Effects of Zero-Point Motion in the High Harmonic Generation Spectrum of Solids

The interpretation of high-harmonic generation (HHG) in solids typically relies on phenomenological dephasing times far shorter than what is expected from microscopic scattering processes. Here we show that zero-point fluctuations associated with optical phonons naturally suppress long-range electronic coherences and generate clean harmonic spectra without introducing ad-hoc decoherence parameters. Using a 1D semiconductor composed of two distinct sites per unit cell and realistic phonon amplitudes, we demonstrate that random per-site optical-phonon jitter reproduces the spectral sharpening typically attributed to ultrafast $T_2$ dephasing. In contrast, acoustic phonons and local strain, whose distortions are correlated over nanometer scales, produce negligible spectral cleaning. We further show that such long-range site coherence leads to carrier-envelope-phase-dependent effects in the HHG spectrum driven by long pulses, but these effects collapse once optical-phonon-induced decoherence is included. Our results (i) identify optical zero-point motion as a key mechanism governing coherence in solid-state HHG, (ii) demonstrate that it can be qualitatively modeled in periodic solids through site-distance-dependent dephasing, and (iii) suggest that CEP-resolved measurements can probe electronic coherence lengths and atomic fluctuations in crystalline materials.