Abstract
Ultrafast optical pulses are an increasingly important tool for controlling quantum materials and triggering novel photoinduced phase transitions. Understanding these dynamic phenomena requires a probe sensitive to spin, charge, and orbital degrees of freedom. Timeresolved resonant inelastic Xray scattering (trRIXS) is an emerging spectroscopic method, which responds to this need by providing unprecedented access to the finitemomentum fluctuation spectrum of photoexcited solids. In this Perspective, we briefly review stateoftheart 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.
Introduction
Understanding and controlling quantum materials—material systems exhibiting quantummechanical effects over wide energy and length scales^{1}—is a central challenge in modern condensed matter physics. Over the last two decades, ultrafast lasers have had a tremendous impact on quantum materials research and provided a novel route to ondemand engineering of their electronic and structural properties. They have not only allowed for tuning wellknown states of matter far from equilibrium, e.g., magnetism^{2,3,4,5,6}, charge/spin order^{7,8,9,10,11}, and ferroelectricity^{12,13,14}, but also led to novel dynamical phenomena, such as transient superconductivity^{15,16,17,18} and Floquet topological phases^{19,20,21}.
In nonequilibrium experiments, a sample is typically excited by a pump pulse and monitored by a subsequent probe. Interpreting the properties of a photoexcited material, especially when different instabilities are intertwined, requires precise knowledge of how the lattice, band structure, and collective fluctuations respond to the pump. To meet these needs, the ultrafast community developed ultrafast Xray and electron diffraction for monitoring the crystal lattice^{22,23,24,25} and time and angleresolved photoemission (trARPES) for probing the electronic structure^{7,9,26}. On the other hand, lightdriven collective excitations are commonly investigated with ultrafast optical methods^{27,28,29}, which however cannot probe their dispersion in reciprocal space owing to the negligible momentum of optical photons. This implies that the microscopic distribution of nonequilibrium fluctuations in quantum materials is largely inaccessible to most existing experimental methods.
Timeresolved resonant inelastic Xray scattering (trRIXS) is a momentumresolved spectroscopy aimed to interrogate nonequilibrium collective modes, which has been recently enabled by the development of femtosecond Xray freeelectron lasers (XFELs)^{30,31}. As shown in Fig. 1a, trRIXS probes nonequilibrium dynamics by scattering ultrashort Xray pulses tuned to a characteristic atomic absorption edge. Once the incoming Xray photon is absorbed, the pumpexcited material transitions to an intermediate state in which a corelevel electron is transferred to (or above) the valence orbitals. Within a few fs, the highly unstable intermediate state decays and a valence electron fills the core hole by emitting a Xray photon (see Fig. 1b). The scattered Xrays are then analyzed in both momentum and energy, yielding information about the pumpinduced collective dynamics. The resonance condition greatly enhances the RIXS crosssection, but the manybody interactions in the intermediate state are what really makes trRIXS sensitive to a wide variety of charge, orbital, and spin excitations of the valence electrons^{32,33}.
In this perspective, we survey recent experimental and theoretical progress in trRIXS. Then, we outline future research opportunities emerging from these new spectroscopic capabilities. While trRIXS will have a tremendous crossdisciplinary impact, ranging from chemistry^{34,35,36} to condensed matter physics, here we specifically focus on quantum materials’ research.
A unique experimental tool
The Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory has been at the forefront in developing trRIXS capabilities in both the soft and hard Xray regime^{30,31}. Over the last five years, these developments motivated a variety of experiments focused on probing nonequilibrium correlations in lightdriven quantum materials, especially in connection to the problem of highT_{c} superconductivity.
Key challenges in the physics of highT_{c} superconductors are understanding the relationship between superconductivity and other lowtemperature instabilities, as well as devising routes to further enhance T_{c}. In the case of copper oxides, while superconductivity appears upon doping, holelike carriers also form unidirectional charge (and sometimes spin) order (CO) modulations close to 1/8 doping and at temperatures above the superconducting T_{c}, which result in diffraction peaks at a finitemomentum Q_{CO}^{37,38,39,40,41,42,43}.
Experimental and theoretical evidence suggest indeed that these two phases interplay and often compete^{39,44,45}. Furthermore, ultrafast optical pulses have been found to enhance superconductivity while melting charge order correlations^{15,16,17,46,47,48}, and vice versa^{49}. Understanding how light affects the balance between these two phases and their collective dynamics with the aim of further optimizing superconductivity requires measuring the transient inelastic charge spectrum.
To this end, a recent trRIXS experiment at the Cu Ledge investigated the lightinduced charge order dynamics of the prototypical stripeordered cuprate La_{2−x}Ba_{x}CuO_{4} (see Fig. 2a)^{50,51}. trRIXS spectra clearly show that 1.55eV photons, which transiently enhance interlayer superconducting tunneling^{46,52}, also deplete the quasielastic charge order peak at Q_{CO} (see Fig. 2b, c). Unlike conventional charge density waves^{53}, the CO is found to undergo a sudden lightinduced sliding motion^{51} and exhibit an exponential recovery dominated by yet unobserved diffusive fluctuations at the submeV scale^{50}. By applying a similar approach to other copper oxides such as YBa_{2}Cu_{3}O_{7−δ} and Nd_{1+x}Ba_{2−x}Cu_{3}O_{7−δ}^{54}, we expect trRIXS to provide new insights about the broader dynamical relationship between charge order and superconductivity.
