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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Effect of Spontaneous Decay on the Rabi Population Oscillation of a Two-Level Atom Coupled to a Monochromatic Field

Sun Kyung Lee, Hai-Woong Lee

Published Aug 1, 2007• 0 citations
Publisher

Abstract

We investigate effects of spontaneous decay on the Rabi population oscillation exhibited by a two-level atom driven by a monochromatic field. We show that the semiclassical theory and the fully quantum-mechanical theory predict in general different damping rates of the Rabi oscillation.
DOI
10.1109/cleopr.2007.4391761

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One of the simplest nontrivial problems involving the atom–field interaction is the coupling of a two-level atom with a single mode of the electromagnetic field. A two-level atom description is valid if the two atomic levels involved are resonant or nearly resonant with the driving field, while all other levels are highly detuned. Under certain realistic approximations, it is possible to reduce this problem to a form which can be solved exactly; allowing essential features of the atom-field interaction to be extracted. In this chapter we present a semiclassical theory of the interaction of a single two-level atom with a single mode of the field in which the atom is treated as a quantum two-level system and the field is treated classically. A fully quantum mechanical theory will be presented in Chapter 6. A two-level atom is formally analogous to a spin-1/2 system with two possible states. In the dipole approximation, when the field wavelength is larger than the atomic size, the atom–field interaction problem is mathematically equivalent to a spin-1/2 particle interacting with a time-dependent magnetic field. Just as the spin-1/2 system undergoes the so-called Rabi oscillations between the spin-up and spin-down states under the action of an oscillating magnetic field, the two-level atom also undergoes optical Rabi oscillations under the action of the driving electromagnetic field. These oscillations are damped if the atomic levels decay. An understanding of this simple model of the atom–field interaction enables us to consider more complicated problems involving an ensemble of atoms interacting with the field.
The interaction of a two-level atom with two monochromatic electromagnetic fields having arbitrary amplitudes and resonance frequencies is considered. It is shown that the time averaged upper-level population can exceed 0.5 and even reach 0.7. Its dependence on the frequency difference reveals resonance satellite peaks, which are concerned with three- and five-photon combination scattering. The widths and the resonance spectrum shifts of these peaks are found. The frequency spectrum of the spontaneous emission of an atom contains fine structure under some conditions. This structure does not exist in the case of one monochromatic field. An asymmetry in the intensity distribution for the Rabi satellites due to a field non-monochromaticity is predicted.
Damping of multiphoton Rabi oscillations due to a finite lifetime of photons is investigated using an algebraic method of the solution of the master equation. The time dependence of the probability of electron transitions between atomic levels is evaluated. In a regime of weak atom–photon coupling (a coupling constant smaller than the photon decay rate), the spontaneous emission of many photons from a single electron transition due to the interaction with a resonant light is found. Thus, a multiphoton counterpart of the Purcell effect is predicted.
A systematic investigation is performed on the damping of Rabi oscillations induced by an external electromagnetic field interacting with a two-level semiconductor system. We have considered a coherently driven two-level system coupled to a dephasing reservoir and shown that, to explain the dependence of the dephasing rate on the driving intensity, it is essential to consider the non-Markovian character of the reservoir. Moreover, we have demonstrated that intensity-dependent damping may be induced by various dephasing mechanisms due to stationary as well as non-stationary effects caused by coupling with the environment. Finally, present results are able to explain a variety of experimental measurements available in the literature.