Electro-optic sampling of the electric-field operator for ultrabroadband pulses of Gaussian quantum light

Quantum light pulses (QLPs) can be described by spatio-temporal modes, each of which is associated with a quantum state. In the mid-infrared spectral range, electro-optic sampling (EOS) provides a means to characterize quantum fluctuations in the electric field of such light pulses. Here, we present a protocol based on the two-port EOS technique that enables the complete characterization of multimode Gaussian quantum light, demonstrating robustness to both the shot noise and cascading effects. We validate this approach theoretically by reconstructing a multimode squeezed state of light generated in a thin nonlinear crystal driven by a single-cycle pulse. Our findings establish the two-port EOS technique as a versatile tool for characterizing ultrafast multimode quantum light, thereby broadening the reach of quantum state tomography. Potential applications include the characterization of complex quantum structures, such as correlations and entanglement in light and matter. Further, extensions to study multimode non-Gaussian QLPs can be envisaged.