Aside from charge dynamics, spin fluctuations — particularly, near the antiferromagnetic wavevector Q_{AF} = (0.5, 0.5) reciprocal lattice units (r.l.u.) — are believed to contribute to the superconducting pairing^{55,56,57,58,59,60}. Thus, their optical excitation is a promising route to manipulate nonequilibrium superconductivity. Being sensitive to spin degrees of freedom through the intermediate state, trRIXS is the only available method for measuring the transient magnetic excitation spectrum as a function of momentum. Pioneering experiments provided a first glimpse of lightinduced spin dynamics in a Mott insulator^{61,62}. Unlike Cu Ledge Xrays (see Fig. 2a), photons at the Ledge of 5d transition metals carry enough momentum to fully map magnetic fluctuations throughout the Brillouin Zone (see Fig. 3a). Among the 5d materials, iridates (Sr_{n+1}Ir_{n}O_{3n+1}) are particularly interesting analogs of copper oxides. These compounds may give rise to unconventional superconductivity upon doping^{63,64}, with pseudospin fluctuations (owing to spinorbit coupling) playing the same role as spins in cuprates. Driving onsite orbital excitations with infrared pump pulses resulted in a significant spectral weight reshaping of pseudospin excitations at the highsymmetry points Q_{1} = (0.5, 0) and Q_{2} = (0.5, 0.5) r.l.u. (see Fig. 3b, c)^{61,62}. These first snapshots of lightstimulated magnetic excitations at the Ir Ledge show that optical pump pulses with a nearzero momentum transfer have profound influence on the finitemomentum spin dynamics throughout the Brillouin Zone of quantum materials.
These experiments, along with further studies of orbital excitations^{65,66}, demonstrate how trRIXS provides simultaneous access to charge, spin, and orbital degrees of freedom far from equilibrium. Its sensitivity to collective fluctuations at large momenta fills a longstanding gap in timeresolved experiments and makes trRIXS a unique tool to advance our microscopic understanding of lightdriven phenomena in quantum materials.
An evolving theoretical framework
A fundamental need for current and future trRIXS research lies in calculating the crosssection and predicting the manybody response of photoexcited quantum materials. Unlike other spectroscopies (e.g., trARPES, and nonresonant light/xray scattering)^{67,68,69,70}, the RIXS process involves a fourtime correlation function, owing to the presence of the resonant intermediate state^{71,72}. Although this complexity entails modeling and numerical challenges, it is precisely the intermediate state dynamics which makes RIXS sensitive to a wide variety of collective excitations. Moreover, these excitations encode highorder correlations beyond the linear response, and thus play a crucial role in emergent phenomena with strong quantum fluctuations.
If the intermediate state is assumed to last for a negligibly short time (ultrashort corehole lifetime (UCL) approximation), the dominant contribution to the equilibrium RIXS spectrum comes from the dynamical structure factors^{32,73,74,75,76}. For this reason, early theories of trRIXS focused on calculating charge and spin structure factors in correlated electron models driven out of equilibrium^{68,77}. For example, an early simulation of a onedimensional Mott insulator excited by a realistic belowgap pump pulse found evidence of lightinduced Floquet replicas in both the spin and charge response. Different from an ideal Floquet picture, these lightengineered excitations persisted and evolved after the pump pulse^{68}, thus indicating that light pulses are conducive to emergent Floquet dynamics at finite momentum.
Although these results constitute an exciting starting point, the UCL approximation ignores physical processes faster than the timescale of the corehole lifetime (longer than 2 fs at the Cu Ledge^{32,78}) as well as highorder correlations^{79}. Therefore, a simple calculation of the structure factors may not capture the full trRIXS spectrum and miss higher order spectral features such as bimagnons and dd excitations. In order to compute the full trRIXS crosssection, one needs to explicitly model the resonant probe process and account for the finite intermediate state lifetime, leading to a computational complexity \(O({N}_{{\rm{t}}}^{4})\), where N_{t} is the number of evolution steps^{71,72}.
Figure 4 shows the numerically calculated trRIXS spectrum of a twodimensional Hubbard model probed through an indirect scattering process (e.g., Cu Kedge) and explicitly accounting for intermediate state effects. Here, excitations are generated through interactions between the valence electrons and the core hole during the intermediate state^{72}. Unlike the structure factors obtained within the UCL approximation, the trRIXS crosssection contains highorder excitations including the bimagnon at energy ~3J (\(J=4{t}_{{\rm{h}}}^{2}/U\) is the spinexchange interaction, t_{h} is the hopping amplitude, and U is the onsite Coulomb repulsion), in addition to Mottgap excitations. After being driven by a pump resonant with the Mott gap, spectral weight gets transferred from the Mott peak to ingap excitations and bimagnons. In this case, the visibility of Floquet replicas of collective excitations is reduced when compared with ref. ^{68,71}, mainly due to the shorter Floquet state lifetime in the presence of electron–electron interactions. The predicted ingap spectral weight transfer resembles the quasielastic scattering intensity enhancement observed in the iridate Ledge trRIXS spectra (see Fig. 3), and could be measured in future Kedge experiments on gapped correlated materials.
Intermediate state effects are not only required to capture richer physics in trRIXS simulations, but will also guide the interpretation of new types of inelastic scattering experiments. RIXS spectra collected while slightly detuning the incident Xray pulse energy away from resonance can be used to selectively enhance the intensity of excitations involving specific intermediate states^{72,80} and to extract information about momentumresolved electron–phonon coupling of wellisolated modes^{78,81,82}. Detuning experiments, in tandem with microscopic calculations, will be particularly impactful in interrogating the electron–phonon coupling in photoexcited charge density waves^{11,49,53}, lightinduced ferroelectricity^{13}, and superconductivity^{83}.
