High harmonic generation in systems with bounded chaos

Abstract

In this paper we study the radiation spectrum generated by the quantum dynamics of a double resonance model and a driven square well system. We use Floquet theory to analyze the radiation generated by these systems. We present the results of numerical simulations that indicate a connection between high harmonic generation and underlying classical chaos in these models. Our results provide a means of predicting the radiative characteristics of multilevel quantum systems subject to a strong periodic driving force.

Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation

“…This is closely tied to the delocalization that is observed in Fig. 6, since the generation of high harmonics depends on the number of energy levels over which the Floquet state is spread [11].…”

“…Of course, since the region of chaos is bounded the states can only delocalize until they reach the boundaries of the chaos. At extremely high values of ǫ, where nearly every "chaotic" state has undergone many broad avoided crossings, we find that all of these states are delocalized and fill the chaotic region [11].…”

“…7. Between ǫ = 170 and ǫ = 175.5 there is a significant increase in the radiation at the highest harmonics (11)(12)(13)(14)(15)(16)(17)(18)(19). However, these harmonics have decreased at ǫ = 180.…”

Statistical properties of a modified standard map in quantum and classical regimes

“…In our case, the phase space has a cylindrical geometry and position is a cyclic variable. For that geometry of phase space, the Wigner function can be written in the following way [13]: (11) and the Husimi function on cylinder is defined by the following formula [14,15]:…”

Chaos-assisted adiabatic passage

“…where the state |x 0 , p 0 is a coherent state that can be represented in the position basis as [32] x|x 0 , p 0 = 1…”