High-harmonic generation driven by quantum light

High-harmonic generation (HHG) is an extreme nonlinear process in which intense pulses of light drive matter to emit high harmonics of the driving frequency, reaching the extreme ultraviolet and X-ray spectral ranges. So far, HHG has always been generated by intense laser pulses that are well described as a classical electromagnetic field. However, the role of the quantum state of light in non-perturbative interactions of intense light with matter has remained unexplored. Here we show that the defining spectral characteristics of HHG, such as the plateau and cutoff, are sensitive to the quantum state of light. While coherent and Fock light states induce the established HHG cutoff law, thermal and squeezed states substantially surpass it, extending the cutoff compared with a coherent light state of the same intensity. Shaping the quantum state of light thus enables the production of far higher harmonics. We develop the theory of extreme nonlinear optics driven by squeezed light, and more generally by arbitrary quantum states of light, introducing the quantum state of the driving field as a degree of freedom.