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Journal of Modern Optics

Laser-induced dynamic radiative corrections in the dressed-state and in the Floquet picture

Gagik Yu. Kryuchkyan, Ulrich D. Jentschura, Jörg Evers, Christoph H. Keitel

Published Jul 7, 2007• 4 citations
Publisher

Abstract

We investigate QED field-dependent effects in radiative shifts of atomic levels driven by a strong laser field. Our focus is on indirect laser-induced corrections to the Lamb shift of an atomic reference state due to a strong laser field which near-resonantly couples two other states, but not the reference state. Our aim is to show how to generalize previous treatments of related scenarios to the case of an induced indirect coupling. We also derive an expression of self-energy corrections in the Floquet picture and analyse various coupling schemes with respect to the shift of Floquet quasi-energies. The semi-classical Floquet picture and the fully quantized dressed-state approach are contrasted.

DOI
10.1080/09500340601156918

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We investigate QED field-dependent effects in radiative shifts of atomic levels driven by a strong laser field. Our focus is on indirect laser-induced corrections to the Lamb shift of an atomic reference state due to a strong laser field which near-resonantly couples two other states, but not the reference state. Our aim is to show how to generalize previous treatments of related scenarios to the case of an induced indirect coupling. We also derive an expression of self-energy corrections in the Floquet picture and analyse various coupling schemes with respect to the shift of Floquet quasi-energies. The semi-classical Floquet picture and the fully quantized dressed-state approach are contrasted.
We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.
This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.
We discuss the interaction of an atom subject to an intense driving laser field with its own radiation field. In contrast to the states of bare atoms, the energy difference between some dressed states with the same total angular momentum, its projection and parity may be very small. The self-interaction of a combined atom–laser system associated with nonradiative transitions between such states is effectively strong. We show that the contribution to the radiative shift of the sidebands of the Mollow spectrum, which comes from such processes, is very significant and may be much larger than the trivial Lamb shift, which is the simple redistribution of the Lamb shifts of the corresponding bare states. In the final part, we discuss the possibility that in the Mollow spectrum nonlocality of electromagnetic interaction, which in other cases is hidden in the regularization and renormalization procedures, can manifest itself explicitly.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
We show that Floquet states can be constructed as strong-field limits of cavity-dressed states. The interaction between laser beams propagating outside the cavity with atoms or molecules are described by Floquet states, constructed from dressed states of average photon number quantized in a cavity of volume V, by taking the limit , , while keeping the photon density constant. Thus, Floquet theory can be seen as a fully quantum-mechanical model in the sense that it describes the photon exchanges between matter and radiation containing a large amount of photons. We discuss in this context adiabatic Floquet theory to treat a slow time dependence of the laser amplitude, to describe pulses, and of its frequency (chirping).