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arXiv:quant-ph/9909043 · Physical Review A

Spontaneous emission and lifetime modification caused by an intense electromagnetic field

Paolo Facchi A, Saverio Pascazio

Published Jul 14, 2000• 52 citations
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Abstract

We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi ``golden rule'' still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an ``inverse'' quantum Zeno effect and can be analyzed in terms of dressed states.

DOI
10.1103/physreva.62.023804

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We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi golden rule'' still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an inverse'' quantum Zeno effect and can be analyzed in terms of dressed states.
The lifetime of an unstable atom can be extended by watching it closely, i.e., illuminating it with an intense electromagnetic field of appropriate frequency. This is an example of ``dominated evolution'' and is closely related to the so-called ``quantum Zeno effect.'' For a metastable atom bathed in a laser beam at the frequency of another of its transitions, we obtain an expression for the modified lifetime as a function of beam intensity. This provides an example of the quantum Zeno effect on a truly decaying system, and also should be useful for probing short distance features of atomic wave functions.
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.
We reconsider the problem of the spontaneous emission of light by an excited atomic state. We scrutinize the survival probability of this excited state for very short times, in the so-called Zeno regime, for which we show that the dynamics is dictated by a coherent, in-phase, response of the on-shell and off-shell vacuum modes. We also develop a perturbative approach in order to interpolate between different temporal regimes: the Zeno, golden rule (linear), and Wigner-Weisskopf (exponential) regimes. We compare results obtained with the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{E}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{x}}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$ interaction Hamiltonians, using successively the dipole approximation and the exact coupling.
For a three-level atom in the ssV configuration (i.e., having two excited states each dipole-coupled to a common ground state), we have found a particular linear combination of bare-atom states in which Rabi oscillations and their associated collapses and revivals do not occur. Moving to a dressed-state picture, we discover that this particular linear combination state is just that dressed state which is decoupled from all the field modes. It is a dressed state for which the transition dipole moments with the other dressed states are zero. The existence of this decoupled dressed state depends on the tuning of the dressing laser field, which in turn depends on the bare-atom excited-state dipole moments and energy-level separation. When we include spontaneous emission, the population decays from the other dressed states into this decoupled state and remains coherently trapped there, producing a system that experiences no dynamical behavior. This is exact for \ensuremath{\delta}-function photon statistics (i.e., if there is no intensity uncertainty). The trapping becomes less perfect as the photon statistics are allowed to have a greater bandwidth. Also, if the applied field is tuned incorrectly, the spontaneous realignment of the atomic state amplitudes does not result in a totally decoupled dressed state, and the dynamics proceed normally.