A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.
The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of
nth-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the
(n,n)th normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is
n! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in
n-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.
Abstract In reporting and explaining the interactions of light with atoms and molecules, a photon-based description is not only appropriate but clearly essential when electronic or other kinds of quantum transition ensue. However, textbook treatments frequently go no further than the Planck relation, in representing the quantum nature of the light itself—often resorting to classical principles when discussing mechanism. Complete consistency and rigour can be achieved by treating both the matter and the radiation in a fully quantised form, which requires the electromagnetic fields to be cast in a quantum field representation. It proves possible to develop a rigorous approach to this theory that is simple to convey and apply, and which lends itself to a significantly enhanced level of appreciation of mechanism. This paper lays a concise foundation and exemplifies the application in three specific cases: absorption, emission and scattering. It is also shown how this formulation affords a basis for applications in higher-order, multiphoton and nonlinear optical processes.
In the preceding chapters we have solved a number of specific problems in which electromagnetic fields interact with charges, atoms, or molecules, and these have been approached in several different ways. For example, for the problem of photoelectric detection, which involves short interaction times, we found it convenient to use a perturbative method, whereas the resonance fluorescence problem was treated by solving the Heisenberg equations of motion. In the following sections we shall encounter a number of general methods for tackling interaction problems that can often simplify the problems substantially when they are applicable. We shall illustrate the utility of these methods by recalculating a number of results that were obtained in a different manner before. The quantum regression theorem It was shown by Lax (1963; see also Louisell, 1973, Sec. 6.6) that, with the help of a certain factorization assumption, it is often possible to express multi-time correlation functions of certain quantum mechanical operators in terms of single-time expectations. The result is now known as the regression theorem . As multi-time correlation functions play a rather important role in quantum optics, the theorem is often of great utility, and it can drastically simplify certain calculations. In the following we largely adopt the procedure given by Lax. We consider two coupled quantum systems, to which, for the sake of convenience, we shall refer as the system ( S ) and the reservoir ( R ).
A thermal Green function theory of resonance long-laser-pulse scattering is developed, correctly taking account of the uncertainty-relation between the time-resolved and the energy-resolved experiments and the effect of the sample surface. The transient scattering efficiency can be calculated by folding the retarded Green's functions which are given by the thermal average of the chronological products of the pulse-current (or -density) and current operators into an uncertainty-principle broadening function. The theory is applied to resonance light scattering from a simple molecule in gas for steady and transient cases, where all the collision processes are treated quantum-statistically. At low pressure, the resonance scattering is mainly composed of Raman scattering (RS), final-state redistribution scattering (FRS), final-state transfer scattering (FTS) and collision-induced redistribution scattering (CIRS). In the steady state, it is shown that ordinary resonance Raman scattering is equivalent to RS in collisionless case, that absorption followed by emission contains RS, FRS and FTS, and that absorption followed by redistribution followed by emission is the same phenomenon as CIRS which is weighted by rotational population of excited molecules. Moreover, recent laser-pulse data by Roussea, Patterson and Williams are satisfactorily explained. Connection between this theory and other work is discussed.