High-order harmonic generation in quantum light by a generalized von Neumann lattice method

Studies of high harmonic generation (HHG) have entered a new stage by using the quantum light instead of the classical field. Recent theoretical progress has demonstrated promising features, such as the significantly higher maximum harmonic photon energy in a squeezed or thermal light field, which is not observed under classical field conditions with the same number of fundamental mode photons. However, there are many approximations in the theoretical treatments. More accurate methods are required to check the appealing results. By employing the generalized von Neumann lattice basis, here we develop a general and precise method to describe the HHG process, taking into account the coherent superposition of the diagonal part components and the nondiagonal part components from the overlap of the coherent states. It can be extended to calculate the multimode quantum light, such as two-mode squeezed vacuum. Our study provides a powerful tool for investigating the full properties of quantum light in HHG.