Coherent control through phonon anharmonicity

Anharmonic lattice vibrations play a key role in many physical phenomena. They govern the heat conductivity of solids, strongly affect the phonon spectra, play a prominent role in soft mode phase transitions, allow ultrafast engineering of material properties and more. The most direct evidence for anharmonicity is to measure the oscillation frequency changing as a function of the oscillation amplitude. For lattice vibrations, this is not a trivial task, and anharmonicity is probed indirectly through its effects on thermodynamic properties and spectral features or through coherent decay of one mode to another. However, measurement and control of the anharmonicity of a single Raman mode is still lacking. We show that ultrafast double pump-probe spectroscopy could be used to directly observe frequency shifts of Raman phonons as a function of the oscillation amplitude and disentangle the coherent contributions from quasi-harmonic sources such as temperature and changes to the carrier density in the thermoelectric materials SnTe and SnSe. Moreover, we show that coherent displacive phononic excitations in tandem with electron-phonon coupling is a pathway to dynamically control phonon anharmonicity. Our results have dramatic implications for the material engineering of future thermoelectrics. Moreover, our methodology could be used to isolate the basic mechanisms driving optically induced phase transitions and other nonlinear phenomena based on their unique timestamps.

💡 Research Summary

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The authors present a novel experimental approach for directly measuring and controlling phonon anharmonicity in thermoelectric materials, specifically SnTe and SnSe. While anharmonicity is known to influence thermal conductivity, phase transitions, and ultrafast material engineering, its most direct signature—frequency shift as a function of vibrational amplitude—has never been observed for a single Raman‑active mode.

To achieve this, the team employs ultrafast double‑pump‑probe spectroscopy. In a conventional single‑pump experiment, a 70–126 fs pulse at 750 nm excites electrons across the Sn–Te (or Sn–Se) bond, initiating a displacive excitation of coherent phonons (DECP). The resulting ΔR/R signal comprises a fast electronic decay, a slower thermal relaxation, and a damped cosine oscillation corresponding to the A_g Raman mode. By varying the pump fluence from 0.68 mJ cm⁻² up to ~4 mJ cm⁻², the authors observe a monotonic softening of the phonon frequency by up to 20 % (from ~3.65 THz to ~2.9 THz). This softening exceeds what would be expected from pure heating, indicating a substantial anharmonic contribution.

The key innovation is the addition of a second, weaker pump pulse (the “trailing” pump) whose arrival time relative to the first (the “leading” pump) can be precisely controlled (Δt_pp). By mechanically chopping only the trailing pump, the contribution of each pump to the reflectivity change can be isolated. When the trailing pump arrives at various delays, the frequency of the coherent phonon exhibits a non‑monotonic, oscillatory dependence on Δt_pp, with amplitude variations as large as 0.3 THz. This behavior is interpreted as a direct manifestation of anharmonicity: the phonon potential is transiently softened by the photo‑induced electron density, then recovers as electrons recombine and the lattice cools, causing the curvature of the potential—and thus the phonon frequency—to oscillate in time. The observed asymmetry between the rising and falling edges of the frequency shift further supports a DECP‑driven, direction‑dependent modulation of the potential.

To quantitatively describe these dynamics, the authors extend the standard DECP model by allowing both the equilibrium position ΔQ(t) and the curvature k(t) of the harmonic potential to evolve exponentially with characteristic electronic (τ_e) and thermal (τ_th) time constants. Fitting this model to the experimental data yields an electron‑phonon coupling constant of ħΔω/Δn ≈ 0.41 meV, an electronic relaxation time of ~0.5 ps, and a thermal relaxation time of ~5 ps. The model reproduces the short‑time oscillatory frequency shifts, the long‑time exponential recovery, and the asymmetric line shapes. Small systematic deviations at large amplitudes suggest the presence of higher‑order anharmonic terms (cubic or quartic) not captured by the quadratic model.

The study demonstrates three major advances. First, it proves that phonon anharmonicity can be amplified and controlled optically through the combined action of DECP‑induced bond softening and subsequent electron‑phonon coupling, beyond simple temperature effects. Second, the double‑pump‑probe technique provides a temporal “fingerprint” that separates electronic, thermal, and anharmonic contributions, enabling quantitative extraction of mode‑specific electron‑phonon coupling. Third, by linking the observed frequency shifts to changes in Umklapp and point‑defect scattering times (which scale as ω⁻² and ω⁻⁴), the work offers a practical pathway to engineer thermal transport in thermoelectric devices via ultrafast light control.

Although the measurements are limited to Γ‑point phonons, the authors argue that the methodology is general and could be extended to other Brillouin‑zone points, to non‑Raman modes, and to a broad class of materials undergoing photo‑induced phase transitions. Consequently, this work opens a new avenue for manipulating lattice dynamics on femtosecond timescales, with potential impact on the design of high‑performance thermoelectrics, ultrafast switches, and nonlinear phononic devices.