Femtosecond Covariance Spectroscopy

In order to reveal a signal arising from a nonlinear interaction, several spectroscopic techniques are nowadays adopted. In spite of their practical and fundamental differences, they have in common to rely on pulse to pulse consistency to deliver information on a nonlinear process. With the work presented in this thesis we show, instead, that we can successfully leverage upon experimental noise. To achieve this goal, we exploited the fact that a weak nonlinear signal introduces a strong spectral correlation, which can be revealed even when the output spectra fully spectrally and spatially overlap with the excitation pulse. Based on these principles, we proposed a novel approach to a nonlinear spectroscopy experiment, called Femtosecond Covariance Spectroscopy. To provide a solid basis for the validation of the technique, we focused on a third order nonlinear process, inelastic light scattering, which is prompted by the mixing of intense electric fields in a transparent material. The interaction implies that the measured intensity at some point in the transmitted spectrum is statistically related to the intensity at other points of the spectrum, whenever their energy distance coincides with an energy level of the sample involved in the scattering. We performed inelastic light scattering experiments from vibrational modes of a benchmark sample, quartz. We employed a near infrared laser with central wavelength in a transparency region of the sample, and bandwidth larger than its lowest energy vibrational modes. We found in the correlation coefficient sidebands that reproduce the vibrational spectrum of the sample. Their lineshape changes according to the presence or absence of a non modulated portion of the spectrum, heterodyning the scattered radiation. In fact we find that a partial spectral randomization is most efficient in preparing a pulse with no pre-existent correlation, that, at the same time, provides a local oscillator for the sample-induced fluctuations to be amplified. In this scheme, the ultrashort pulse provides, at the same time, intense electric fields to stimulate a response, and noninteracting components to reveal it. The self-heterodyned nature of the acquisition is accounted for in a fully quantum model. The technique can be adapted to a pump - probe scheme by exciting the sample with a separate, intense and spectrally coherent, pump pulse. Our measurements of the average transmitted probe intensity performed using a pump to excite coherent vibrational states, reveal that oscillations in the response are initiated in-phase by the pump and evolve at the vibrational frequencies. Such a response is an ideal candidate to test a covariance based probe, as the spectrum undergoes a red-shift or a blue-shift alternatively in time, and the correlation coefficient is found to oscillate in time at the phonon frequency. The investigation we started with this Thesis aims, primarily, at establishing the signatures in the correlation that resolve a thermal from a coherent vibrational state. In fact, if a quantum optics model describes accurately the results of a standard pump probe experiment on quartz, the theoretical framework must be completed in order to describe a pump probe approach employing randomized pulses and a covariance based retrieval. The experiments have shown that consistent information is present in the correlation maps, but more incisive analytical and conceptual tools are needed to assess the different contributions. The proposed method has proven to be a powerful probing scheme in a optical spectroscopy experiment, and can be successfully translated into the language of stochastic X-ray pulses, complex materials, electronic scattering processes. To fully characterize the FCS technique there are still steps to take. Nonetheless we believe that the present work sets the basis for the development of a technique that successfully conveys information beyond traditional schemes.