In summary, advances in trRIXS experiments are accompanied by a steadily evolving theoretical framework aimed at understanding the observed lightinduced dynamics. Current computational capabilites and stateoftheart algorithms allow for performing accurate and predictive nonequilibrium simulations of the trRIXS spectrum in photoexcited correlated electron systems. In the future, we expect trRIXS theory to play an ever important role not just in interpreting timeresolved scattering experiments, but in leading the field towards new discoveries.
A new scientific opportunity
As shown in previous sections, trRIXS is rapidly growing into a major spectroscopy of lightdriven quantum materials, and its future developments are critically tied to the pace of technological advances at XFEL facilities. Owing to the small inelastic cross sections, trRIXS will benefit from a dramatic increase in the average XFEL spectral brightness from 10^{20} (LCLS) to 10^{24}−10^{25} photons s^{−1} mm^{−2} mrad^{−2} (0.1% bandwidth)^{−1} at 1 keV^{30,84}. This brightness enhancement will be mainly achieved through increased repetition rates, e.g., at both the LCLSII and the European XFEL, and will lead to orderofmagnitude improvements of the signaltonoise ratio. Furthermore, higher energy resolution (especially in the soft Xray regime) will enable observing lowenergy collective fluctuations, such as phonons and spin waves. At the time of this writing, large spectrometers are in construction at both the LCLSII (NEH2.2/qRIXS instrument)^{84} and the European XFEL (hRIXS instrument). The target resolving power at 1 keV would be of order 3.0 × 10^{4} (~0.03 eV resolution), thus implying a 20× improvement with respect to the data shown in Fig. 2^{85}. Other experimental endstations with different features are being developed at the Trieste Free Electron laser Radiation for Multidisciplinary Investigations (FERMI/Italy), the Pohang Accelerator Laboratory Xray Free Electron Laser (PALXFEL/S. Korea), and the Switzerland’s Xray freeelectron laser (SwissFEL). These enhanced capabilities open up a new frontier for the investigation of nonequilibrium spin, charge and orbital dynamics in strongly correlated and topologically nontrivial materials.
A tantalizing application of trRIXS is the study of spin excitations in lightdriven quantum materials. Multiple theoretical studies have proposed that spinexchange interactions can be controlled by renormalizing the effective Hamiltonian interactions through a periodic drive (see Fig. 5a), in the spirit of the socalled “Floquetengineering”^{86,87,88,89}. In this idealized scheme, photons dress the intermediate electronic states of the exchange (or superexchange) process, leading to an effective energy scale J_{eff} (see Fig. 5b). Although the parameter renormalization is rigorous only for an infinitelylong periodic pump, it could also be achieved with an ultrashort laser pulse^{70}. Alternatively, the spin excitations could be dynamically altered through other protocols, e.g., by distorting the lattice via a nonlinear phonon coupling^{90,91}. Once J_{eff} is modified by the pump, trRIXS measurements will interrogate changes in the dispersion, linewidth and spectral weight of the spin fluctuation spectrum (see Fig. 5c). A measurement of the dispersion allows us to disentangle renormalization effects of multiple coexisting exchange interactions^{92}, which cannot be discerned from the bimagnon peak in the optical Raman spectrum. Furthermore, a lineshape analysis throughout the Brillouin zone enables exploring excitations beyond magnons, e.g., incoherent fluctuations in geometrically frustrated lattices^{93,94,95,96}. As the experimental energy resolution will be of order ~0.03 eV in the near future^{84,85}, this technique will be particularly effective for studying materials with relatively large exchange scales, such as cuprates, iridates and certain nickelates, where the spin excitations disperse over energies larger than 0.1 eV.
In addition to spin fluctuations, trRIXS will play as well a pivotal role as a probe of ultrafast charge and orbital dynamics. We envision here two promising research directions involving the charge sector of lowdimensional quantum materials, namely the timeresolved investigation of fractionalized excitations, and the search for new photoinduced condensation phenomena. In one dimension, electrons cannot propagate freely, but instead displace their neighbors due to electron–electron interactions. This leads to a breakdown (“fractionalization”) of the electron into a variety of collective excitations propagating with different velocities^{97}. trRIXS provides an opportunity to study these fundamental phenomena in real time by exciting a transient particlehole plasma with a high photon energy pump and directly observing the timedependent behavior of the collective modes contained in the transient RIXS spectrum. First experiments could focus on fractionalization in Sr_{2}CuO_{3}^{98} or CaCu_{2}O_{3}^{99}, and on manipulating their excitations by dynamically tuning the balance between spinorbit coupling and crystal field^{100}. Similarly, trRIXS experiments in photoexcited Mott insulators could reveal the fingerprints of new condensation phenomena, such as ηpairing^{101,102} and dynamical pwave superconductivity^{103}. The ηpaired phase is a superfluid of doubly occupied electronic states carrying finitemomentum Q_{η} and arising from a broken SU(2) symmetry of the Hubbard Hamiltonian. As the ηpairing is an eigenstate, but not necessarily a ground state, pump light pulses open the possibility of stabilizing this yet unobserved phase^{104,105,106,107,108,109,110}. A periodic pump is theoretically predicted to enhance pairing correlations and establish true offdiagonal longrange order by dynamically renormalizing the onsite Coulomb repulsion^{108}. trRIXS would then search for ηpairing signatures in the finitemomentum pairing susceptibility^{111}, namely a divergent quasielastic structure factor at Q_{η} and a triplet of collective modes at energies ℏω = 0, ±(U−2μ) (μ being the chemical potential)^{102}. Beyond ηpairing, resonantly driving orbital degrees of freedom in doped Mott insulators has also been proposed as a route to dynamically stabilize pwave superconductivity^{103}.
