Non-Markovian heat production in ultrafast phonon dynamics

Abstract

High-intensity THz laser pulses enable the light-mediated control of lattice vibrations by resonantly driving selected phonon modes. On ultrafast timescales, memory effects influence the phonon dynamics and must be accounted for to describe the heat production associated with energy dissipation. Here, we establish a microscopic framework for non-Markovian phonon dynamics by deriving the noise and dissipation kernels governing a driven phonon mode. Using large-scale molecular dynamics simulations, we reconstruct these kernels directly from the many-body lattice dynamics and determine the corresponding heat production rate. Our results provide a quantitative picture of the crossover between Markovian and non-Markovian dynamics on picosecond timescales and show how the finite bandwidth of the driving field limits the dynamically relevant bath spectrum. Furthermore, we demonstrate that thermodynamic quantities such as heat production can be inferred directly from the dynamics of an individual phonon mode, enabling their experimental measurement using time-resolved spectroscopy.

Figures (2)

• Figure 1: (a) Schematic illustrating of driven by a THz laser pulse, leading to pumping of the ferroelectric mode, which on decay leads to the ultrafast generation of heat. The inset shows the primitive unit cell. (b) Phonon band structure along a high-symmetry path through the Brillouin zone. Solid blue lines show the harmonic dispersion corresponding to the zero-temperature limit. The green color map shows the spectral energy density representing the dispersion at 300. The ferroelectric mode (marked A), has a pronounced temperature dependence. The other $\Gamma$-modes are labeled B through D (see \ref{['sfig:temperature-dependence-gamma-modes']} for a more explicit illustration of their temperature dependence). (c) Excitation field due to the laser (in orange; with envelope indicated) and the mode amplitude of the ferroelectric mode (in blue) as a function of time. The inset shows the sampling of the phase space of the driven mode as a kernel-density map over the distribution of trajectories with markers representing specific simulations at approximately 5.59 corresponding to the maximum amplitude. The line shows the average path through phase space up to this time.
• Figure 2: (a) Total energy and heat production rate $\dot{q}(t)$ during pulse, where $\dot{q}(t)$ is obtained as the time derivative of the total energy. (b) Deviation in heat production rate between simulation and theory. (c) Noise $\mathcal{F}\left[\langle\xi(t)\xi(0)\rangle\right]$ of the ferroelectric mode (A in \ref{['fig:simulation-overview']}b) in comparison with the dos. The vertical dashed lines indicate the frequencies of the $\Gamma$-point modes (see \ref{['sfig:noise-acf-modes-and-dos']} for the noise for all modes).