Quantum heat current in Terahertz-driven phonon systems

TL;DR

The paper develops a quantum open-system description of a THz-driven optical phonon interacting with a structured bath via a Caldeira–Leggett model, deriving an exact expression for the non-Markovian quantum heat current. It analyzes how ultrafast pulses probe bath memory by contrasting long and short drive durations, showing revivals and energy backflow in the non-Markovian regime. A Lorentzian bath spectrum is used to illustrate memory effects and to define a metric for backflow, $\mathcal{M}_J$, as a diagnostic of non-Markovianity. The work provides a predictive framework for pump–probe experiments on driven phonons in solids and offers routes to extract bath spectral information from observed heat-flow signatures.

Abstract

The advent of high-intensity ultrafast laser pulses has opened new opportunities for controlling and designing quantum materials. In particular, terahertz (THz) pulses can resonantly drive optical phonon modes, enabling dynamic manipulation of lattice degrees of freedom. In this work, we investigate the ultrafast quantum thermodynamics of optical phonon mode driven by a THz pulse by treating the phonon as an open quantum system coupled to a thermal environment within a Caldeira-Leggett-type framework. We derive the quantum heat current between the phonon and the bath and analyze its behavior under realistic pulse protocols. Our results demonstrate that ultrafast laser driving can reveal and even induce significant deviations from the commonly adopted Markovian approximation, thereby providing a pathway to probe and control non-Markovian dissipation in driven solid-state systems.

Figures (3)

• Figure 1: (a) Quantum criterion $\coth\left[\hbar\omega_0(T)/(2k_{\mathrm{B}}T)\right]$ for the ferroelectric soft mode of $\text{SrTiO}_3$ (blue solid), $\text{KTaO}_3$ (red dashed) and a fixed frequency $\omega_0=2.0~\text{THz}$ (purple dotted). The data for the temperature-dependent soft-mode frequency is taken from Ref. vogt1995. (b) Power spectral density $S(\omega)$ of the quantum noise for different temperatures. The bath spectral density $J(\omega)$ is taken to be Lorentzian as defined in Eq. \ref{['eq:Jw']}, The parameters are set to be $\Omega = 1.0~\text{THz}$, $\Gamma = 0.1\,\Omega$ and $g = 0.3\,\Omega^2$.
• Figure 2: (a) Time profiles of a long Gaussian laser pulse $F_L(t)$ (blue solid) and a short Gaussian laser pulse $F_S(t)$ (red dotted), both centered at $t_0$. (b) Schematic illustration of the corresponding frequency distributions: the spectra of the long pulse $\tilde{F}_L(\omega)$ (blue solid), the short pulse $\tilde{F}_S(\omega)$ (red dotted) and the system’s response function $\chi(\omega)$ (purple dashed).
• Figure 3: Influence of the pulse duration $\tau$ of the laser force on the dynamics of $\langle \hat{Q}(t)\rangle$ and on the quantum heat current $J(t)$. (a) Dynamics of the phonon displacement $\langle \hat{Q}(t)\rangle$ driven by a long pulse with $\tau = 5.0~\text{ps}$; (b) $\langle \hat{Q}(t)\rangle$ driven by a short pulse with $\tau = 1.0~\text{ps}$; (c) quantum heat current calculated from Eq. \ref{['eq:J_t2']} for the long pulse; and (d) the corresponding heat current for the short pulse. The fixed parameters of the spectral density $J(\omega)$ are $\Gamma = 0.1~\omega_{0}$ and $g = 0.3~\omega_{0}^2$.