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arXiv:1808.02604 · Physical review. B./Physical review. B

Theory of time-resolved Raman scattering in correlated systems: Ultrafast engineering of spin dynamics and detection of thermalization

Yao Wang, Thomas Devereaux, Cheng-Chien Chen

Published Dec 4, 2018• 14 citations
arXivHTMLPDF

Abstract

Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics, especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-probe dynamics of correlated electrons in the square-lattice single-band Hubbard model. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, we show that the Floquet theory works well in capturing the softening of bimagnon excitation. By comparing the Stokes and anti-Stokes spectra, we also show that effective heating dominates at small pump fluences, while a coherent many-body effect starts to take over at larger pump amplitudes and frequencies on resonance to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore different ultrafast processes and design material properties out of equilibrium.

DOI
10.1103/physrevb.98.245106

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Ultrafast characterization and control of many-body interactions and elementary excitations are critical to understanding and manipulating emergent phenomena in strongly correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics, especially out of equilibrium, are still lacking. To address this question, we develop a theory for nonresonant time-resolved Raman scattering, which can be a generic and powerful tool for nonequilibrium studies. We also use exact diagonalization to simulate the pump-probe dynamics of correlated electrons in the square-lattice single-band Hubbard model. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, we show that the Floquet theory works well in capturing the softening of bimagnon excitation. By comparing the Stokes and anti-Stokes spectra, we also show that effective heating dominates at small pump fluences, while a coherent many-body effect starts to take over at larger pump amplitudes and frequencies on resonance to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore different ultrafast processes and design material properties out of equilibrium.
Raman spectroscopy uses light scattering to extract information on low-energy excitations of solids. The Raman process is described by diagrams which are fourth order in the light-matter interaction and in particular the resonant contribution, which involves four different space-time arguments, is difficult to evaluate. If one instead simulates explicitly the incoming (classical) light pulse, the Raman signal is given by the outgoing photon flux and can be determined from a two-point correlation function. Such a formalism can be used to compute the time-resolved Raman spectrum of nonequilibrium systems, as well as nonlinear signals which are higher order in the incoming field, such as hyper-Raman scattering. Here we explain how to implement this time-dependent formalism within the dynamical mean field theory framework. The method is illustrated with applications to the Holstein-Hubbard model in the strong electron-phonon coupling regime. We demonstrate hyper-Raman scattering in measurements with strong probe fields and frequency mixing signals in the presence of a pump field and simulate the evolution of Stokes and anti-Stokes features after photoexcitations of metallic and Mott insulating systems.
We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump- probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. We describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.
Collective excitations contain rich information about photoinduced transient states in correlated systems. In a Mott insulator, charge degrees of freedom are frozen, but can be activated by photodoping. The energy-momentum distribution of the charge excitation spectrum reflects the propagation of charge degrees of freedom and provides information about the interplay among various intertwined instabilities on the timescale set by the pump. To reveal charge excitations out of equilibrium, we simulate time-resolved x-ray absorption and resonant inelastic x-ray scattering using a Hubbard model. After pumping, the former resolves photodoping, while the latter characterizes the formation, dispersion, weight, and nonlinear effects of collective excitations. Intermediate-state information from time-resolved resonant inelastic x-ray scattering (trRIXS) can be used to decipher the origin of these excitations, including bimagnons, Mott-gap excitations, doublon and single-electron in-gap states, and anti-Stokes relaxation during an ultrafast pump. This paper provides a theoretical foundation for existing and future trRIXS experiments.
Nonequilibrium dynamics in correlated materials has attracted attention due to the possibility of characterizing, tuning, and creating complex ordered states. To understand the photoinduced microscopic dynamics, especially the linkage under realistic pump conditions between transient states and remnant elementary excitations, we performed nonperturbative simulations of various time-resolved spectroscopies. We used the Mott antiferromagnetic insulator as a model platform. The transient dynamics of multiparticle excitations can be attributed to the interplay between Floquet virtual states and a modification of the density of states, in which interactions induce a spectral weight transfer. Using an autocorrelation of the time-dependent spectral function, we show that resonance of the virtual states with the upper Hubbard band in the Mott insulator provides the route towards manipulating the electronic distribution and modifying charge and spin excitations. Our results link transient dynamics to the nature of many-body excitations and provide an opportunity to design nonequilibrium states of matter via tuned laser pulses.
Abstract Manipulating spin fluctuations with ultrafast laser pulses is a promising route to dynamically control collective phenomena in strongly correlated materials. However, understanding how photoexcited spin degrees of freedom evolve at a microscopic level requires a momentum- and energy-resolved characterization of their nonequilibrium dynamics. Here, we study the photoinduced dynamics of finite-momentum spin excitations in two-dimensional Mott insulators on a square lattice. By calculating the time-resolved resonant inelastic x-ray scattering cross-section, we show that an ultrafast pump above the Mott gap induces a prompt softening of the spin excitation energy, compatible with a transient renormalization of the exchange interaction. While spin fluctuations in a hole-doped system (paramagnons) are well described by Floquet theory, magnons at half filling are found to deviate from this picture. Furthermore, we show that the paramagnon softening is accompanied by an ultrafast suppression of d-wave pairing correlations, indicating a link between the transient spin excitation dynamics and superconducting pairing far from equilibrium.
We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean-field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the infinite-dimensional spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the A1g{A}_{1\mathrm{g}}A1g​ and B2g{B}_{2\mathrm{g}}B2g​ sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.