[Paper Review] Probing phonon dynamics with multi-dimensional high harmonic carrier envelope phase spectroscopy

Ofer Neufeld, Jin Zhang+3 more|arXiv (Cornell University)|Mar 9, 2022

Laser-Matter Interactions and ApplicationsPhysics and Astronomy68 references58 citations

TL;DR

This study introduces multi-dimensional high harmonic generation (HHG) spectroscopy using carrier envelope phase (CEP) sensitivity to probe ultrafast phonon dynamics in monolayer hexagonal boron nitride (hBN). By exciting coherent phonons with a terahertz pump and probing with an intense infrared pulse, the authors demonstrate that phonon-induced lattice distortions transform discrete HHG spectra into continuous plateaus, with HHG yield oscillating on a 1-femtosecond timescale due to sub-cycle contrast, enabling unprecedented temporal resolution and CEP-dependent sensitivity to instantaneous structural changes.

ABSTRACT

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-Boron-Nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab-initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons, and is no longer comprised of discrete harmonic orders, but rather of a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as bond compression or stretching. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope-phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity vs. pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing a new approach for ultrafast multi-dimensional HHG-spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ~1 femtosecond, which is much shorter than the probe pulse duration because of the inherent sub-cycle contrast mechanism. Our work paves the way towards novel routes of probing phonons and ultrafast material structural changes and provides a mechanism for controlling the high harmonic response.

Motivation & Objective

• To develop a new method for probing ultrafast lattice dynamics in 2D materials with sub-femtosecond resolution.
• To investigate how coherent phonons alter high harmonic generation (HHG) spectra in monolayer hBN.
• To explore the emergence of carrier-envelope-phase (CEP) sensitivity in HHG when phonons are coherently excited.
• To establish HHG as a multi-dimensional probe of structural dynamics via pump-probe delay and CEP dependence.
• To demonstrate that phonon-induced symmetry breaking leads to continuous HHG emission and enhanced nonlinear response.

Proposed method

• The study uses time-dependent density functional theory (TDDFT) within the Kohn-Sham formulation and the local-density approximation (LDA) to simulate electronic and ionic dynamics in hBN.
• Ionic motion is modeled via Ehrenfest dynamics, where forces on nuclei are computed from the electron density and laser field, allowing for electron-phonon coupling.
• The HHG process is driven by an intense infrared laser pulse with a vector potential 𝐀(𝑡) = 𝐴₀𝑓(𝑡)cos(𝜔𝑡 + 𝜙𝐶𝐸𝑃)𝐞̂, where f(t) is a super-sine envelope with Tp ≈ 25 fs (8T at 1600 nm).
• The time-dependent current density 𝐣(𝐫, 𝑡) is computed from Kohn-Sham orbitals, and the HHG spectrum is obtained via Fourier transform of the time derivative of the current, filtered with the laser envelope.
• Phonon modes—longitudinal optical (LO) at 38.9 THz (25.7 fs period) and out-of-plane optical (ZO) at 24.3 THz (41.1 fs)—are excited with amplitudes of a few percent of the lattice parameter.
• The system is simulated using the open-source octopus code on a 0.3 Bohr grid, with absorbing boundaries and a 0.2 a.u. time step to ensure convergence and minimize ionization.

Experimental results

Research questions

• RQ1 How do coherent phonons in hBN modify the structure of the high harmonic generation (HHG) spectrum?
• RQ2 Can the carrier-envelope-phase (CEP) of a long-duration IR pulse induce measurable sensitivity in HHG when phonons are coherently excited?
• RQ3 What is the temporal resolution of phonon dynamics achievable via this HHG-based probe?
• RQ4 How does the degree of CEP sensitivity correlate with instantaneous lattice distortions such as bond compression or stretching?
• RQ5 To what extent does phonon-induced lattice modulation break time-translation symmetry and lead to continuous harmonic emission?

Key findings

• The presence of coherent phonons transforms the HHG spectrum from discrete harmonic orders into a continuous emission in the plateau region due to the breaking of time-translation symmetry.
• The HHG yield exhibits strong, periodic oscillations with pump-probe delay, with a period matching the phonon oscillation (25.7 fs for LO mode), directly reflecting bond compression and stretching.
• A 1-femtosecond temporal resolution is achieved, significantly shorter than the 25-fs probe pulse duration, due to a sub-cycle contrast mechanism inherent in the HHG process.
• CEP sensitivity emerges in the HHG yield only when coherent phonons are excited, despite the multi-cycle nature of the IR pulse, indicating a novel coupling mechanism.
• The degree of CEP sensitivity varies with pump-probe delay and serves as a highly selective, real-time probe of instantaneous structural changes in the lattice.
• The method enables multi-dimensional HHG spectroscopy by simultaneously varying pump-probe delay, CEP, and laser polarization, offering a new route to study ultrafast lattice dynamics.