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Characterizing and controlling entanglement in quantum materials is crucial for the development of next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in macroscopic solids is theoretically and experimentally challenging. At equilibrium the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopic observables and a nonequilibrium extension of this method could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials with time-resolved resonant inelastic x-ray scattering. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced many-body entanglement due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via ultrafast spectroscopic measurements. Quantum Fisher information is a measure of entanglement that has been previously extracted from equilibrium spectra of quantum materials. Here the authors extend this approach to non-equilibrium systems probed by time-resolved resonant inelastic x-ray scattering measurements.

The optical properties of graphene are made unique by the linear band structure and the vanishing density of states at the Dirac point. It has been proposed that even in the absence of a bandgap, a relaxation bottleneck at the Dirac point may allow for population inversion and lasing at arbitrarily long wavelengths. Furthermore, efficient carrier multiplication by impact ionization has been discussed in the context of light harvesting applications. However, all of these effects are difficult to test quantitatively by measuring the transient optical properties alone, as these only indirectly reflect the energy- and momentum-dependent carrier distributions. Here, we use time- and angle-resolved photoemission spectroscopy with femtosecond extreme-ultraviolet pulses to directly probe the non-equilibrium response of Dirac electrons near the K-point of the Brillouin zone. In lightly hole-doped epitaxial graphene samples, we explore excitation in the mid- and near-infrared, both below and above the minimum photon energy for direct interband transitions. Whereas excitation in the mid-infrared results only in heating of the equilibrium carrier distribution, interband excitations give rise to population inversion, suggesting that terahertz lasing may be possible. However, in neither excitation regime do we find any indication of carrier multiplication, questioning the applicability of graphene for light harvesting. Previous studies have suggested that even in the absence of a graphene bandgap, a relaxation bottleneck at the Dirac point may allow for population inversion and lasing. Now, using time- and angle-resolved photoemission spectroscopy with femtosecond extreme-ultraviolet pulses, it is shown that interband excitations give rise to population inversion, suggesting that terahertz lasing may be possible.

A normal metal exhibits a valence plasmon, which is a sound wave in its conduction electron density. The mysterious strange metal is characterized by non-Boltzmann transport and violates most fundamental Fermi-liquid scaling laws. A fundamental question is, do strange metals have plasmons? Using momentum-resolved inelastic electron scattering, we recently showed that, rather than a plasmon, optimally dopedBi2.1Sr1.9Ca1.0Cu2.0O8+x (Bi-2212) exhibits a featureless, temperature-independent continuum with a power-law form over most energy and momentum scales [M. Mitrano et al., Proc. Natl. Acad. Sci. U.S.A. 115, 5392 (2018)]. Here, we show that this continuum is present throughout the fan-shaped, strange metal region of the phase diagram. Outside this region, dramatic changes in spectral weight are observed: In underdoped samples, spectral weight up to 0.5 eV is enhanced at low temperature, biasing the system toward a charge order instability. The situation is reversed in the overdoped case, where spectral weight is strongly suppressed at low temperature, increasing quasiparticle coherence in this regime. Optimal doping corresponds to the boundary between these two opposite behaviors at which the response is temperature independent. Our study suggests that plasmons do not exist as well-defined excitations in Bi-2212 and that a featureless continuum is a defining property of the strange metal, which is connected to a peculiar crossover where the spectral weight change undergoes a sign reversal.

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. The manipulation of spins with ultrafast lasers is a promising route to control the properties of a wide variety of quantum materials. Here, the authors present a simulation of Floquet-engineered spin fluctuations in a correlated system and of their fingerprints in ultrafast inelastic X-ray scattering experiments.

Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La1.8–xEu0.2SrₓCuO₄ over a range of doping 0.07 ≤ x ≤ 0.20. We find that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau–Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in all families of cuprates forms by a common mechanism.

Ultrafast lasers are an increasingly important tool to control and stabilize emergent phases in quantum materials. Among a variety of possible excitation protocols, a particularly intriguing route is the direct light engineering of microscopic electronic parameters, such as the electron hopping and the local Coulomb repulsion (HubbardU). In this work, we use time-resolved x-ray absorption spectroscopy to demonstrate the light-induced renormalization of the HubbardUin a cuprate superconductor,La1.905Ba0.095CuO4. We show that intense femtosecond laser pulses induce a substantial redshift of the upper Hubbard band while leaving the Zhang-Rice singlet energy unaffected. By comparing the experimental data to time-dependent spectra of single- and three-band Hubbard models, we assign this effect to an approximately 140-meV reduction of the on-site Coulomb repulsion on the copper sites. Our demonstration of a dynamical HubbardUrenormalization in a copper oxide paves the way to a novel strategy for the manipulation of superconductivity and magnetism as well as to the realization of other long-range-ordered phases in light-driven quantum materials.

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. This work leverages the intrinsic carrier-envelope phase instability of pulsed lasers to measure the photon number distribution of ultrashort probes, providing a new way to study quantum fluctuations in light-driven materials.

Ultrafast optical pulses are an increasingly important tool for controlling quantum materials and triggering novel photo-induced phase transitions. Understanding these dynamic phenomena requires a probe sensitive to spin, charge, and orbital degrees of freedom. Time-resolved resonant inelastic X-ray scattering (trRIXS) is an emerging spectroscopic method, which responds to this need by providing unprecedented access to the finite-momentum fluctuation spectrum of photoexcited solids. In this Perspective, we briefly review state-of-the-art trRIXS experiments on condensed matter systems, as well as recent theoretical advances. We then describe future research opportunities in the context of light control of quantum matter. Interrogating emergent nonequilibrium phenomena in light-driven quantum materials requires probing microscopic spin, charge and orbital excitations at ultrafast timescales. In this Perspective, time-resolved resonant inelastic X-ray scattering is discussed as a nascent method to investigate photoinduced states of matter.

Magnetic van der Waals (vdW) materials have opened new frontiers for realizing novel many-body phenomena. Recently NiPS 3 has received intense interest since it hosts an excitonic quasiparticle whose properties appear to be intimately linked to the magnetic state of the lattice. Despite extensive studies, the electronic character, mobility, and magnetic interactions of the exciton remain unresolved. Here we address these issues by measuring NiPS 3 with ultra-high energy resolution resonant inelastic x-ray scattering (RIXS). We find that Hund’s exchange interactions are primarily responsible for the energy of formation of the exciton. Measuring the dispersion of the Hund’s exciton reveals that it propagates in a way that is analogous to a double-magnon. We trace this unique behavior to fundamental similarities between the NiPS 3 exciton hopping and spin exchange processes, underlining the unique magnetic characteristics of this novel quasiparticle. Recently, excitons with unconventional properties were reported in a van der Waals antiferromagnet NiPS 3 . Here, using resonant inelastic x-ray scattering, the authors show that the formation of these excitons is primarily driven by Hund’s coupling and that they propagate similarly to two-magnon excitations.

Abstract Ultrafast optical pulses are an increasingly important tool for controlling quantum materials and triggering novel photo-induced phase transitions. Understanding these dynamic phenomena requires a probe sensitive to spin, charge, and orbital degrees of freedom. Time-resolved resonant inelastic X-ray scattering (trRIXS) is an emerging spectroscopic method, which responds to this need by providing unprecedented access to the finite-momentum fluctuation spectrum of photoexcited solids. In this Perspective, we briefly review state-of-the-art trRIXS experiments on condensed matter systems, as well as recent theoretical advances. We then describe future research opportunities in the context of light control of quantum matter.