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International Journal of Modern Physics B

INTERACTION OF A THREE-LEVEL ATOM WITH A SINGLE-MODE FIELD IN A TWO PHOTON RESONANT CAVITY

Debraj Nath, Pradip Das

Published Jan 30, 2011• 2 citations
Publisher

Abstract

In this paper we discuss an extension of Jaynes–Cummings model by adding a further atomic level to support a second resonance and cooperative effects in multi-atom systems. A successive passage of a three-level atom in the V configuration interacting with one quantized mode of electromagnetic field in a cavity will be considered to study atomic inversion and entropy evolution of the state.

DOI
10.1142/s021797921105802x

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In this paper we discuss an extension of Jaynes–Cummings model by adding a further atomic level to support a second resonance and cooperative effects in multi-atom systems. A successive passage of a three-level atom in the V configuration interacting with one quantized mode of electromagnetic field in a cavity will be considered to study atomic inversion and entropy evolution of the state.
In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.
The problem of the interaction of a single two-level atom with a single mode of the quantized electromagnetic field in a coherent state in an ideal resonator in the resonance case is considered. The evolution in time of the atomic inversion, represented by the Jaynes-Cummings sum, is studied. On the basis of the application of the theorem on the approximation of a trigonometric sum by a shorter one (ATS), a new efficient method for approximating the Jaynes-Cummings sum is constructed. New asymptotic formulas for the atomic inversion are found, which approximate it on various time intervals, defined by relation between the atom-field coupling constant and the average photon number in the resonator field before the interaction of the field with the atom. The asymptotics that we obtain give the possibility to predetermine the details of the process of the inversion in the Jaynes-Cummings model depending on the field characteristics.
The dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.
The temporal evolution of entanglement for a single-mode field interacting with a two-level atom via intensity-dependent coupling in the off-resonant case has been studied, where the leakage of photon through the cavity is taken into account. The effects of cavity damping on the coherence properties of the atom and the field are studied. The amount of entanglement is compared with the total correlations. It is found that the atom–field system is inhibited from going into a pure state in the off-resonant case.