Multimode Heterodyne Detection for Ultrafast Investigation of Quantum Materials

Ultrafast spectroscopy techniques, which employ ultrashort laser pulses, are a formidable tool to investigate the fundamental mechanisms in complex materials at their typical femtosecond timescale. Improving these methodologies is crucial to extract more information from the experiments and reveal new and deeper insights about the examined samples. In this doctoral thesis, we develop a novel experimental methodology to perform ultrafast optical pump&probe studies of samples out of equilibrium. We design and commission Time-resolved Multimode Heterodyne Detection and we employ it to investigate light-matter interactions in transparent quartz and complex materials such as the transition metal antiferromagnet TiOCl and the cuprate superconductor YBCO. We focus, in particular, in the study of coherent vibrational excitations. The pump&probe approach consists in driving the sample under examination out of equilibrium with an intense pulse, the pump, and measure at a controlled delay the scattered light of a second pulse, the probe. The goal of the developed heterodyne technique is to maximize the amount of information which can be extracted from the experiment. Indeed, while the standard approach consists in measuring the average intensity of the probe pulse, the presented method allows for the full reconstruction of the quantum state of ultrashort pulses and in turn explores new multimode photon observables which are usually neglected in time-domain experiments. Precisely, thanks to heterodyne interferential amplification and single-pulse detection, we gain sensitivity to amplitude, phase and to the statistical distribution of the quadrature of each spectral component of the multimode probe field. We report that we are able to discriminate the quantum limited multimode statistics of the probe pulse and disentangle the amplitude and phase responses in the ultrafast dynamics of the examined samples. We show that amplitude and phase dynamics are in general different and carry distinct information about the interaction processes.