Optical Time-Domain Quantum State Tomography on a Subcycle Scale

Electro-optic sampling represents a powerful tool to sample the waveform of a free-space mid-infrared pulse in the time domain by measuring the effect of the sampled mid-infrared pulse on an ultra-short near-infrared probe pulse after interaction in a nonlinear crystal. Recent experiments applied this technique to sample the electric field fluctuations of the squeezed vacuum on a subcycle scale. However, a full quantum tomography scheme in the time domain is still missing. Here we present a theoretical description of a possible (time-local) quantum tomography scheme with subcycle resolution [https://arxiv.org/abs/2307.13090 accepted in PRX]. Furthermore, we demonstrate that some states exhibit (quantum) correlations in the time domain which limit the access to the full quantum state together with its dynamics. By extending the previously time-local measurement to include temporal correlations, our proposed tomography scheme is able to fully reconstruct a quantum state together with its dynamics, as long as the Wigner function of the state is Gaussian. We support our analysis by devising a notion of entanglement in the time domain based on a quantum information theoretical approach, which is experimentally verifiable with the proposed setup.