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.
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Data availability
All data presented here is available online89.
Code availability
The Python code supporting the results can be obtained from the GitLab repository: https://gitlab.inf.uni-konstanz.de/emanuel.hubenschmid/subcycleq. A archived version of the specific code used here is available online89.
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We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) - Project No. 425217212 - SFB 1432.
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E.H. performed the calculations and wrote the manuscript. G.B. improved the manuscript and supervised the project.
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Communications Physics thanks Ileana-Cristina Benea-Chelmus, Aleksei Gaier and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Hubenschmid, E., Burkard, G. Time-domain field correlation measurements enable tomography of highly multimode quantum states of light. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02493-y
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DOI: https://doi.org/10.1038/s42005-026-02493-y
