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arXiv:2610.04863

Long-lived Coherent Phonons Reveal Competing Thermal and Many-Body Dynamics in $α$-In$_{2}$Se$_{3}$

Xuanchao Zhang, Dehao Yuan, Junhua Zhou, Vandana Tiwari, Fulu Zheng, Ajay Jha, Hong-Guang Duan

quant-phphysics.atm-clusSubmitted Oct 4, 2026• Announced Oct 6, 2026
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Abstract

The fate of quantum coherence following photoexcitation is a central problem in nonequilibrium condensed-matter physics, especially in low-dimensional solids where electronic, structural and many-body energy scales are strongly coupled. Here, we investigate this interplay in ferroelectric $α$-In$_{2}$Se$_{3}$ using broadband transient-grating spectroscopy with $\sim$5 fs laser pulses. Photoexcitation launches pronounced oscillations dominated by a $\sim$104 cm$^{-1}$ mode that persists for several picoseconds. Measurements from 10 to 300 K show that its frequency remains nearly unchanged while its coherence is progressively suppressed, distinguishing the lattice coordinate from thermally activated dephasing. Varying excitation energy reveals a distinct crossover in which increasing photoexcitation progressively modifies and damps the coherent response. First-principles calculations assign the dominant oscillation to a 101.47 cm$^{-1}$ $Γ$-point optical phonon involving collective In-Se displacement, while quantum-dynamical simulations reproduce the main transient-grating oscillations. These results establish $α$-In$_{2}$Se$_{3}$ as a model system for independently probing lattice coherence, thermal fluctuations and carrier-density-dependent interactions, revealing how a polar van der Waals semiconductor evolves from coherent lattice motion toward an incoherent many-body state after ultrafast excitation.

