W. M. Schreiber

Transition amplitudes for time‐dependent harmonic oscillators

Utilizing the Green’s function for a time dependent harmonic oscillator, we calculate the corresponding transition amplitudes. Particular examples of damped and runaway oscillators are discussed.

Time dependent linear quantum systems

The solution to the linear Heisenberg equations which result from the most general quadratic time dependent Hamiltonian is developed. The Green’s function is obtained, and the transition amplitudes between harmonic states are calculated.

Damped quantum mechanical oscillators with thermal fluctuations

The solution for the relevant Heisenberg operators of a quadratic time‐dependent quantum mechanical Hamiltonian is presented in convolution form suitable for the inclusion of thermal fluctuations. The approach to equilibrium of an oscillator in contact with a thermal bath is studied. An expression is obtained for the reduction of the random fluctuation width of the position coordinate as a consequence of the non‐Markovian nature of a quantized thermal bath.

The quantum mechanical linearly damped forced oscillator

The solution is obtained to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force. This solution allows the calculation of interesting quantum quantities such as the Green’s function and the transition amplitudes between harmonic oscillator states. The specific results for a harmonic driving force are given.

Dipole interaction of an unequally spaced multilevel atom with a monochromatic electromagnetic field

The solution is obtained for the fully quantized dipole interaction between monochromatic photons in the number representation and a multilevel atomic system with unequal energy level spacing. An operator form of the rotating wave model is used. Specific results for three‐level and four‐level systems are presented.

Expansion technique for the dipole interaction of a spin-J system with a monochromatic electromagnetic field

SummaryAn expansion technique for the dipole interaction of a spin-J system with a quantized monochromatic electromagnetic field is developed. The energy levels are equally spaced and the rotating-wave approximation is used. Particular results of the application of the method are presented.RiassuntoSi sviluppa una tecnica di sviluppo per l’interazione dipolare di un sistema con spinJ con un campo elettromagnetico monocromatico quantizzato. I livelli di energia sono egualmente spaziati e si usa l’approssimazìone ad onda rotante. Si presentano risultati particolari dell’applicazione del metodo.РезюмеРазвивается техника разложения для дипольного взаимодействия системы со спиномJ с квантованным монохроматическим электромагнитным полем. Уровни энергии эквидистантны и используется приближение вращающихся волн. Приводятся некоторые результаты, иллюстрирующие применение предложенного метода.

Field and pressure induced four‐wave mixing line shapes

A closed density matrix formalism for four‐wave mixing applicable to strong fields is discussed. The resulting line shapes are analyzed for weak, intermediate, and strong intensities.

Transient Response of a Two-Level Atom to Bichromatic Excitation with Pump Detuning

In a recent article, Eberly and Popov1 studied the interaction of two-level atom with two distinct electromagnetic waves using a semiclassical formalism. They have shown that time averaged line shapes near the principal Rabi side band and its subharmonics axe critically dependent on the initial state of the two-level atom and the initial phase relationship between the pump and the probe fields. Furthermore, Mossberg and Lewenstein2 recently showed that bichromatic excitation sometimes leads to complete polarization of the atom-resonant- field dressed states. We extend their results by including pump detuning in the analysis.

Exact Semiclassical Solution for Four-Wave Mixing

Four-wave mixing is of importance both fundamentally and for spectroscopic diagnostics. Extensive perturbational investigations of the process have been done both directly1 and diagramatically.2,3 Exact solutions for various particular physical processes have been previously obtained.4–10 In this paper, we develop a technique for the semiclassical exact solution of a four-wave mixing process. For the sake of brevity, we will specialize to the dominant path, but the technique is applicable to other paths as well.

Simultaneous Multiphoton Processes in the Interaction of Atoms with Electromagnetic Fields

It is impossible to obtain an exact description of multiphoton processes in the interaction of electromagnetic fields with atomic systems. Approximate approaches must be used to describe the physically different effects that can occur. One effect is the stepwise absorption/emission of many photons by a N-level system that evolves dynamically in between each absorption/emission. The exact solution for this non-adiabatic process has been presented in many papers.1’2,3 A different physical effect is described in the theories of Raman processes where the simultaneous absorption/emission of many photons is considered. These calculations involve summing over all possible arrangements of multiple photon interactions neglecting the time evolution of the system in between each absorption.4 The resulting adiabatic theory has been successful in explaining many features of Raman scattering.