The search for new lightdriven phenomena in materials dominated by local electronic correlations also calls for the development of more advanced spectroscopic methods. One such approach is trRIXS interferometry. Thanks to the local nature of the intermediate core holes and the intrinsic coherence of the scattering process, the RIXS signal can indeed exhibit interference among different intermediate states^{112}. In the dimerized spinorbit coupled insulator Ba_{3}CeIr_{2}O_{9}^{113}, the intermediate state involves a coherent superposition of a single core hole on either of the two atoms in the dimer. This leads to a \({\cos }^{2}({\bf{Q}}\cdot {\bf{d}}/2)\) modulation of the RIXS intensity in momentum space (d being the intradimer distance). Importantly, the interference pattern varies in amplitude and phase depending on the symmetry of the excitedstate wavefunction^{113}, thus providing an interferometric measurement of the local atomic orbitals. By sampling multiple interference fringes in the hard Xray regime (e.g., Ir Ledge, and Cu Kedges), it would be possible to exquisitely resolve transient changes to the local electronic structure down to the picometer level with energy selectivity. Not just limited to dimerized compounds, this technique could likewise be applied to study nonequilibrium dynamics of confined electrons along one or two directions, such as in ladder compounds^{114} or layered cuprates^{83} and nickelates^{115,116}.
In a very different context, confined electronic motion is also a defining property of edge states in lightinduced topological phases, which could be revealed by trRIXS experiments^{80}. Circularly polarized laser pulses have been shown to break timereversal symmetry and induce transient states with nontrivial Chern numbers^{21,117,118,119}. An intriguing application of this experimental approach is the creation of tunable Floquet topological insulators (FTIs), in which topology can be manipulated by varying pump amplitude, energy, and polarization^{120,121,122,123,124}. As shown in Fig. 6a, a possible route for creating a FTI in two dimensions starts from a material with bulk massless Dirac fermions. The circularly polarized pump induces a gap opening at the Dirac point and chiral edge modes at the sample boundary, which disperse across the lightinduced bandgap (see Fig. 6b). Detecting these edge states entails probing either the transient band structure with trARPES, or their collective modes in the dynamic structure factor through trRIXS, depending on the experimental constraints. However, trRIXS offers a crucial advantage. By resonantly tuning the incident photon energy to transitions from core states into the lightinduced bandgap, this technique can boost the visibility of the topological edge states over the bulk signal, and hence distinguish their dispersion from other bulk collective modes^{80} (see Fig. 6c). Future developments in nanotrRIXS may enable the direct spatial imaging of edge state dynamics and, thus, further increase their visibility over bulk excitations (although these experiments would require a special handling of Xray irradiation effects). Finally, an additional area of interest (particularly for hard Xray trRIXS) is the lightcontrol of candidate topological superconductors under high pressures^{125,126,127,128}, which are inaccessible to photoemission experiments.
This short, and by no means complete, array of examples underscores how trRIXS measurements, alongside new theoretical methods, will play an essential role in detecting and understanding new dynamic phenomena in lightcontrolled quantum materials. Increased XFEL beamtime availability, Xray brightness and spectrometer performance will enable more sophisticated trRIXS experiments with higher energy resolution and polarization control. The possibilities opened by these advances are difficult to grasp, but are certainly positioning trRIXS to be on the leading edge of a decade of discovery.
References
Keimer, B. & Moore, J. E. The physics of quantum materials. Nat. Phys. 13, 1045–1055 (2017).
Stanciu, C. D. et al. Alloptical magnetic recording with circularly polarized light. Phys. Rev. Lett. 99, 047601 (2007).
Nova, T. F. et al. An effective magnetic field from optically driven phonons. Nat. Phys. 13, 132–136 (2016).
Afanasiev, D. et al. Lightdriven ultrafast phonomagnetism. arXiv (2019). 1912.01938v1.
Mikhaylovskiy, R. V. et al. Ultrafast optical modification of exchange interactions in iron oxides. Nat. Commun. 6, 8190 (2015).
Disa, A. S. et al. Polarizing an antiferromagnet by optical engineering of the crystal field. Nat. Phys. 16, 937–941 (2020).
Schmitt, F. et al. Transient electronic structure and melting of a charge density wave in TbTe_{3}. Science 321, 1649–1652 (2008).
Perfetti, L. et al. Femtosecond dynamics of electronic states in the Mott insulator 1TTaS_{2} by time resolved photoelectron spectroscopy. N. J. Phys. 10, 053019 (2008).
Rohwer, T. et al. Collapse of longrange charge order tracked by timeresolved photoemission at high momenta. Nature 471, 490–493 (2011).
Kim, K. W. et al. Ultrafast transient generation of spindensity wave order in the normal state of BaFe_{2}As_{2} driven by coherent lattice vibrations. Nat. Mater. 11, 497–501 (2012).
Lee, W. S. et al. Phase fluctuations and the absence of topological defects in a photoexcited chargeordered nickelate. Nat. Commun. 3, 257–6 (2012).
Kubacka, T. et al. Largeamplitude spin dynamics driven by a THz pulse in resonance with an electromagnon. Science 343, 1333–1336 (2014).
