Symmetry-conserving treatment of the random-phase problem in nonlinear coherent optics modeling in solids

For electro-optical modeling in solids, the transition dipole phase and the related Berry connection carry important symmetry information about the system. This is especially important in the extremely nonlinear optics regime. One example is the even order harmonic intensity in high harmonic generation from solids. Semiconductor Bloch equations are widely used as theoretical model of this phenomenon. Recently, what has been denoted as the "random-phase problem"or "random gauge"in density-functional theory has gained increasing attention, since it complicates phase sensitive modeling within this framework. Here, we propose and evaluate a phase-sensitive approximation based on a triple dipole product as a solution to this problem. We further evaluate the approximation in a semiconductor Bloch equations model for high harmonic generation in GaAs and compare it to the twisted parallel transport gauge.