon detection. In CHD, both quadratures of a quantum field violate classical inequalities even if photon correlations look classical. We calculate the amplitude-intensity correlations for the resonance fluorescence of a two-level atom and a three-level atom in the V configuration, notable producers of quantum effects (antibunching, squeezing, and sub-Poissonian statistics). In the V atom, where we consider that the ground state is coupled strongly (weakly) to a short (long) lived state, the strong transition resembles the two-level atom features, albeit with larger oscillations and a slower decay. However, the autocorrelation of the fluorescence of the weak transition is clearly asymmetric around a zero delay, indicating the breakdown of detailed balance, and violating the inequalities by orders of magnitude due to the low photon flux. Cross correlations of strong and weak channels also display antibunching and the loss of bounds.