Nova, T. F., Disa, A. S., Fechner, M. & Cavalleri, A. Metastable ferroelectricity in optically strained SrTiO_{3}. Science 364, 1075–1079 (2019).
Li, X. et al. Terahertz field–induced ferroelectricity in quantum paraelectric SrTiO_{3}. Science 364, 1079–1082 (2019).
Fausti, D. et al. Lightinduced superconductivity in a stripeordered cuprate. Science 331, 189–191 (2011). Discovery of lightinduced superconductivity by resonantly driving a phonon mode in a chargeordered cuprate.
Hu, W. et al. Optically enhanced coherent transport in YBa_{2}Cu_{3}O_{6.5} by ultrafast redistribution of interlayer coupling. Nat. Mater. 13, 705–711 (2014).
Kaiser, S. et al. Optically induced coherent transport far above Tc in underdoped YBa_{2}Cu_{3}O_{6+δ}. Phys. Rev. B 89, 184516 (2014).
Mitrano, M. et al. Possible lightinduced superconductivity in K_{3}C_{60} at high temperature. Nature 530, 461–464 (2016).
Wang, Y. H., Steinberg, H., JarilloHerrero, P. & Gedik, N. Observation of FloquetBloch States on the Surface of a Topological Insulator. Science 342, 453–457 (2013). Discovery of FloquetBloch bands induced by ultrafast midinfrared pulses.
Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–310 (2016).
McIver, J. W. et al. Lightinduced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2019).
Siders, C. W. et al. Detection of nonthermal melting by ultrafast Xray diffraction. Science 286, 1340–1342 (1999).
Fritz, D. M. et al. Ultrafast bond softening in bismuth: mapping a solid’s interatomic potential with Xrays. Science 315, 633–636 (2007).
SokolowskiTinten, K. et al. Femtosecond Xray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature 422, 287–289 (2003).
Gedik, N., Yang, D., Logvenov, G., Bozovic, I. & Zewail, A. Nonequilibrium phase transitions in cuprates observed by ultrafast electron crystallography. Science 316, 425 (2007).
Smallwood, C. L. et al. Tracking cooper pairs in a cuprate superconductor by ultrafast angleresolved photoemission. Science 336, 1137–1139 (2012).
Ulbricht, R., Hendry, E., Shan, J., Heinz, T. F. & Bonn, M. Carrier dynamics in semiconductors studied with timeresolved terahertz spectroscopy. Rev. Mod. Phys. 83, 543–586 (2011).
Giannetti, C. et al. Ultrafast optical spectroscopy of strongly correlated materials and hightemperature superconductors: a nonequilibrium approach. Adv. Phys. 65, 58–238 (2016).
Nicoletti, D. & Cavalleri, A. Nonlinear light–matter interaction at terahertz frequencies. Adv. Opt. Photonics 8, 401 (2016).
Bostedt, C. et al. Linac Coherent Light Source: The first five years. Rev. Mod. Phys. 88, 015007 (2016).
Cao, Y. et al. Ultrafast dynamics of spin and orbital correlations in quantum materials: an energyand momentumresolved perspective. Philos. Trans. R. Soc. A 377, 20170480 (2019).
Ament, L. J. P., van Veenendaal, M., Devereaux, T. P., Hill, J. P. & van den Brink, J. Resonant inelastic xray scattering studies of elementary excitations. Rev. Mod. Phys. 83, 705–767 (2011). Authoritative review article discussing theoretical and experimental basics of equilibrium RIXS, including early experimental work.
Haverkort, M. W. Theory of resonant inelastic xray scattering by collective magnetic excitations. Phys. Rev. Lett. 105, 167404 (2010).
Wernet, P. et al. Orbitalspecific mapping of the ligand exchange dynamics of Fe(CO)_{5} in solution. Nature 520, 78–81 (2015).
Jay, R. M. et al. Disentangling transient charge density and metalligand covalency in photoexcited ferricyanide with femtosecond resonant inelastic soft Xray scattering. J. Phys. Chem. Lett. 9, 3538–3543 (2018).
Lundberg, M. & Wernet, P. Resonant Inelastic Xray Scattering (RIXS) Studies in Chemistry: Present and Future. 1–52 (Springer International Publishing, Cham, 2019).
Tranquada, J. M. et al. Quantum magnetic excitations from stripes in copper oxide superconductors. Nature 429, 534–538 (2004).
Abbamonte, P. et al. Spatially modulated ’Mottness’ in La_{2−x}Ba_{x}CuO_{4}. Nat. Phys. 1, 155–158 (2005).
Ghiringhelli, G. et al. Longrange incommensurate charge fluctuations in (Y,Nd)Ba_{2}Cu_{3}O_{6+x}. Science 337, 821–825 (2012).
Comin, R. et al. Charge order driven by FermiArc instability in Bi_{2}Sr_{2−x}La_{x}CuO_{6+δ}. Science 343, 390–392 (2014).
da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and hightemperature superconductivity in cuprates. Science 343, 393–396 (2014).
Huang, E. W. et al. Numerical evidence of fluctuating stripes in the normal state of highTc cuprate superconductors. Science 358, 1161–1164 (2017).
Zheng, B.X. et al. Stripe order in the underdoped region of the twodimensional Hubbard model. Science 358, 1155–1160 (2017).
Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa_{2}Cu_{3}O_{6.67}. Nature Physics 8, 871–876 (2012).
Jiang, H.C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with nextnearest hopping t. Science 365, 1424–1428 (2019).
