Low-energy physics in strongly correlated materials via nonlinear spectroscopies

In this thesis, I studied low-energy phenomena in condensed matter out of its equilibrium state via various approaches linked to non-equilibrium spectroscopies. In the first part, I studied an out-of-equilibrium phase transition in magnetite. Magnetite is an iron oxide and displays an insulating low-temperature phase and a metallic high-temperature phase. Ultrashort light pulses in the near-infrared range are able to photo-induce the phase transition between these two phases on the timescale of the picosecond. When this process happens close to the threshold for its triggering, the sample displays out-of-equilibrium phase separation between the insulating and metallic phases. In this work, we show what signatures this out-of-equilibrium phase transition has on the reflectivity of the sample. The near-infrared pulses produced by commercial lasers are not always well suited to study condensed matter, especially when one wants to study low-energy degrees of freedom. For the second work presented in this thesis, I built an optical set-up for the production of ultrashort mid-infrared pulses, with the goal of studying the out-of-equilibrium dynamics of low-energy degrees of freedom in a hight-critical-temperature superconductor, the yttrium-doped Bi2Sr2CaCu2O8. In this work, we show that the response of the material is markedly different in different directions. In particular, at room temperature, the B2g-symmetry response of the material is coupled to a charge density wave. In the third and fourth part of the thesis, I tackled some questions from a theoretical point of view. What is the thermalization dynamics in condensed matter out-of-equilibrium? Can we study them via the measurement of the fluctuations of the optical properties of the system? To answer this questions, we performed numerical calculations of the out-of-equilibrium behaviour of the Holstein model, in non-equilibrium dynamical mean field theory. We show that the thermalization dynamics of the system after an excitation is non-trivial and that it strongly depends on the coherent oscillations which are photoinduced in the system. Moreover, the thermalization dynamics of the system can be studied through the fluctuations of the optical properties of the system. The last part of the thesis describes a proposal for an enhancement of the standard set-up for time-resolved photoemission experiments. The Heisenberg uncertainty principle is at the core of quantum mechanics. The uncertainty relation between energy and time is often erroneously considered to be stemming from the uncertainty principle, and its consequences on the temporal and energetic resolutions in time-resolved photoemission experiments have always been taken as fundamental. In this part of my thesis, we show that the tradeoff between the two resolutions can be, instead, overcome in a particular experimental scheme, analogously to what is done in optical multidimensional spectroscopy