High harmonic generation and the billiards

Abstract

The problem of underlying classical dynamics chaotic and regular in quantum and classical billiards and their influence on high-order harmonic generation are investigated. The results concerning the Bunimovich stadium and rectangular billiards are given. The quantum billiard with an electron in a micron-sized quantum dot is assumed. Then the quantum dot in the kicking electric field is considered. The reflection symmetry of billiards is crucial for the emergence of harmonics. The harmonics can have different forms from an ideal δ-spike to a barely recognizable form. For the Bunimovich stadium with fully chaotic dynamics, emission peaks in the spectrum can have such a barely recognizable shape for some initial states and this may depend on the electric field orientation. In the case of rectangular quantum billiard with regular dynamics, emission peaks in the form of ideal δ-spikes always appear. Thus, it would be a new experimentally verifiable signature of quantum chaos. The same problem is also but strictly classically considered. It has been shown that the emission spectrum with high-order harmonics exists in this case as well. Comparison of intensities of harmonics for Bunimovich stadium, circular and rectangular billiards is given. It is highlighted that the harmonic peaks for the Bunimovich stadium are lower than for the other two regular billiards. This can be the criterion for the existence of classical chaos as well.