Light-Driven Transitions in Quantum Paraelectrics

Motivated by recent measurements of terahertz field-induced ferroelectric transitions in the quantum paraelectric SrTiO$_3$, we study a driven phonon system close to a second order phase transition. Exploring the system’s classical dynamics, we find that at sufficiently large fluence, there are polarization-sensitive transitions into ordered phases, some of which are inaccessible in equilibrium. More specifically for certain polarizations we demonstrate the existence of two-step transitions to ordered phases and at still higher fluence the onset of chaotic behavior. Moving beyond classical dynamics, we develop a formalism for including quantum corrections in a controlled way and we study the effects of quantum fluctuations on the critical fluences with observable consequences.