Parametric resonances in Floquet materials

Abstract

In this thesis I explore the consequences of parametric resonance in Floquet materials, i.e. matter with periodically varying properties in time, and show that they give rise to universal features in experimental observables that can explain a host of modern experimental work. I illustrate, how Floquet materials can be realised both in condensed matter systems pumped by light and in artificially created ultra-cold gases under shaking. I demontrate how shaken 1-D ultra-cold condensates offer an ideal platform to study analytically quantum properties of Floquet matter. In particular, I study analytically the generation of many-body many-mode squeezing during shaking. In pump and probe experiments on condensed matter systems, I explain how pumping can be viewed in special cases as creating a Floquet material. I uncover ubiquitous signatures in optical reflectivity of Floquet materials that arise due to parametric resonances. The line-shapes of the resonant signatures are universal and are controlled by the competition between dissipation and driving. I illustrate the universality of my results by applying the Floquet material framework developed in this thesis on two concrete experimental examples, THz pumping in the cuprate superconductor, $\rm{YBa_2Cu_3O_{6.5}}$, and optical pumping in the excitonic insulator candidate, $\rm{Ta_2 Se Ni_5}$. First, in experiments on $\rm{YBa_2Cu_3O_{6.5}}$, I unveil that photo-induced edge features in optical reflectivity spectra both below and above the transition temperature correspond to parametric driving of plasma Josephson plasmons. Second, in $\rm{Ta_2 Se Ni_5}$, I demonstrate that parametrically amplified reflectivity in the terahertz region is evidence that terahertz coherent oscillations are excited through high frequency optical pumping. Using DFT calculations we show that strong-electron phonon coupling mediated by the order parameter is responsible for the dramatic frequency down conversion.

In essence, the effects of parametric resonances in Floquet materials revealed by my work are: a) Generation of squeezed states and entanglement occurring through parametrically resonant excitation of collective mode pairs. b) Compensation of dissipation of collective excitations, revealing overdamped dynamics in many body systems. c) Appearance of universal resonance features in frequency dependent reflectivity spectra, whose resonance shapes depend on the competition between dissipation and parametric driving. d) Onset of lasing instabilities of collective modes when parametric driving offered by the Floquet medium is far stronger than dissipation. The approach I develop in this work pushes beyond the static approximation of Floquet systems which uses high frequency perturbative Magnus expansion. At the heart of the physics described in this thesis is the frequency mixing in Floquet materials responsible for parametric resonances.