The Cu- L 3 RIXS cross-section in cuprates is extremely rich. It is sensitive to charge order correlations (Comin and Damascelli, 2016; Frano et al., 2020; Tranquada et al., 1995; Hoffman et al., 2002; Vershinin et al., 2004; Howald et al., 2003; Abbamonte et al., 2005; Wise et al., 2008; Ghiringhelli et al., 2012; Chang et al., 2012; Comin et al., 2014; da Silva Neto et al., 2014; Tabis et al., 2014; da Silva Neto et al., 2015; 2016; Arpaia and Ghiringhelli, 2021; Chaix et al., 2017; da Silva Neto et al., 2018; Arpaia et al., 2019; Yu et al., 2020; Miao et al., 2017; Miao et al., 2019; Li et al., 2020; Lee et al., 2021; Boschini et al., 2021; Huang et al., 2021; Lu et al., 2022; Scott et al., 2023; Arpaia et al., 2023), phonons (including studies of electron-phonon coupling and two-phonon processes) (Chaix et al., 2017; Rossi et al., 2019; Lin J. Q. et al., 2020; Peng et al., 2020; Li et al., 2020; Wang et al., 2021; Lee et al., 2021; Lu et al., 2022; Braicovich et al., 2020; Huang et al., 2021; Peng et al., 2022; Scott et al., 2023; 2024), superconducting and pseudo gaps (Suzuki et al., 2018; Merzoni et al., 2024), magnetic excitations (magnon and bi-magnon excitations) (Hill et al., 2008; Braicovich et al., 2010; Le Tacon et al., 2011; Lee et al., 2014; Ishii et al., 2014; Peng et al., 2015; Minola et al., 2015; Fumagalli et al., 2019; Betto et al., 2021), plasmons (Hepting et al., 2018; Lin J. et al., 2020; Nag et al., 2020; Singh et al., 2022; Hepting et al., 2022; Hepting et al., 2023), dd orbital excitations (Sala et al., 2011; Fumagalli et al., 2019), and the charge transfer gap. Within this rich cross-section, static CO appears prominently as an enhancement of the elastic line at in-plane wavevectors along the Cu-O bond direction, i.e., q = ( ± q C O , 0 ) and q = ( 0 , ± q C O ) . However, dynamic CO correlations do not appear as a salient feature of the Cu- L 3 RIXS energy-loss spectrum. In fact, an agnostic minimal model of the spectrum in the zero to 1 eV range, requires the following five components though not necessarily a dynamic CO feature: (i) a quasi-elastic peak, (ii) the bond-stretching phonon around 70 meV, (iii) two-phonon mode (from the bond-stretching phonon) near 140 meV, (iv) a damped harmonic oscillator representing spin-flip processes in the 100–800 meV range, and (v) a small broad background Scott et al. (2023). The origin of (v) remains unknown, but some possibilities include scattering from extra charge carriers from doping, a Stoner continuum or high energy quasi-circular dynamic correlations (QCDCs), see Figures 1A, B. Beyond those, great caution must be taken when attempting to add additional terms to the curve fitting functions, although other contributions can be inferred, as depicted in Figure 1C. Indeed, subtler features relating to dynamic CO correlations can be detected by performing careful momentum mapping measurements as a function of temperature, as discussed in Section 2.2. Furthermore, an important quantity that can significantly aid in separating overlapping signals in the spectrum is the polarization of the outgoing photon, which provide information to distinguish between charge and spin scattering. This is accomplished in polarimetric RIXS (pol-RIXS), where the scattered photons are analyzed not only in terms of their energy loss but also in terms of their polarization (Braicovich et al., 2014; Minola et al., 2015; Fumagalli et al., 2019; Betto et al., 2021; da Silva Neto et al., 2018; Hepting et al., 2018; Scott et al., 2024). For example, pol-RIXS measurements were used to demonstrate the two-phonon origin of the feature near 140 meV, showing that it appears in the non-cross polarized scattering channel, σ - σ ′ , but not in the cross-polarized channel, σ - π ′ , where the unprimed (primed) symbol refers to the incoming (scattered) photon polarization (Scott et al., 2024). In another example, pol-RIXS measurements show that the damped harmonic oscillator feature, often simply called a “paramagnon” feature, is actually composed of one- and two-magnon processes (Betto et al., 2021). Despite being a very powerful technique which can resolve fundamental aspects of the scattered signals, the current state-of-the-art pol-RIXS technology is inefficient, typically requiring ten times longer acquisition times than standard RIXS. These lengthy acquisition times have led scientists to focus more on standard RIXS measurements rather than pol-RIXS. However, even with these current limitations, many potential pol-RIXS experiments in cuprates and other materials are feasible with existing technology, indicating potential for a wider exploration of pol-RIXS studies. Moreover, as the method becomes more efficient, it will enable new experiments that will undoubtedly uncover important information.

