Quantum theory of nonlinear phononics

The recent capability to use THz pulses to control the nuclear quantum degrees of freedom in crystals has opened promising avenues for the advanced manipulation of material properties. While numerical approaches exist for studying the time evolution of the quantum nuclear density matrix, an interpretable analytical framework to explicitly analyze the influence of quantum fluctuations on nuclear dynamics remains lacking. In this work, we present an analytical quantum theory of nonlinear phononics. This framework is a basis for deriving models of realistic materials, allowing for exact solutions of the nuclear time evolution with full consideration of quantum fluctuations. This is accomplished by treating for all possible third- and fourth-order phonon couplings and expressing forces as analytic functions of such fluctuations. We demonstrate that, in general, a strong pulse displacing a phonon mode from equilibrium induces the quenching, or squeezing, of its quantum lattice fluctuations. This finding introduces a new paradigm in nonlinear phononics, harnessing this cooling effect to drive symmetry breaking in quantum paraelectric materials.