Nicoletti, D. et al. Optically induced superconductivity in striped La_{2−x}Ba_{x}CuO_{4} by polarizationselective excitation in the near infrared. Phys. Rev. B 90, 100503 (2014).
Först, M. et al. Melting of charge stripes in vibrationally driven La_{1.875}Ba_{0.125}CuO_{4}: assessing the respective roles of electronic and lattice order in frustrated superconductors. Phys. Rev. Lett. 112, 157002 (2014).
Först, M. et al. Femtosecond x rays link melting of chargedensity wave correlations and lightenhanced coherent transport in YBa_{2}Cu_{3}O_{6.6}. Phys. Rev. B 90, 184514 (2014).
Wandel, S. et al. Lightenhanced charge density wave coherence in a hightemperature superconductor. arXiv:2003.04224 (2020).
Mitrano, M. et al. Ultrafast timeresolved xray scattering reveals diffusive charge order dynamics in La_{2–x}Ba_{x}CuO_{4}. Sci. Adv. 5, eaax3346 (2019). Observation of diffusive charge order dynamics in a cuprate superconductor with soft Xray trRIXS.
Mitrano, M. et al. Evidence for photoinduced sliding of the chargeorder condensate in La_{1.875}Ba_{0.125}CuO_{4}. Phys. Rev. B 100, 205125 (2019).
Cremin, K. A. et al. Photoenhanced metastable caxis electrodynamics in stripeordered cuprate La_{1.885}Ba_{0.115}CuO_{4}. Proc. Natl Acad. Sci. 116, 19875–19879 (2019).
Huber, T. et al. Coherent structural dynamics of a prototypical chargedensitywavetometal transition. Phys. Rev. Lett. 113, 026401 (2014).
Arpaia, R. et al. Dynamical charge density fluctuations pervading the phase diagram of a Cubased highT_{c} superconductor. Science 365, 906–910 (2019).
Scalapino, D., Loh Jr, E. & Hirsch, J. Dwave pairing near a spindensitywave instability. Phys. Rev. B 34, 8190 (1986).
Gros, C., Joynt, R. & Rice, T. Superconducting instability in the largeU limit of the twodimensional Hubbard model. Z. Phys. B Condens. Matter 68, 425–432 (1987).
Kotliar, G. & Liu, J. Superexchange mechanism and dwave superconductivity. Phys. Rev. B 38, 5142 (1988).
Tsuei, C. & Kirtley, J. Pairing symmetry in cuprate superconductors. Rev. Modern Phys. 72, 969 (2000).
Scalapino, D. J. A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383–1417 (2012).
Maier, T. A. et al. Pairing in a dry Fermi sea. Nat. Commun. 7, 1–6 (2016).
Dean, M.P. et al. Ultrafast energyand momentumresolved dynamics of magnetic correlations in the photodoped Mott insulator Sr_{2}IrO_{4}. Nat. Mater. 15, 601–605 (2016). First hard Xray trRIXS investigation of lightdriven pseudospins in a stronglycorrelated material.
Mazzone, D. et al. Trapped transient magnons in the gapped antiferromagnet Sr_{3}Ir_{2}O_{7}. arXiv:2002.07301 (2020).
Wang, F. & Senthil, T. Twisted Hubbard model for Sr_{2}IrO_{4}: magnetism and possible high temperature superconductivity. Phys. Rev. Lett. 106, 136402 (2011).
Kim, Y. K. et al. Fermi arcs in a doped pseudospin1/2 heisenberg antiferromagnet. Science 345, 187–190 (2014).
Parchenko, S. et al. Orbital dynamics during an ultrafast insulator to metal transition. Phys. Rev. Res. 2, 023110 (2020).
Dell’Angela, M. et al. Extreme ultraviolet resonant inelastic Xray scattering (RIXS) at a seeded freeelectron laser. Sci. Rep. 6, 38796 (2016).
Freericks, J. K., Krishnamurthy, H. R. & Pruschke, T. Theoretical description of timeresolved photoemission spectroscopy: application to pumpprobe experiments. Phys. Rev. Lett. 102, 136401 (2009).
Wang, Y., Claassen, M., Moritz, B. & Devereaux, T. Producing coherent excitations in pumped Mott antiferromagnetic insulators. Phys. Rev. B 96, 235142 (2017).
Freericks, J., Matveev, O., Shvaika, A. & Devereaux, T. Nonresonant pump/probe electronic Raman scattering within nonequilibrium dynamical meanfield theory. In Ultrafast Bandgap Photonics III, vol. 10638, 1063807 (International Society for Optics and Photonics, 2018).
Wang, Y., Devereaux, T. P. & Chen, C.C. Theory of timeresolved Raman scattering in correlated systems: ultrafast engineering of spin dynamics and detection of thermalization. Phys. Rev. B 98, 245106 (2018).
Chen, Y. et al. Theory for timeresolved resonant inelastic xray scattering. Phys. Rev. B 99, 104306 (2019). This paper provides a comprehensive theoretical derivation of the trRIXS crosssection.
Wang, Y., Chen, Y., Jia, C., Moritz, B. & Devereaux, T. P. Timeresolved resonant inelasticxray scattering in a pumped Mott insulator. Phys. Rev. B 101, 165126 (2020). This paper reports the first numerical simulation of the indirect trRIXS spectrum of a correlated electron system.
Van Den Brink, J. The theory of indirect resonant inelastic Xray scattering on magnons. Europhys. Lett. 80, 47003 (2007).
