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Physical Review A

Two-photon resonance fluorescence

Moorad Alexanian, Subir K. Bose

Published Dec 26, 2006• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.74.063418

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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.
The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.
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.
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.
Some typical resonance nonlinear-optics phenomena taking place when light interacts with atoms are considered. The multitude of such phenomena reduces to scattering of the perturbing light, perturbation of the atomic spectrum, excitation of an atom and its ionization. In all these cases the investigations are carried out using the simplest model—an isolated atom in a monochromatic external field. Such a model enables one to give an exact description of many elementary processes. On the other hand it is sufficiently realistic. A detailed investigation is carried out of resonance fluorescence, spontaneous Raman scattering, multiphoton excitation of atoms, resonance shifts and splitting of atomic levels and resonance lonication of atoms. The nature of these processes is investigated as a function of the intensity of the external field, its frequency, a specific atomic spectrum, the nature of polarization of the perturbing field, and the degree of its nonlinearity. The role played by the field of the electromagnetic vacuum is analyzed. Theoretical predictions are compared with the results of many experiments describing resonance processes of the interaction of an intense light field with atoms.
Resonance fluorescence consists of photon absorption and photon reemission by an atom interacting with a monochromatic, resonant and intense laser wave. The aim of this paper is to show that all fluorescence signals can be quantitatively calculated through the dressed atom method and that simple physical pictures can be associated to the results obtained in this manner. In such a method, the compound system «atom plus laser photons interacting together» (atom dressed by the laser photons) is first considered and the emission of fluorescence photons is then included as a radiative relaxation of this new quantum system. Emission frequencies thus appear as allowed Bohr frequencies of the dressed atom and Rabi nutation appears as a quantum beat signal between dressed states. Photon correlation and photon counting signals are well understood when fluorescence is considered as a radiative cascade of the dressed atom downwards its energy diagram. Mixed analysis time-frequency, for example study of temporal correlations between photons emitted in some sidebands of the fluorescence spectrum, is suggested by the dressed atom approach. Finally, when compared with the well known optical Bloch equations method, the dressed atom is shown to have a larger validity domain for the Markov approximation On montre que la methode de l'atome habille permet un calcul quantitatif de tous les signaux de fluorescence et associe les resultats a des interpretations physiques simples. Discussion des resultats et presentation des avantages de cette methode