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Nature Photonics

Sub-cycle multidimensional spectroscopy of strongly correlated materials

V. N. Valmispild, Evgeny Gorelov, Martin Eckstein, Alexander I. Lichtenstein, Hideo Aoki, Mikhail I. Katsnelson, Misha Ivanov, Olga V. Smirnova

Published Jan 24, 2024• 31 citations
Publisher

Abstract

Abstract Strongly correlated solids are complex and fascinating quantum systems, where new electronic states continue to emerge, especially when interaction with light triggers interplay between them. In this interplay, a sub-laser-cycle electronic response is particularly attractive as a tool for the ultrafast manipulation of matter at the petahertz scale. Here we introduce a new type of nonlinear multidimensional spectroscopy, which allows us to unravel charge and energy flows in strongly correlated systems interacting with few-cycle infrared pulses and the complex interplay between different correlated states evolving on the sub-femtosecond timescale. We demonstrate that the sub-cycle spectroscopy of a single-particle electronic response is extremely sensitive to correlated many-body dynamics and provides direct access to many-body response functions. For the two-dimensional Hubbard model under the influence of ultrashort, intense electric-field transients, we resolve the sub-femtosecond pathways of charge and energy flows between localized and delocalized many-body states and the creation of a highly correlated state surviving after the end of the laser pulse. Our findings open the way towards a regime of imaging and manipulating strongly correlated materials at optical rates, beyond the multicycle approach employed in Floquet engineering, with the sub-cycle response being a key tool for accessing many-body phenomena.

DOI
10.1038/s41566-023-01371-1

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Abstract Strongly correlated solids are complex and fascinating quantum systems, where new electronic states continue to emerge, especially when interaction with light triggers interplay between them. In this interplay, a sub-laser-cycle electronic response is particularly attractive as a tool for the ultrafast manipulation of matter at the petahertz scale. Here we introduce a new type of nonlinear multidimensional spectroscopy, which allows us to unravel charge and energy flows in strongly correlated systems interacting with few-cycle infrared pulses and the complex interplay between different correlated states evolving on the sub-femtosecond timescale. We demonstrate that the sub-cycle spectroscopy of a single-particle electronic response is extremely sensitive to correlated many-body dynamics and provides direct access to many-body response functions. For the two-dimensional Hubbard model under the influence of ultrashort, intense electric-field transients, we resolve the sub-femtosecond pathways of charge and energy flows between localized and delocalized many-body states and the creation of a highly correlated state surviving after the end of the laser pulse. Our findings open the way towards a regime of imaging and manipulating strongly correlated materials at optical rates, beyond the multicycle approach employed in Floquet engineering, with the sub-cycle response being a key tool for accessing many-body phenomena.
Multidimensional coherent spectroscopy (MDCS) has been established in quantum chemistry as a powerful tool for studying the nonlinear response and nonequilibrium dynamics of molecular systems. More recently, the technique has also been applied to correlated electron materials, where the interplay of localized and itinerant states makes the interpretation of the spectra more challenging. Here we use the Keldysh contour representation of effective models and nonequilibrium dynamical mean field theory to systematically study the MDCS signals of prototypical correlated lattice systems. By analyzing the current induced by sequences of ultrashort laser pulses we demonstrate the usefulness of MDCS as a diagnostic tool for excitation pathways and coherent processes in correlated solids. We also show that this technique allows to extract detailed information on the nature and evolution of photo-excited nonequilibrium states.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23rd^{rd}rd order in the prototypical Mott insulator La2_22​CuO4_44​. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.
Solid-state high-harmonic spectroscopy is becoming an emerging tool for probing nonequilibrium many-body dynamics. Yet, direct measurements of strongly driven, sub-optical-cycle dynamics in correlated materials during high-harmonic emission remain largely unexplored. Here, we measure high-harmonic emission chirp in a prototypical one-dimensional Mott insulator, which encodes strongly driven doublon-holon dynamics at sub-optical-cycle timescales. We observe a positive chirp for above band gap harmonics, indicating that high harmonics are dominated by doublon-holon recombinations. We further show a harmonic order-dependent dephasing, which can be understood through different doublon-holon excursion distances associated with each harmonic. These results reveal coherent doublon-holon dynamics and their ultrafast dephasing in Mott insulators, which is relevant to other nonequilibrium light-induced phenomena, such as Floquet engineering.
Interactions between particles in quantum many-body systems play a crucial role in determining the electric, magnetic, optical, and thermal properties of the system. The recent progress in the laser-pulse technique has enabled the manipulations and measurements of physical properties on ultrafast timescales. Here we propose a method for the direct and ultrafast probing of quantum many-body interaction through coherent two-dimensional (2D) spectroscopy. Using a two-band fermionic Hubbard model for the minimum two-site lattice system, we find that the 2D spectrum of a noninteracting system contains only diagonal peaks; the interparticle interaction manifests itself in the emergence of off-diagonal peaks in the 2D spectrum before all the peaks coalesce into a single diagonal peak as the system approaches the strongly interacting limit. The evolution of the 2D spectrum as a function of the time delay between the second and third laser pulses can provide important information on the ultrafast time variation of the interaction.
The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.