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Long-lived Coherent Phonons Reveal Competing Thermal and Many-Body Dynamics in ααα-In2_{2}2​Se3_{3}3​
The fate of quantum coherence following photoexcitation is a central problem in nonequilibrium condensed-matter physics, especially in low-dimensional solids where electronic, structural and many-body energy scales are strongly coupled. Here, we investigate this interplay in ferroelectric ααα-In2_{2}2​Se3_{3}3​ using broadband transient-grating spectroscopy with ∼\sim∼5 fs laser pulses. Photoexcitation launches pronounced oscillations dominated by a ∼\sim∼104 cm−1^{-1}−1 mode that persists for several picoseconds. Measurements from 10 to 300 K show that its frequency remains nearly unchanged while its coherence is progressively suppressed, distinguishing the lattice coordinate from thermally activated dephasing. Varying excitation energy reveals a distinct crossover in which increasing photoexcitation progressively modifies and damps the coherent response. First-principles calculations assign the dominant oscillation to a 101.47 cm−1^{-1}−1 ΓΓΓ-point optical phonon involving collective In-Se displacement, while quantum-dynamical simulations reproduce the main transient-grating oscillations. These results establish ααα-In2_{2}2​Se3_{3}3​ as a model system for independently probing lattice coherence, thermal fluctuations and carrier-density-dependent interactions, revealing how a polar van der Waals semiconductor evolves from coherent lattice motion toward an incoherent many-body state after ultrafast excitation.
The three-dimensional confinement created by the ultrasmall semiconductor structures known as quantum dots greatly modifies the optical properties of the spatially localized carriers. These systems are presently of great interest to the research community, both for the improved understanding of the physics of confined structures, and for the potential applications of these systems to areas such as optoelectronics and quantum computing. Here, the techniques of transient coherent nonlinear optical spectroscopy are applied to the investigation of excitons confined within InAs/GaAs self-assembled quantum dots. These methods provide a powerful tool for the study of dynamic processes in these novel materials. The nonlinear measurements are based on the differential transmission experimental geometry, and utilize ultrafast pulsed lasers in order to temporally resolve the carrier dynamics after excitation. The experiments performed here are resonant with the ground state absorption of the quantum dots, as evidenced by comparison with the photoluminescence measurements which are used to characterize the sample. The incoherent relaxation dynamics of the population of photoexcited excitons are examined, allowing for a determination of both the lifetime of the excitons and the time scale for relaxation between the two polarization eigenstates of the system. The three-dimensional quantum confinement results in the suppression of these relaxation processes, as predicted. The use of coherent spectroscopic techniques allows for the first unambiguous demonstration of an optically-induced nonradiative Raman coherence in these quantum dots. Simultaneous excitation of both polarization states of the exciton results in a coherent superposition state, whose temporal evolution is observed through the homodyne-detection scheme. In these transient experiments, this is manifested as a beating in the nonlinear response, which allows us to directly measure the fine-structure splitting between the polarization states. Utilizing optical pulse shaping techniques, transient spectral hole burning is performed, which allows for the nonlinear response to be spectrally resolved. As expected for the strongly confined quantum dot excitons, the results show that diffusion among the localized states is not a significant effect. Temperature dependent measurements show that at elevated temperatures, extra dephasing processes, potentially related to acoustic phonon scattering, become important. Finally, this technique allows for the first direct observation of the induced absorption from the exciton to biexciton transition in these InAs quantum dots, and a measurement of the associated binding energy. These results lay the foundation for future studies in this material system, and for the possible development of quantum logic devices utilizing quantum dots.
We analyze the thermalization of a photoexcited charge carrier coupled to a single branch of quantum phonons within the Holstein model. To this end, we calculate the far-from-equilibrium time evolution of a pure many-body state and compare it with predictions of the thermal Gibbs ensemble. We show that at strong enough carrier excitation, the nonequilibrium system evolves towards a thermal steady state. Our analysis is based on two classes of observables. First, the occupations of fermionic momenta, which are the eigenvalues of the one-particle density matrix, match in the steady state the values in the corresponding Gibbs ensemble. This indicates thermalization of static fermionic correlations on the entire lattice. Second, the dynamic current-current correlations, including the time-resolved optical conductivity, also take the form of their thermal counterparts. Remarkably, both static and dynamic fermionic correlations thermalize with identical temperatures. Our results suggest that the subsequent relaxation processes, observed in time-resolved ultrafast spectroscopy, may be efficiently described by applying quasithermal approaches, e.g., multitemperature models.
The dynamics of electrons and holes in semiconductors and semiconductor heterostructures have been extensively discussed in the literature, and are governed by their mutual Coulomb interaction, by their interaction with lattice vibrations (phonons) and by their radiative recombination (for an overview see e.g. Ref. [1]). A powerful technique to study the carrier dynamics in semiconductors utilizes short optical pulses to photoexcite electrons from the valence to the conduction band (i.e. to create electron-hole pairs) that subsequently relax until the photon energy stored in the medium is dissipated and the system has recovered the thermal equilibrium. The dynamics of the carriers photoexcited by the short optical pulse can be followed by monitoring two main optical observables: the interband population difference and the induced polarization. Both quantities decay with time after the photoexcitation due to the carrier dynamics. While the induced polarization (which is an ensemble average over many photoexcited dipole moments) is sensitive to scattering events that break the phase relationship among the individual dipoles and/or with the light field creating them (dephasing processes), the population difference is sensitive only to events that change the energy state of the carriers. Transient coherent optical spectroscopy addresses the time-evolution of the induced polarization in the time-regime during and immediately following the photoexcitation by a short laser pulse, in which the photoexcited dipoles have retained a defined phase relationship among each other and with the exciting coherent radiation.
We study theoretically electron transients in semiconductor alloys excited by light pulses shorter than 100 fs and tuned above the absorption edge during and shortly after the pulse, when disorder scattering is dominant. We use nonequilibrium Green functions employing the field-dependent self-consistent Born approximation. The propagators and the particle correlation function are obtained by a direct numerical solution of the Dyson equations in differential form. For the purely elastic scattering in our model system the solution procedures for the retarded propagator and for the correlation function can be decoupled. The propagator is used as an input in calculating the correlation function. Numerical results combined with a cumulant expansion permit one to separate in a consistent fashion the dark and the induced parts of the self-energy. The dark behavior reduces to propagation of strongly damped quasiparticles; the field induced self-energy leads to an additional time nonlocal coherence. The particle correlation function is formed by a coherent transient and an incoherent back-scattered component. The particle number is conserved only if the field induced coherence is fully incorporated. The transient polarization and the energy balance are also obtained and interpreted.
Ultrafast pump-probe spectroscopy provides a powerful means to investigate electron-phonon (e-ph) interactions in strongly correlated systems. Nevertheless, the question of how different microscopic e-ph coupling mechanisms influence the lattice's nonequilibrium response has not been widely addressed. We perform time-dependent density matrix renormalization group simulations on a pumped one-dimensional Mott insulator coupled to phonons through either Holstein or Su-Schrieffer-Heeger (SSH) interactions. The electronic responses of the two models are qualitatively similar in the Mott-insulating regime and are governed by the same excitations and resonance conditions of the Hubbard model. In contrast, the lattice dynamics of the two models differ substantially. While the Hubbard-Holstein model exhibits long-lived coherent phonon oscillations when the pump resonates with the bare phonon frequency, no such oscillations are observed for the Hubbard-SSH model. These contrasting responses remain robust against changes in phonon frequency and pump parameters, suggesting that coherent lattice dynamics can provide a direct nonequilibrium probe of the microscopic form of e-ph coupling.
We have studied the coherent emission from bulk semiconductors by spectrally resolved and spectrally integrated four-wave mixing (FWM) with broadband 16-fs pulses in the carrier density range from $1\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ to $6\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ In GaAs, only continuum transitions are excited, while both excitonic and continuum transitions are excited in Al0.06Ga0.94As.{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}.Al0.06​Ga0.94​As. The decay of the FWM signal for positive time delays unambiguously reflects the dephasing of the continuum, irrespective of the excitation of excitonic transitions. We find identical ultrafast sub-20-fs decay times of the coherent emission from continuum transitions in GaAs and Al0.06Ga0.94As,{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As},Al0.06​Ga0.94​As, independent of the excess excitation energy. These decay times depend only weakly on the carrier density for densities below ${10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The continuum dephasing is analyzed considering carrier-carrier and carrier-LO-phonon scattering in a relaxation rate approach. The excitonic transitions in Al0.06Ga0.94As{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}Al0.06​Ga0.94​As dominate the FWM signal at negative time delays.