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arXiv:quant-ph/0307047 · Physical Review Letters

Lamb Shift of Laser-Dressed Atomic States

Ulrich D. Jentschura, Jörg Evers, Martin Haas, Christoph H. Keitel

Published Dec 16, 2003• 31 citations
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Abstract

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.

DOI
10.1103/physrevlett.91.253601

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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.
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.
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 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.
The incoherent inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of ${(Z\ensuremath{\alpha})}^{2}$ and $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{2}$, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen $1S\text{\ensuremath{-}}2{P}_{1∕2}$ and $1S\text{\ensuremath{-}}2{P}_{3∕2}$ transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.
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.