Ament, L. J., Forte, F. & van den Brink, J. Ultrashort lifetime expansion for indirect resonant inelastic xray scattering. Phys. Rev. B 75, 115118 (2007).
Jia, C., Wohlfeld, K., Wang, Y., Moritz, B. & Devereaux, T. P. Using RIXS to uncover elementary charge and spin excitations. Phys. Rev. X 6, 021020 (2016).
Ament, L. J. P., Ghiringhelli, G., Sala, M. M., Braicovich, L. & van den Brink, J. Theoretical Demonstration of How the Dispersion of Magnetic Excitations in Cuprate Compounds can be Determined Using Resonant Inelastic XRay Scattering. Phys. Rev. Lett. 103, 117003 (2009).
Paeckel, S. et al. Detecting superconductivity out of equilibrium. Phys. Rev. B 101, 180507 (2020).
Rossi, M. et al. Experimental determination of momentumresolved electronphonon coupling. Phys. Rev. Lett. 123, 027001 (2019).
Tohyama, T. & Tsutsui, K. Spectral weight of resonant inelastic xray scattering in doped cuprates: effect of corehole lifetime. Int. J. Modern Phys. B 32, 1840017 (2018).
Chen, Y., Wang, Y., Claassen, M., Moritz, B. & Devereaux, T. P. Observing photoinduced chiral edge states of graphene nanoribbons in pumpprobe spectroscopies. arXiv:2005.00684 (2020).
Ament, L., Van Veenendaal, M. & Van Den Brink, J. Determining the electronphonon coupling strength from resonant inelastic xray scattering at transition metal Ledges. EPL 95, 27008 (2011).
Geondzhian, A. & Gilmore, K. Generalization of the FranckCondon model for phonon excitations by resonant inelastic xray scattering. Phys. Rev. B 101, 214307 (2020).
Mankowsky, R. et al. Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa_{2}Cu_{3}O_{6.5}. Nature 516, 71–73 (2014).
Dunne, M. Lcls strategic facility development plan (2019). https://lcls.slac.stanford.edu/sites/lcls.slac.stanford.edu/files/LCLS_Strategic_Development_Plan.pdf.
Dunne, M. Xray freeelectron lasers light up materials science. Nat. Rev. Mater. 3, 290–292 (2018).
Mentink, J. H. & Eckstein, M. Ultrafast quenching of the exchange interaction in a Mott insulator. Phys. Rev. Lett. 113, 057201 (2014).
Mentink, J. H., Balzer, K. & Eckstein, M. Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 1–8 (2015). Theoretical proposal for the transient manipulation of the exchange interaction via Floquet engineering of the intermediate electronic state.
Chaudhary, S., Hsieh, D. & Refael, G. Orbital floquet engineering of exchange interactions in magnetic materials. Phys. Rev. B 100, 220403 (2019).
Walldorf, N., Kennes, D. M., Paaske, J. & Millis, A. J. The antiferromagnetic phase of the Floquetdriven Hubbard model. Phys. Rev. B 100, 121110 (2019).
Först, M. et al. Nonlinear phononics as an ultrafast route to lattice control. Nat. Phys. 7, 854–856 (2011).
Subedi, A., Cavalleri, A. & Georges, A. Theory of nonlinear phononics for coherent light control of solids. Phys. Rev. B 89, 220301 (2014).
Peng, Y. Y. et al. Influence of apical oxygen on the extent of inplane exchange interaction in cuprate superconductors. Nat. Phys. 4, 2459–7 (2017).
Sandilands, L. J., Tian, Y., Plumb, K. W., Kim, Y.J. & Burch, K. S. Scattering continuum and possible fractionalized excitations in αRuCl_{3}. Phys. Rev. Lett. 114, 147201 (2015).
Chun, S. H. et al. Direct evidence for dominant bonddirectional interactions in a honeycomb lattice iridate Na_{2}IrO_{3}. Nat. Phys. 11, 462–466 (2015).
Gretarsson, H. et al. Magnetic excitation spectrum of Na_{2}IrO_{3} probed with resonant inelastic Xray scattering. Phys. Rev. B 87, 220407 (2013).
Nasu, J., Knolle, J., Kovrizhin, D. L., Motome, Y. & Moessner, R. Fermionic response from fractionalization in an insulating twodimensional magnet. Nat. Phys. 12, 912–915 (2016).
Giamarchi, T. Quantum physics in one dimension. International Series of Monographs on Physics (Clarendon Press, Oxford, 2004).
Schlappa, J. et al. Spinorbital separation in the quasionedimensional Mott insulator Sr_{2}CuO_{3}. Nature 485, 82–85 (2012).
Bisogni, V. et al. Orbital control of effective dimensionality: from spinorbital fractionalization to confinement in the anisotropic ladder system CaCu_{2}O_{3}. Phys. Rev. Lett. 114, 096402 (2015).
Chen, C.C., van Veenendaal, M., Devereaux, T. P. & Wohlfeld, K. Fractionalization, entanglement, and separation: understanding the collective excitations in a spinorbital chain. Phys. Rev. B 91, 165102 (2015).
Yang, C. N. η pairing and offdiagonal longrange order in a Hubbard model. Phys. Rev. Lett. 63, 2144–2147 (1989).
Zhang, S. Pseudospin symmetry and new collective modes of the Hubbard model. Phys. Rev. Lett. 65, 120–122 (1990).
Werner, P., Strand, H. U., Hoshino, S., Murakami, Y. & Eckstein, M. Enhanced pairing susceptibility in a photodoped twoorbital Hubbard model. Phys. Rev. B 97, 165119 (2018).
