High-order harmonic generation spectrum from two coupled Floquet resonances – a non-Hermitian formulation

Abstract

The quantity $⟨\psi (t-{\mathrm{\Delta }}_t/2)|\hat{a}|\psi (t+{\mathrm{\Delta }}_t/2)⟩$ given for a square integrable wavefunction ψ allows one to define very different kinds of measurables, such as absorption spectrum (as a Fourier transform (FT) over ${\mathrm{\Delta }}_t$ for t=0) as well as high-order harmonic generation (HHG) spectrum (as a FT over t for ${\mathrm{\Delta }}_{t=0}$). The main objective of this paper is to define this quantity based on a spectral decomposition of ψ to non-Hermitian wavefunctions obtained in complex scaling calculations. The obtained formal expression combines matrix elements based on the non-Hermitian c-inner product, as expected, and surprisingly also Cartesian (Euclidean) norms and overlaps of complex scaled wavefunctions. The latter feature diminishes in cases such as absorption spectra, however, it does take place in expressions obtained for the HHG spectrum. The exact non-Hermitian formalism is necessary for theoretical calculations of HHG at coupled photoionisation resonances, illustrated here for a multiphoton conversion in helium atom near a conical intersection.

GRAPHICAL ABSTRACT

Keywords:

• High-order harmonic generation
• non-Hermitian quantum mechanics
• non-adiabatic coupling

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was financially supported by the Czech Ministry of Education (grant number LTT17015).