Propagation of intense squeezed vacuum light in non-linear media

Recent developments in quantum light engineering have enabled the use of infrared bright squeezed vacuum (BSV) femtosecond pulses in highly nonlinear optics, particularly strong field physics and high-harmonic generation. However, theoretical studies were focused on the microscopic interaction with a single atom, neglecting the crucial macroscopic aspect of light propagation through the media. This raises a key question: How does BSV propagates in strongly light-driven nonlinear media and how this affects the generation of non-linear optical signals? We address this question by introducing a fully quantized framework that accounts for the propagation in gas media. We find that atomic ionization caused by strong BSV fluctuations and the associated infrared photon losses introduce decoherence effects that can substantially limit the propagation length in the medium, reduce the harmonic yield, and decrease the number of emitted harmonics at high intensities. However, these effects are not detrimental. We identify conditions under which propagation-induced decoherence is minimized while the generated harmonics remain clearly detectable--an issue of particular importance for future studies exploring the connection between strong-field physics and quantum optics. Our results lay the foundation for future studies of BSV in strong-field physics, nonlinear optics, and ultrafast science, and establish a basis for exploring its propagation through all states of matter in a fully quantized framework.