The dynamics of two atoms coupled to the vacuum radiation field is investigated within the framework of a one-dimensional model in the resonance dipole approximation. The exact solution of the resonance energy transfer problem is obtained. A many-atom generalization of the model is also discussed.
The exact solution for a problem of N identical two-level molecules interacting through a dipole coupling with a single-mode quantized radiation field at resonance is given. Approximate expressions for the eigenvectors and eigenvalues for the ground and low-lying excited states, as well as the most highly excited states, are developed and compared with the exact results.
Exact solutions to a one-dimensional, time-dependent Schrodinger equation with two colliding delta-function potentials of different strengths are presented. The equation can serve as a model for resonant and quasi-resonant ion-atom collisions. Electrons initially bound to one of the potentials may be transferred to the other potential or to a continuum state and probabilities for these processes are calculated. The model reproduces the damped oscillatory behaviour of the charge-transfer probability seen in quasi-resonant collisions when the collision energy is varied.
We study the dynamics of a system consisting of a two-level atom and a quantum oscillator coupled by the vacuum radiation field. The oscillator and the atom are assumed to have the same resonance frequency. In contrast to the two-atom or two-oscillator case, the atom-oscillator system leads to an unclosed hierarchy of equations for the operators that determine the radiation pattern emitted by the atom-oscillator system. Instead of using the operator equations, we formulate the problem in terms of density-matrix equations which can be solved once the initial conditions are specified. As an example, we looked at the radiation pattern, the decay dynamics, and the spectrum for an initial condition in which the oscillator is in its n=1 state and the atom is in its excited state. Dressed states (dressed by the static interaction between the atom and oscillator) prove to be especially useful for interpreting the results and comparing them with the two-atom and two-oscillator systems. All calculations are carried out using the resonance or rotating-wave approximation. The relationship of our work to damped Jaynes-Cummings models is noted.
We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).
The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.