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Journal of Physics B Atomic and Molecular Physics

QED calculation of the resonant Stark effect

Martin E. Smithers, Helen S. Freedhoff

Published Nov 11, 1974• 21 citations
Publisher

Abstract

Quantum electrodynamic calculations involving the resonant Stark effect are reported. By including the effects of multiple spontaneous emissions for a two-level atom in a resonant applied field solutions are obtained which are valid over many radiative lifetimes. The resonance fluorescence spectrum is also calculated as a function of the detuning parameter. The theoretical results are in agreement with the experimentally observed long term fluorescence spectrum.

DOI
10.1088/0022-3700/7/16/002

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Journal of Physics B Atomic and Molecular Physics•May 14, 1981•1 citation
Quantum electrodynamic calculations involving the resonant Stark effect are reported. By including the effects of multiple spontaneous emissions for a two-level atom in a resonant applied field solutions are obtained which are valid over many radiative lifetimes. The resonance fluorescence spectrum is also calculated as a function of the detuning parameter. The theoretical results are in agreement with the experimentally observed long term fluorescence spectrum.
A fully quantum-mechanical treatment is presented of the interaction of a two-level atom with an intense applied field. The resonant Stark effect spectrum is calculated for a single decay process in the case of an arbitrarily detuned applied field, and for a sequence of many fluorescent decays in the case of a resonant applied field. The results of these calculations agree with recent experimental observations, and with previous theoretical calculations using different methods. In addition, a misinterpretation contained in a previous letter by the present authors (see ibid., vol.7, L.432 (1974)) is pointed out.
A QED calculation of the resonance fluorescence spectra of a two-level atom in a strong, nearly resonant field, is reported, taking into account multiple spontaneous emissions (in any order) and interference effects. The results of this calculation are compared with the results of the quantum statistical theories, and the role of the elementary processes analysed. At resonance, in the high-field limit, the exact agreement of the QED and statistical theories is demonstrated. It is pointed out that the interference effects are of the greatest importance.
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.
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.
Attention is focused on the dynamic evolution of the emission spectrum following abrupt excitation of a near-resonant two-level absorber by a strong laser field. The multiphoton character of the absorption-emission process is evident in the AC Stark splitting of the spectrum, which begins approximately half an atomic lifetime after excitation, if the laser field is strong enough. Analytic expressions for the spectra are given of arbitrary laser field strength, atomic lifetime, laser-atom detuning, and the bandwidth of the spectrometer used to analyse the spectrum. Selected graphs are included to illustrate various time-dependent features of the spectrum. The influence on the transient spectrum of three different states of atomic excitation prior to laser irradiation and the effect on the spectrum of irradiation by a phase-noisy laser are also considered. Comparison of the transient spectra from atoms initially prepared in ' pi /2' and '3 pi /2' states show clearly that phase relationships between the irradiating field and the emitting dipole are important even in fluorescence.