The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).
The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two separate molecules give signals that appear on top of a genuine direct higher-order process with a single molecule. These many-body contributions are known as cascading and complicate the interpretation of multidimensional stimulated Raman and other nonlinear signals. In a quantum electrodynamic treatment, these cascading processes arise from second-order expansion in the molecular coupling to vacuum modes of the radiation field, i.e., single-photon exchange between molecules, which also gives rise to other collective effects. We predict the relative phase of the direct and cascading nonlinear signals and its dependence on the microscopic dynamics as well as the sample geometry. This phase may be used to identify experimental conditions for distinguishing the direct and cascading signals by their phase. Higher-order cascading processes involving the exchange of several photons between more than two molecules are discussed.
Spectroscopy, the study of matter via its interactions with light, is a vast subject that includes many of humanity's principle means of probing the fundamental structure of matter. Though usually understood from the perspective of classical light, important effects arise due to the quantum nature of the electromagnetic field. Additionally, the quantum vacuum can serve as an effective couple between molecules in the system, generating many-body interactions and cooperative processes in the material. While many techniques are well-described classically, quantum-field corrections can dominate the desired signals in certain cases, such as cascading in higher-order n-wave mixing signals, and are key for experimental interpretation. Even spontaneous emission and light scattering are best understood from the perspective of quantum fields. In this thesis, we utilize a systematic procedure, based on the density matrix in Liouville space, to give a rigorous description of elementary quantum-field effects in nonlinear spectroscopy, with specific examples made to ultrafast x-ray and optical techniques.
Classical, semi-classical, and quantum-field descriptions for the interaction of light with matter are systematically discussed. Applications of interest include precise determinations of the linear and the non-linear electromagnetic response relevant to resonant pump-probe optical phenomena, such as electromagnetically induced transparency. In the quantum-mechanical description of matter systems, we introduce a general reduced-density-matrix framework. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner, using a Liouville-space operator representation. A preliminary semi-classical perturbation treatment of the electromagnetic interaction is adopted, in which the electromagnetic field is described as a classical field satisfying the Maxwell equations. Compact Liouville-space operator expressions are derived for the linear and the general (nth order) non-linear electromagnetic-response tensors describing moving many-electron systems. The tetradic matrix elements of the Liouville-space self-energy operators, which are introduced in the time-domain and frequency-domain formulations, are evaluated for environmental collisional and radiative interactions, in order to provide explicit forms for the quantum kinetic equations and the spectral-line shape formulas. It is emphasized that a quantized-field approach is essential for a fully self-consistent quantum-mechanical description of the interacting light-matter system.
Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schri:idinger and Maxwell equations selfconsistently. The case of linear response is' described in detail. As a manifes tation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for a two-level atom in vacuum. The interaction of electromagnetic (EM) radiation with matter has been studied in various aspects for quite a long time. The relevant phenomena range, in the scale of wavelength, from rf wave (NMR, for example) to gamma ray (Mossbauer effect): They are related with the absorption, reflection, transmission, propagation, refrac tion, scattering, diffraction, emission, etc. of EM wave in linear and nonlinear manner. For the theoretical treatment of these phenomena, we need Schrodinger equation for the description of matter and Maxwell equations in classical or quantized form for radiation field. When the Maxwell equations are treated in classical form, this is called semiclassical treatment of radiation-matter interaction. Though it has a certain limitation, the semiclassical treatment can be appliedto most of the phenom ena mentioned above. For the treatment of the interaction of EM radiation with solids, it is usual to employ a susceptibility function to describe the solid, and solve the Maxwell equa tions containing that susceptibility as an integral kernel. In doing so, we must consider the boundary conditions (BC) arising from the shape of the sample in question. However, we do not consider BC's in treating microscopic systems such as an atom or small molecule. This would mean that the use of BC(s is in general not compulsory, although we are so much accustomed to it. In this respect, there has been a long debated problem of additional boundary condition (ABC) in relation with exciton polaritons in semiconductors or insulators, where the nonlocal nature of the medium allows the existence of two or more eigenmodes of the coupled exciton-EM radiation. After the long history of the ABC problem,r>- 4 > we now have a recipe to derive the appropriate form(s) of ABC(s) from a microscopic model of the medium including the details of the surface. 5 >-s> Another form of the microscopic solution of the ABC problem has been given as an ABC-free formulation, 9 >-n> where one needs
The interaction of a propagating pulse of quantum radiation with a localized quantum system can be described by a cascaded master equation with a distinct initially populated input and a finally populated output field mode [Kiilerich and M\o{}lmer, Phys. Rev. Lett. 123, 123604 (2019)]. By transformation to an appropriate interaction picture, we break the cascaded nature of the master equation and recover an effective time-dependent interaction with a lossless single mode and a supplementary lossy mode. The former closely represents the traveling pulse, while the latter constitutes a non-Markovian component in the exchange of quanta between the scatterer and the quantized field. The transformed master equation offers important insights into the system dynamics, and it permits numerically efficient solutions.