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Following recent progress in the experimental application of electro-opticsampling to the detection of the quantum fluctuations of theelectromagnetic-field ground state and ultrabroadband squeezed states on asubcycle scale, we propose an approach to elevate broadband electro-opticsampling from a spectroscopic method to a full quantum tomography scheme, ableto reconstruct a broadband quantum state directly in the time-domain. Bycombining two recently developed methods to theoretically describe quantumelectro-optic sampling, we analytically relate the photon-count probabilitydistribution of the electro-optic signal to a transformed phase-spacequasiprobability distribution of the sampled quantum state as a function of thetime delay between the sampled mid-infrared pulsed state and an ultrabroadbandnear-infrared pump/probe pulse. We catalog and analyze sources of noise andshow that in quantum electro-optic sampling with an ultrabroadband pump pulseone can expect to observe thermalization due to entanglement breaking.Mitigation of the thermalization noise enables a tomographic reconstruction ofbroadband quantum states while granting access to its dynamics on a subcyclescale.

Optical time-domain quantum state tomography on a subcycle scale