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IEEE Journal of Quantum Electronics

Photon statistics and quantum jumps: the picture of the dressed atom radiative cascade

Serge Reynaud, Jean Dalibard, Claude N. Cohen-Tannoudji

Published Jul 1, 1988• 45 citations
Publisher

Abstract

The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>

DOI
10.1109/3.979

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The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>
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
In recent papers by Cohen-Tannoudji and Dalibard1 and Zoller et al.2 the statistics of quantum jumps in a three-level atom are analyzed in terms of the joint probability density W(t + τ;t) for a photon emission at time t followed by the next photon emission at time t+ τ. W(t+ τ;t) differs from the second-order correlation function G(2) (t + τ;t) often used to characterize photon statistics; the latter gives the joint emission probability without the condition that there be no emissions in the interval t to t + τ. Alter dividing by the density for single-photon emission, W(t + τ;t) gives the probability density for a delay τ between photon emissions.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
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.
We describe the coherence properties of light emitted by driven atoms in terms of dressed-atom survival amplitudes. Such amplitudes can be used to construct analytic expressions for the function describing the delay between successive photon emissions and used to construct the appropriate radiation correlation functions. This approach is used to calculate the radiative dynamics of three-level atoms appropriate to recent quantum-jump experiments. We contrast our simple approach to that normally employed which relies on the numerical solutions of density-matrix equations of motion followed by the application of the quantum-regression theorem.