Intensity and fluctuation dynamics in pump-probe experiments in complex materials

The work presented in this thesis is focused on out-of-equilibrium experiments on strongly correlated systems, both with ``standard'' pump-probe spectroscopy and time resolved single pulse statistics. We applied these techniques mainly on a High Temperature Superconductor, an optimally doped Bi2 Sr2 Y0.08 Ca0.92 Cu2 O(8+x) (Y-Bi2212). These materials show intriguing and still unexplained properties, such as the presence of the pseudogap phase. The aim of the first part of the thesis is to analyze the phase transition between superconducting and pseudogap phases, through the combination of time resolved techniques, suitable for the study of strongly correlated systems, and electronic Raman spectroscopy, which allows to detect anisotropic behaviors in the reciprocal space. The experimental result was a map of the de-excitation dynamics as a function of temperature across Tc The excitation was provided by mid-infrared pulses at two different photon energies (above and below the superconducting gap) and polarizations. The results show that a low photon energy pump polarized along the Cu-Cu direction causes a larger dynamical superconducting response with respect to the Cu-O polarized excitation, both below and above the critical temperature. The results are supported by an effective theoretical model based on BCS theory for a superconductor with an anisotropic d-wave gap typical of cuprates. The model reveals a dynamical enhancement of the superconducting order parameter for a Cu-Cu polarized pump, which is due to the increase of phase coherence of the pair operator, whereas the density of Cooper pairs seems not to be strongly affected by the excitation. In the second part of the thesis we wanted to move a step forward and to study the statistical distribution of the probe pulses. The intrinsic noise of the photon number distribution reveals a completely distinct behavior in the various phases of the sample: it follows the mean photon number dynamics in the metallic states, whereas it has a different time resolved signal (and in particular the noise has a longer time decay) in the superconducting state. A simple quantum model, which describes the dissipative processes of the set-up as perfect beam splitters, has been implemented to simulate the observed peculiar results. From the model it turns out that the non-selected polarization contributes to the final noise signal, giving rise to a completely different dynamics for high and low temperatures. This interpretation shows how, whereas it is always possible to select photons with certain features (such as polarization) in ``standard'' intensity measurements, footprints of every interaction are kept in the noise.