Nonclassical light generation and control from laser-driven semiconductor intraband excitations

The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically-and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high -order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al. , Sci. Rep. 6 , 32821 (2016) and N. Tsatrafyllis et al. , Nat. Commun. 8 , 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al. , Nat. Phys. 17 , 1104 (2021) and P. Stammer et al. , Phys. Rev. Lett. 128 , 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong -field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.