Kitamura, S. & Aoki, H. ηpairing superfluid in periodicallydriven fermionic Hubbard model with strong attraction. Phys. Rev. B 94, 174503 (2016).
Kaneko, T., Shirakawa, T., Sorella, S. & Yunoki, S. Photoinduced η Pairing in the Hubbard model. Phys. Rev. Lett. 122, 077002 (2019).
Cook, M. W. & Clark, S. R. Controllable finitemomenta dynamical quasicondensation in the periodically driven onedimensional FermiHubbard model. Phys. Rev. A 101, 033604 (2020).
Fujiuchi, R., Kaneko, T., Sugimoto, K., Yunoki, S. & Ohta, Y. Superconductivity and charge density wave under a timedependent periodic field in the onedimensional attractive Hubbard model. Phys. Rev. B 101, 235122 (2020).
Peronaci, F., Parcollet, O. & Schiró, M. Enhancement of local pairing correlations in periodically driven Mott insulators. Phys. Rev. B 101, 161101 (2020).
Sentef, M. A., Tokuno, A. Georges, A. & Kollath, C. Theory of LaserControlled Competing Superconducting and Charge Orders. Phys. Rev. Lett. 118, 087002 (2017).
Tindall, J. et al. Dynamical Order and Superconductivity in a Frustrated ManyBody System. Phys. Rev. Lett. 125, 137001 (2020).
Suzuki, H. et al. Probing the energy gap of hightemperature cuprate superconductors by resonant inelastic xray scattering. npj Quantum Mater. 3, 65 (2018).
Ma, Y. & Blume, M. Interference of fluorescence x rays and coherent excitation of core levels. Rev. Sci. Instrum. 66, 1543–1545 (1995).
Revelli, A. et al. Resonant inelastic xray incarnation of Young’s doubleslit experiment. Sci. Adv. 5, p.eaav4020 (2019). Experimental observation of intermediate state interference in the RIXS spectrum of a dimerized oxide.
Abbamonte, P. et al. Crystallization of charge holes in the spin ladder of Sr_{14}Cu_{24}O_{41}. Nature 431, 1078–1081 (2004).
Zhang, J. et al. Stacked charge stripes in the quasi2D trilayer nickelate La_{4}Ni_{3}O_{8}. Proc. Natl Acad. Sci. USA 113, 8945–8950 (2016).
Zhang, J. et al. Large orbital polarization in a metallic squareplanar nickelate. Nat. Phys. 13, 864–869 (2017).
Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensedmatter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015 (1988).
Claassen, M., Jia, C., Moritz, B. & Devereaux, T. P. Alloptical materials design of chiral edge modes in transitionmetal dichalcogenides. Nat. Commun. 7, 1–8 (2016).
Hübener, H., Sentef, M. A., De Giovannini, U., Kemper, A. F. & Rubio, A. Creating stable Floquet–Weyl semimetals by laserdriving of 3D Dirac materials. Nat. Commun. 8, 13940 (2017).
Kitagawa, T., Oka, T., Brataas, A., Fu, L. & Demler, E. Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels. Phys. Rev. B 84, 235108 (2011).
Gu, Z., Fertig, H., Arovas, D. P. & Auerbach, A. Floquet spectrum and transport through an irradiated graphene ribbon. Phys. Rev. Lett. 107, 216601 (2011).
Usaj, G., PerezPiskunow, P. M., Torres, L. F. & Balseiro, C. A. Irradiated graphene as a tunable Floquet topological insulator. Phys. Rev. B 90, 115423 (2014).
Torres, L. F., PerezPiskunow, P. M., Balseiro, C. A. & Usaj, G. Multiterminal conductance of a Floquet topological insulator. Phys. Rev. Lett. 113, 266801 (2014).
Dehghani, H., Oka, T. & Mitra, A. Outofequilibrium electrons and the Hall conductance of a Floquet topological insulator. Phys. Rev. B 91, 155422 (2015).
Zhang, J. et al. Pressureinduced superconductivity in topological parent compound Bi_{2}Te_{3}. Proc. Natl Acad. Sci. 108, 24–28 (2011).
Kirshenbaum, K. et al. Pressureinduced unconventional superconducting phase in the topological insulator Bi_{2}Se_{3}. Phys. Rev. Lett111, 087001 (2013).
Zhou, Y. et al. Pressureinduced superconductivity in a threedimensional topological material ZrTe_{5}. Proc. Natl Acad. Sci. 113, 2904–2909 (2016).
He, L. et al. Pressureinduced superconductivity in the threedimensional topological Dirac semimetal Cd_{3}As_{2}. npj Quantum Mater. 1, 16014 (2016).
Acknowledgements
We acknowledge E. Baldini, M. Buzzi, R. Comin, G. Coslovich, M.P.M. Dean, J. Freericks, A.A. Husain, D. Nicoletti, A.H. Reid, and K. Wohlfeld for valuable discussions. We also thank M.P.M. Dean for providing the original data from ref. ^{61}. The experiments reported in Fig. 2 were supported by the US Department of Energy, Office of Basic Energy Sciences grant no. DEFG0206ER46285. Use of the LCLS, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DEAC0276SF00515. The calculation reported in Fig. 4 used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under Contract No. DEAC0205CH11231.
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Mitrano, M., Wang, Y. Probing lightdriven quantum materials with ultrafast resonant inelastic Xray scattering. Commun Phys 3, 184 (2020). https://doi.org/10.1038/s42005020004476
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DOI: https://doi.org/10.1038/s42005020004476
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