Floquet analysis of real-time wavefunctions without solving the Floquet equation

TL;DR

This paper introduces a method to extract Floquet states and quasi-energies directly from real-time wavefunctions, enabling analysis of non-periodic, time-dependent quantum phenomena without solving the Floquet equation.

Contribution

The method allows analysis of Floquet states from real-time wavefunctions in non-strictly periodic systems, bypassing the need to solve the Floquet equation.

Findings

Observation of even harmonics in inversion-symmetric potentials.

Dependence of Floquet state populations on gauge transformations.

Spectral enhancements at channel closings due to ponderomotive shifts.

Abstract

We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily discussed: (i) the observation of even harmonics for an inversion-symmetric potential with a single bound state; (ii) the dependence of the population of Floquet states on (gauge) transformations and the emergence of an invariant, observable photoelectron spectrum; (iii) the driving of resonant transitions between dressed states, i.e., the dressing of dressed states, and (iv) spectral enhancements at channel closings due to the ponderomotive shift of above-threshold ionization peaks.