Quantum second harmonic generation in terms of elementary processes

Jacob Katriel

Olesia Krupnitska, Wolfram Brenig

We study electric-field-induced second harmonic generation (SHG) in the Kitaev model. This frustrated magnet hosts a quantum spin liquid, featuring fractionalization in terms of mobile Majorana fermion and static ${\mathbb{Z}}_{2}$ flux-vison elementary excitations. We show that finite-temperature SHG allows to probe characteristic features of both fractional quasiparticle types. In the homogeneous flux state at low temperatures, the SHG susceptibility displays an oscillatory spectrum, which is set by only the fermionic excitations and is subject to temperature-induced Fermi blocking, generic to all higher harmonic generation (HHG). In the intermediate to high-temperature range, intrinsic randomness, which emerges from thermally excited visons leads to drastic changes of the SHG susceptibility, resulting from resonance decoupling over a wide range of energies. At the flux proliferation crossover, we suggest an interpolation between these two temperature regimes. Our results satisfy previously established symmetries for electric-field-induced SHG in Kitaev magnets.

G. S. Agarwal

Daniel F. Walls, C. T. Tindle

Ladislav Mišta, Radim Filip

A new non-perturbative method enabling to treat the nonlinear quantum optical systems in a finite-dimensional subspace is illustrated on the example of second-harmonic generation process. The method, being a counterpart of the traditional Schrödinger picture method, is based on a finite operator expansion into the elementary processes. In this way one can calculate the time dependence of the mean value of any operator in the subspace.

В. Н. Горбачев, P. N. Zanadvorov