Quantum theory of nonlinear phononics

TL;DR

This work develops an analytic quantum theory of nonlinear phononics by reformulating the TD-SCHA with a fourth-order Taylor expansion of the potential, enabling exact ensemble averages and closed-form dynamics of lattice fluctuations. It demonstrates that a strong, out-of-equilibrium phonon excitation quenches its own quantum fluctuations (density cooling), reshaping the potential energy surface to facilitate symmetry breaking in materials with double-well soft modes. The theory recovers established quenching models in appropriate limits and provides a new paradigm for driving light-induced phase transitions through quantum fluctuation cooling. The framework offers an efficient, atomistically grounded tool for predicting and engineering quantum nuclear dynamics in real materials under ultrafast excitations.

Abstract

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 provide an analytic proof that, in general, a strong pulse displacing a phonon mode from equilibrium induces the quenching, or squeezing, of its quantum lattice fluctuations. This finding, which establishes a systematization of the mechanism observed in Ref. 1, introduces a new paradigm in nonlinear phononics, harnessing this cooling effect to drive symmetry breaking in quantum paraelectric materials.

Figures (4)

• Figure 1: The selective excitation of a phonon mode with a strong laser pulse induces a cooling of its lattice fluctuations, resulting in a narrowing of its density. This narrowing significantly affects the ensemble average of the potential energy $\langle V \rangle$, and can restore the double-well shape of the bare PES.
• Figure 2: The blue line represents the FES of the one-dimensional model calculated at 0 K, as defined in Eq. \ref{['free_surface_eq']}. To enhance the visibility of its minima, it has been scaled by a factor of 5. The black dashed line corresponds to the bare potential energy, as defined in Eq. \ref{['V_1d']}. The grey and light blue lines represent the ensemble-averaged potential energy, computed for $\mathcal{A} = \mathcal{A}_{GS}$ and $\mathcal{A} = \mathcal{A}_{MS}$, respectively. Notably, the minimum of the grey curve aligns with the equilibrium position of the GS ($\mathcal{R}_{GS} = 0$), while the minimum of the light blue curve corresponds to the MS ($\mathcal{R}_{MS} \simeq 1\ \mathrm{\AA\sqrt{amu}}$).
• Figure 3: The upper and lower panels show the dynamics of $\mathcal{R}$ and $\mathcal{A}$, respectively, for different electric field strengths. In the left panels, $\mathcal{A}$ is evolved according to Eq. \ref{['single']}, while in the right panels it is kept constant to the initial equilibrium value.
• Figure 4: Phase portrait of the dynamics of $\mathcal{A}$ for different electric fields. The starting point is marked with a circle, while the end point with a star.