Analysis of high-harmonic generation in terms of complex Floquet spectral analysis

Abstract

Recent developments on intense laser sources is opening a new field of optical sciences. An intense coherent light beam strongly interacting with the matter causes a coherent motion of a particle, forming a strongly dressed excited particle. A photon emission from this dressed excited particle is a strong nonlinear process causing high-harmonic generation(HHG), where the perturbation analysis is broken down. In this work, we study a coherent photon emission from a strongly dressed excited atom in terms of complex spectral analysis in the extended Floquet-Hilbert-space. We have obtained the eigenstates of the total Hamiltonian with use of Feshbach-Brilloiun-Wigner projection method. In this extended space, the eigenstates of the total Hamiltonian consisting of the radiation field and the atom system have complex eigenvalues whose imaginary part represents the decay rate. Time evolution of the system is represented by the complex eigenvector expansion so that the correlation dynamics between the photon and the atom is fully taken into account. The HHG is interpreted as the irreversible spontaneous photon emission due to the resonance singularity in terms of the multiple Floquet states that are generated by periodic external field. We have found that the interference between the emitted photons over the different Floquet states causes spatial pulse emission correlated with the decay process of the excited atom.

Ultrafast Dynamics of High-Harmonic Generation in Terms of Complex Floquet Spectral Analysis

“…The problem with these theories is the validity of the Markovian approximation in deriving the kinetic equation of the electron, as its applicability remains uncertain for the far-from-equilibrium situation caused by the driving field [63]. Conversely, the present method attempts to solve the stationary eigenvalue problem in the Floquet space, independent of the initial condition [46,53], where the irreversible time-symmetry breaking is not derived as a result of the Markov approximation for the equation but as a rigorous result of the dynamics caused by the resonance singularity [41,42,44,55]. The present method is an extension of the complex eigenvalue problem of the total Hamiltonian to the Floquet space.…”

“…where κ n ≡ nω = 2πn/T (n = 0, 1, · · · ) [53]. It is well known that the Floquet eigenstate possesses mode-translational symmetry [50] |Φ (n)…”

“…The eigenvalue problem of the Floquet Hamiltonian was solved in terms of the Brillouin-Wigner-Feshbach projection method, as shown in Appendix B [46][47][48]53].…”

“…The left-resonance eigenstates are also obtained by first taking the Hermite conjugate, and then the same analytic continuation with the + index instead of the opposite analytic continuation [41,46,53]. The complex eigenvalue of the resonance state is obtained by solving the nonlinear dispersion equation…”

“…where |Φ [19]. The eigenstates satisfy the bi-completeness and bi-orthonormal relation [9,14,22]. The eigenvalue problem of the Floqeut Hamiltonian was solved in terms of the Brillouin-Wigner-Feshbach projection method [15,16].…”