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arXiv:2403.04209 · Nano Letters

Phonon State Tomography of Electron Correlation Dynamics in Optically Excited Solids

Mattia Moroder, Matteo Mitrano, Ulrich Schollwöck, Sebastian Paeckel, John Sous

Published Nov 26, 2024• 3 citations
arXivHTMLPDF

Abstract

We introduce phonon state tomography (PST) as a diagnostic probe of electron dynamics in solids whose phonons are optically excited by a laser pulse at initial time. Using a projected-purified matrix-product states algorithm, PST decomposes the exact correlated electron-phonon wavefunction into contributions from purely electronic states corresponding to statistically typical configurations of the optically accessible phononic response, enabling a "tomographic" reconstruction of the electronic dynamics generated by the phonons. Thus, PST may be used to diagnose electronic behavior in experiments that access only the phonon response, such as thermal diffuse X-ray and electron scattering. We study the dynamics of a metal whose infrared phonons are excited by an optical pulse at initial time and use it to simulate the sample-averaged momentum-resolved phonon occupancy and accurately reconstruct the electronic correlations. We also use PST to analyze the influence of different pulse shapes on the light-induced enhancement and suppression of electronic correlations.

DOI
10.1021/acs.nanolett.4c04314

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We introduce phonon state tomography (PST) as a diagnostic probe of electron dynamics in solids whose phonons are optically excited by a laser pulse at initial time. Using a projected-purified matrix-product states algorithm, PST decomposes the exact correlated electron-phonon wavefunction into contributions from purely electronic states corresponding to statistically typical configurations of the optically accessible phononic response, enabling a "tomographic" reconstruction of the electronic dynamics generated by the phonons. Thus, PST may be used to diagnose electronic behavior in experiments that access only the phonon response, such as thermal diffuse X-ray and electron scattering. We study the dynamics of a metal whose infrared phonons are excited by an optical pulse at initial time and use it to simulate the sample-averaged momentum-resolved phonon occupancy and accurately reconstruct the electronic correlations. We also use PST to analyze the influence of different pulse shapes on the light-induced enhancement and suppression of electronic correlations.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
Measuring fluctuations in matter's low-energy excitations is the key to unveiling the nature of the non-equilibrium response of materials. A promising outlook in this respect is offered by spectroscopic methods that address matter fluctuations by exploiting the statistical nature of light-matter interactions with weak few-photon probes. Here we report the first implementation of ultrafast phase randomized tomography, combining pump-probe experiments with quantum optical state tomography, to measure the ultrafast non-equilibrium dynamics in complex materials. Our approach utilizes a time-resolved multimode heterodyne detection scheme with phase-randomized coherent ultrashort laser pulses, overcoming the limitations of phase-stable configurations and enabling a robust reconstruction of the statistical distribution of phase-averaged optical observables. This methodology is validated by measuring the coherent phonon response in α-quartz. By tracking the dynamics of the shot-noise limited photon number distribution of few-photon probes with ultrafast resolution, our results set an upper limit to the non-classical features of phononic state in α-quartz and provide a pathway to access non-equilibrium quantum fluctuations in more complex quantum materials.
The non-equilibrium dynamics of matter excited by light may produce electronic phases, such as laser-induced high-transition-temperature superconductivity, that do not exist in equilibrium. Here we simulate the dynamics of a metal driven at initial time by a spatially uniform pump that excites dipole-active vibrational modes which couple nonlinearly to electrons. We provide evidence for rapid loss of spatial coherence, leading to emergent effective disorder in the dynamics, which arises in a system unitarily evolving under a translation-invariant Hamiltonian, and dominates the electronic behavior as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. Our framework provides a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of realizing dynamically induced disorder in translation-invariant systems.
The nonequilibrium interplay of electrons and phonons plays an important role in the thermalization of solids, yet the microscopic picture of transient states and relaxation pathways remains incomplete. Previous nonequilibrium Green's function (NEGF) studies with full two-time dependence were restricted to local phonons and local self-energy approximations, leaving momentum-dependent phonon dynamics largely unexplored. Here, we demonstrate the recently developed quantics-tensor-train (QTT) NEGF framework via large-scale lattice simulations of models with arbitrary phonon dispersions. QTTs provide a memory-efficient representation of full two-time Green's functions, enabling momentum-resolved simulations with full electron-phonon feedback on lattices up to 256x256 sites. Comparing optical and acoustic phonon models, we reveal a hierarchy of relaxation bottlenecks that extends the well-known phonon-window bottleneck effect. For optical phonons, we confirm the main phonon-energy window and uncover an additional reduced window separating momentum-space regions with excess and deficit electronic population. We also identify a separate phonon-thermalization bottleneck rooted in momentum-dependent coupling to the particle-hole continuum. High momentum and frequency resolution makes the phonon--charge correspondence directly visible. For acoustic phonons, the phonon-energy window acquires pronounced momentum dependence dictated by energy and momentum conservation. The reduced window becomes asymmetric, and directional scattering between Brillouin-zone regions produces a persistent bottleneck for low-momentum phonon modes. Our results establish diagrammatic QTT-NEGF simulations as a scalable framework for quantitative nonequilibrium electron-phonon dynamics, overcoming previous lattice-size and propagation-time limitations and providing accurate reference data for time-resolved spectroscopies.
Real-time time-dependent density functional theory provides a first-principles description of coherent electron dynamics in laser-driven solids, but its unitary formulation cannot capture the irreversible scattering, relaxation, and decoherence processes that drive excited carriers toward equilibrium. Here, we develop a dissipative rt-TDDFT framework in which first-principles electron-phonon interactions enter the evolution of the reduced one-body density matrix through self-energy-derived collision integrals within the Born-Markov approximation. The approach retains the quantum-coherent real-time propagation of the electronic system while introducing phonon-mediated transitions that redistribute carriers in energy and crystal momentum, thereby incorporating the microscopic momentum-transfer processes responsible for relaxation in real materials. The resulting framework provides a practical first-principles route to simulate relaxation, decoherence, and time-resolved spectroscopic signatures in realistic crystalline materials.
Abstract Semiconductor quantum dots are solid state few‐level systems which can interact strongly with light. As such, they can be used as a single photon source or to perform solid‐state quantum‐optics experiments. A major difference to atoms is the interaction with the lattice vibrations, that is, the phonons, which strongly affect the optical signals from a quantum dot. In this paper, we calculate the time‐resolved pump‐probe signals from a continuously driven quantum dot accounting for detuned excitation and electron–phonon interaction. We provide analytical equations giving insight into the different phenomena observed in the spectra like an oscillation between absorptive and dispersive line shapes. For detuned excitation, the electron–phonon interaction can lead to phonon‐assisted occupation of the exciton, giving rise to a strong asymmetry in the dynamical behavior depending on the sign of the detuning. The time‐resolved spectra monitor this relaxation path, which helps understanding the effect of electron–phonon interaction in quantum dots.