Time-domain field correlation measurements enable tomography of highly multimode quantum states of light

Abstract Recent progress in ultrafast optics facilitates the investigation of the dynamics of highly multimode quantum states of light. Yet, the complete tomographic reconstruction of optical quantum states with prior unknown statistics and dynamics is still challenging, since state-of-the-art tomographic methods require the measurement of orthogonal and distinguishable modes. Here, we propose a tomography scheme based on time-domain quadrature correlation measurements and theoretically demonstrate its ability to reconstruct highly multimode Gaussian states. In contrast to (eight-port) homodyne detection, the two local oscillator pulses are shorter in time and are (independently) time-delayed against the pulsed quantum state. The distinguishable mode structure is obtained in post-processing from the correlation measurement data by orthogonalization. We show that the number of reconstructable modes increases with the number of time delays used and decreases with the temporal extent of the local oscillator. Additionally, we compare dual-pulse homodyne detection and electro-optic sampling. By analysing the (quantum) correlations present in the measurement data, we show how thermalisation of the quantum state during detection leads to the requirement of correlation measurements. Furthermore, we open an avenue to extending our tomography scheme to non-Gaussian states.