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Journal of Physics B Atomic Molecular and Optical Physics

Long-time dynamics of self-dressing

G. Compagno, Davide Valenti

Published Sep 27, 1999• 9 citations
Publisher

Abstract

We consider a system formed by a two-level atom initially in its bare ground state and the electromagnetic field in the absence of radiation. The interaction of the atom with the radiation field leads to the formation of a dressed ground state. To describe the dynamics of self-dressing, we study the time evolution of the permanence amplitude in the initial state. We adopt non-relativistic QED and take the atom-field interaction Hamiltonian in the minimal coupling form, within the electric dipole approximation. In order to follow the evolution of the permanence amplitude for long enough time periods we use the van Hove resolvent technique with appropriate partial summation of Feynman graphs. We show that the self-dressing process presents the typical behaviour of a decay process and occurs with a timescale a *-1 , which is long compared with both the atom's inverse transition frequency 0 -1 and the excited state decay time -1 . This time is comparable with the lifetime of the excited state due to ordinary two-photon decay. We consider the reasons for such a long time period of self-dressing and make comparison with previous results.

DOI
10.1088/0953-4075/32/19/310

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We consider a system formed by a two-level atom initially in its bare ground state and the electromagnetic field in the absence of radiation. The interaction of the atom with the radiation field leads to the formation of a dressed ground state. To describe the dynamics of self-dressing, we study the time evolution of the permanence amplitude in the initial state. We adopt non-relativistic QED and take the atom-field interaction Hamiltonian in the minimal coupling form, within the electric dipole approximation. In order to follow the evolution of the permanence amplitude for long enough time periods we use the van Hove resolvent technique with appropriate partial summation of Feynman graphs. We show that the self-dressing process presents the typical behaviour of a decay process and occurs with a timescale a *-1 , which is long compared with both the atom's inverse transition frequency 0 -1 and the excited state decay time -1 . This time is comparable with the lifetime of the excited state due to ordinary two-photon decay. We consider the reasons for such a long time period of self-dressing and make comparison with previous results.
We study the radiative emission due to the self-dressing of a two-level atom, initially in its bare ground state, interacting with the zero-point electromagnetic field. Evolution in time leads to the formation of a dressed ground state of lower energy. This energy difference between bare and dressed ground state is taken into account by the emission of real photons. In order to describe this aspect of the self-dressing process we study the transition probability amplitude from the initial bare state to an asymptotic state consisting of the atom in its dressed ground state plus some real photons. Adopting nonperturbative techniques based on the resolvent method we find that the bare-dressed transition occurs at the lowest order with the emission of two photons. The spectral distribution obtained shows that there is a probability for emission of photons at frequency of the order of the atom's transition frequency.
As shown by Hegerfeldt, positivity of energy in quantum mechanics leads to nonlocal effects, where a state that is initially localized immediately develops infinite tails. In a previous paper we have described the mechanism of such effects for relativistic free fields. In this paper we discuss the nonlocal effects for a more complex system that consists of a two-level atom interacting with a radiation field. We study the dressing process of the bare ground state in terms of the photon density. In this process there appears a nonlocal cloud that remains around the atom and ``Zeno'' photons that move away from the atom with the speed of light. Nonlocality is seen to be to due to a ``curtain'' effect where the cloud is initially covered by the Zeno photons, and immediately afterwards is uncovered as the photons move away from the atom. No superluminal speeds are involved. We also consider nonlocal effects associated with a partially dressed state where the atom is excited starting from the true ground state. The excitation of the atom produces a nonlocal rearrangement of the photon cloud, which leads to precursors to the usual retarded field.
We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.
We consider a multilevel atom such as an hydrogen atom, interacting with the quantum electromagnetic field, in the dressed ground state of the interacting system. We evaluate by perturbation theory the dressed ground state of the system, within dipole approximation; we investigate and review the effect of the self-dressing of the atom on several field and atomic observables. Specifically, we obtain general expressions of the renormalized electric and magnetic field fluctuations and energy densities around the atom, and analyze their scaling with the distance from the atom, obtaining approximated expressions in the so-called near and far zone. We also investigate nonlocal spatial field correlations around the atom. We stress how the quantities we evaluate can be probed through two- and three-body nonadditive Casimir-Polder dispersion interactions. We also investigate the effect of the self-dressing, i.e. of the virtual transitions occurring in the dressed ground state, on atomic observables, for example the average potential energy of the electron in the nuclear field; this also allows us to obtain a more fundamental quantum basis for the Welton interpretation of the Lamb shift of a ground-state hydrogen atom, in terms of the atomic self-dressing processes.
We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach, which uses a nonnormalizable dressed state for the excited atom.
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.