<br/>We study nonlinear spectroscopy with quantum light combined with interferometry. We consider a general scheme that includes possible interference at two separate stages, preparation and detection of the field. Light-matter coupling generates multiple possibilities of matter excitation and relaxation pathways (histories). Each sequence corresponds to the generation of coherence at different time. When a classical light source is used, the resulting optical signal reveals matter correlations functions that are independent of the order of interaction with light. Complementarily, quantum fields do not commute, and thus quantum light is sensitive to the order of interaction. Each time-ordered matter correlation function, essentially imprinted on the respective light correlation function that act as weights. We identify the associated quantum information obtained by controlling these weights as pathway selectivity, and offer several interferometric schemes to collect it experimentally. <br/><br/>Due to the linear dispersion of free photons, their optical paths and propagation times are linearly related via the speed of light. Therefore, interference of such quantum fields generated by matter correlation functions, introduces ex- ternally controlled time-ordering shuffling. These nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOC); they reveal how perturbations spread throughout a quantum system (information scram- bling). OTOCs are notoriously hard to measure [1, 2]. We find that multiphoton signals (more than one) generated by matter, can be manipulated in post-interaction interferometry to reveal their contribution explicitly [3]. OTOC appear in quantum-informatics studies in other fields, including black holes, high energy, and condensed matter physics.

Interferometric spectroscopy: Steering and detection of quantum coherent pathways out of time ordering

ACS Fall 2021

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