The interaction of matter with a quantized electromagnetic mode is considered. Representing a strong exciting field, the mode is assumed to contain a large number of photons. As a result, the material response is highly nonlinear: the completely quantized description results in generation of high harmonics. In order to understand the essence of the physical processes that are involved, we consider a finite dimensional model for the material system. Using an appropriate description in phase space, this approach leads to a transparent picture showing that the interaction splits the initial, exciting coherent state into parts, and the rapid change of the populations of these parts (that are coherent states themselves) results in the generation of high-order harmonics as secondary radiation. The method we use is an application of the discrete lattice of coherent states that was introduced by J. von Neumann.PACS numbers:

Abstract. Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on numerical methods, arbitrary space and time dependence of the potential can be treated, provided it is zero before an initial time instant. In this case, appropriate version of the Dyson and Keldysh equations lead to a transparent description with clear physical interpretation. The interaction of a short laser pulse and an electron propagating initially in free space is discussed as an example.

No abstract

Optical generation of high-order harmonics is a prototypical example of nonlinear light–matter interactions in the high-field regime. Quantum optical effects have recently been demonstrated to have a significant influence on this phenomenon. These findings underline the importance of understanding the dynamics of the quantized electromagnetic field during high-order harmonic generation. In the following, we discuss the challenges that are related to the theoretical description of this process and summarize the results that were obtained using the high-field, multimode generalization of well-known quantum optical models that are based on the concept of the two-level atom.

The Ortvay Rudolf international competition was first organized in 1970. The focus is usually not on routine school-level problems but rather on problem-solving relying on physical reasoning and skills in recognizing the fundamental character and “heart” of the problem. Some problems lead the contestants to so-far unsolved, open questions, while some are accessible to first-year students. However, only for a relatively small number of problems do official solutions exist. The intention of this paper is to be the first in a series of published solutions discussing the competition problems. The problem treated below is a simple exercise about heat transfer in a thermodynamic system, which highlights the limitations and consequences of accepting seemingly intuitive approximations, and gives a didactical example of “explosive” dynamics. The calculation does not use mathematical techniques beyond those commonly expected of high school students.