Control of collective phenomena in complex materials through cavity electrodynamics

The hybridization between light and matter within optical cavities has emerged as a promising avenue for controlling macroscopic functionalities in quantum material in both the weak and strong coupling regimes. In recent years, optical resonators have been shown to dramatically modify the path and rate of chemical reactions as well as the energy exchange and the electronic transport in semiconductors. Confining light fields in cavities provides therefore a novel approach towards the control of the ground state of quantum materials, establishing a connection between the manipulation through external static stimuli (like electric or magnetic fields) and the generation of non equilibrium light-driven phases. In the present thesis we focus on the experimentally possibility of exploiting the light-matter interaction in cavity-confined systems to dress collective excitations in complex materials and eventually gain control over their cooperative properties. For this purpose we developed a unique set-up to study the strong and weak coupling regimes between low energy excitations in correlated solid-state materials and tunable cavity modes. This has been realized in a Terahertz Fabry-Pérot resonator whose unique strength lies in its capability of tuning its fundamental mode in a cryogenic environment. The high versatility of the set-up makes it ideally suited to study a wide range of low energy modes in quantum materials and to subsequently investigate how their coupling with the extended cavity field may affect their collective dynamics. We firstly study the strong coupling of vibrational excitations in CuGeO3, a benchmark dielectric material exhibiting a strong phononic resonance in the Terahertz spectral range. Motivated by the possibility of reaching the strong and weak coupling limit in the designed resonators, we study the effect of cavity electrodynamics on the metal-to-insulator transition in the Charge Density Wave (CDW) material 1T-TaS2. We observe a large modification of the linear response when 1T-TaS2 is embedded within low energy Terahertz cavities. Importantly, the cavity electrodynamics enables a reversible control of the metal-to-insulator phase transition, where a switch between the conductive and dielectric phases can be obtained by both tuning the cavity frequency and its alignment. Guided by the possibility offered by the cavity environment of controlling materials dissipations, we study how charge dissipations across the metal-to-insulator transition in 1T-TaS2 influence the cavity response. We reveal that the free charges responsible of the conductive behaviour can couple to cavity modes and modify their dissipative dynamics. The presence of free charges in the system can induce a vibrational weak coupling regime when the cavity mode is hybridized with the phonons of the insulating CDW phase. Finally, motivated by the strong connection between electronic excitations in cuprates and their high-temperature superconducting response, we explore the possibility of hybridizing the charge transfer transition in YBCO in tailored cavity heterostructures. Our findings show how cavity electrodynamics can play a role in the intricate equilibrium physics of complex materials, possibly providing a new tool to control and engineer their static cooperative properties.