High harmonic generation and wave mixing in graphene quantum dots by bichromatic laser fields of circular polarization

We investigate high-order harmonic generation and wave mixing in graphene quantum dots of various shapes and symmetries driven by intense bichromatic laser fields with circular polarization. The efficiency of these nonlinear optical processes is shown to be highly sensitive to the quantum dot symmetry, as well as to the relative phase, frequency ratio, and amplitude of the two commensurate laser components. Under specific conditions, the superposition of two circularly polarized fields forms symmetric Lissajous figures in the dipole approximation, effectively acting as a homogeneous electric undulator. When the symmetry of the driving field matches that of the graphene quantum dot, harmonic and wave mixing yields are significantly enhanced. Using a microscopic quantum kinetic approach based on numerical solutions of the density matrix equations, we demonstrate strong nonlinear responses in triangular and hexagonal zigzag-edge graphene quantum dots irradiated by bichromatic counter-rotating circularly polarized pulses. • Symmetry-controlled HHG and wave mixing are demonstrated in graphene quantum dots driven by bichromatic circularly polarized laser fields. • Tunable Lissajous-type electric undulators enable enhanced nonlinear emission through symmetry-assisted electron dynamics. • Graphene quantum dots show strong harmonic enhancement when field and lattice symmetries are matched. • Distinct harmonic selection rules emerge in triangular and hexagonal dots due to inversion symmetry. • Phase-robust enhancement suggests feasibility for ultrafast nanoscale frequency conversion applications.