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Optics Letters

Theory of two-photon resonance fluorescence

David A. Holm, Murray Sargent

Published Aug 1, 1985• 11 citations
Publisher

Abstract

We present calculations of the spontaneous-emission spectrum from a two-photon two-level system in the presence of an arbitrarily intense monochromatic field at half of the two-photon transition frequency. The single-photon counterpart to this is called resonance fluorescence. Because of the complexity of the two-photon two-level model, many effects arise that are absent in the one-photon problem. In particular, we show how the Rayleigh scattering from this system is markedly different and discuss the role of Stark shifts on the emission spectrum.

DOI
10.1364/ol.10.000405

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Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation
We present calculations of the spontaneous-emission spectrum from a two-photon two-level system in the presence of an arbitrarily intense monochromatic field at half of the two-photon transition frequency. The single-photon counterpart to this is called resonance fluorescence. Because of the complexity of the two-photon two-level model, many effects arise that are absent in the one-photon problem. In particular, we show how the Rayleigh scattering from this system is markedly different and discuss the role of Stark shifts on the emission spectrum.
We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.
Resonance fluorescence of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser’s linewidth under weak monochromatic excitation. These properties are commonly explained in terms of two disjoined pictures, i.e., the emitter’s single photon saturation or passively scattering light. Here, we propose a unified model that treats all fluorescence photons as spontaneous emission, one at a time, and can explain simultaneously both the spectral and correlation properties of the emission. We theoretically derive the excitation power dependencies, measurable at the single-photon incidence level, of the first-order coherence of the whole resonance fluorescence and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides an intuitive understanding of coherent light-matter interaction and may stimulate new applications. Standard descriptions of resonance fluorescence consider either absorption and re-emission in a single-photon picture or passive scattering. This study shows that resonance fluorescence can be described by a pure quantum state of the emitter and photon, revealing a coherent superposition that challenges the conventional view of spontaneous emission as an incoherent process.
A simple theoretical model is formulated which describes dynamical features of the interaction of two-level atoms with a continuum of radiation oscillators. In particular, this paper is concerned with resonance scattering by single atoms in the presence of an external classical field, and spontaneous emission by a system of identical atoms. In the case of resonance scattering, the response of an atom to rapid changes of the amplitude of the external field is studied. The model for spontaneous emission by a system of atoms is based on the assumptions that all atoms have the same resonance frequency, and that the atoms are contained in a volume whose extension is small compared with the wavelength of the emitted radiation. The complete evolution of a system of mmm atoms is determined by a set of coupled first-order linear differential equations, and explicit solutions are presented for the values m=1,2,3,4,and8m=1,2,3,4, \mathrm{and} 8m=1,2,3,4,and8. Pair correlations of the atoms and photon-number fluctuations are discussed. An approximation for resonance fluorescence by a system of atoms with a broad distribution of resonance frequencies is included in an Appendix.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.