Given the complexity of the RIXS signal discussed above, how can we detect dynamic CO correlations within such a rich spectrum? This is typically accomplished through careful momentum mapping which reveal subtle dynamic features near the charge order wavevector, q C O . These features can be broadly categorized into low-energy excitations, below the bond-stretching phonon energy (i.e., E < 70 meV), and high-energy excitations, spanning the 150–700 meV range. Low-energy features, existing within the same energy range as various phonon branches, have been identified in Bi-2212 (Chaix et al., 2017; Lee et al., 2021; Lu et al., 2022; Scott et al., 2023), Bi-2201 (Li et al., 2020), YBCO (Arpaia et al., 2019; Arpaia et al., 2023), HgBCO (Yu et al., 2020), L a 2 − x S r x C u O 4 (Huang et al., 2021), and L a 2 − x B a x C u O 4 (Miao et al., 2019), with experimental methodologies varying between studies due to the peculiarities of different materials. For instance, in Bi-based materials, the presence of low-energy CO correlations is inferred through the observation of a softening of the RIXS-measured bond-stretching phonon (Chaix et al., 2017; Lee et al., 2021; Lu et al., 2022; Scott et al., 2023), while in YBCO, the detection of a similar low-energy CO mode was achieved through the careful subtraction of temperature-dependent data (Arpaia et al., 2019; Arpaia et al., 2023). High-energy features, observed in NCCO (da Silva Neto et al., 2018), HgBCO (Yu et al., 2020), and Bi-2212 (Boschini et al., 2021; Scott et al., 2023), overlap with paramagnon excitations and are broader. They are usually detected by examining the momentum-dependence of the RIXS spectrum integrated over an energy window or through meticulous temperature-dependent measurements and background subtraction.

In exploring the relationship between strong electron correlations and CO, high-energy CO features offer valuable insights. These higher energy scales, comparable to the magnetic exchange coupling J , are more compatible with strong correlation physics. Perhaps, the clearest realization of the high-energy signal is observed in the electron-doped cuprate NCCO, as discussed in the following section.

The first indications of CO in electron-doped cuprates came from EI-RXS measurements in NCCO (da Silva Neto et al., 2015). The peak at q C O decreases in intensity with increasing temperature, but, up to 420 K, an onset temperature is not clear in the EI-RXS measurements (da Silva Neto et al., 2015; da Silva Neto et al., 2016), Figures 2A, B. This linear temperature dependence, also observed in Bi-2212 (Boschini et al., 2021), contrasts with typical mean-field-like order parameter behavior. It suggests that dynamic correlations, expected to persist at very high temperatures, significantly contribute to the peak spectral width in the EI-RXS measurements. To analyze the different static and dynamic contributions to this peak, RIXS measurements were employed (da Silva Neto et al., 2018). It was observed that approximately 50% of the low-temperature peak in EI-RXS is composed of dynamic CO correlations, clearly observed in the energy-momentum maps at q C O in the same energy range as the paramagnon excitations, Figures 2C–E. At 300 K, the elastic peak disappears, but dynamic CO correlations remain, Figures 2C,E. Given the overlap between the high-energy feature at q C O and the dispersive paramagnon feature, a natural question arose about whether the scattering was spin-flip or non-spin-flip in nature. The use of pol-RIXS revealed that the enhancement was primarily in the σ - π ′ channel (cross-polarization) but not in the σ - σ ′ (non-crossed) channel, indicating a spin-flip scattering process (da Silva Neto et al., 2018), Figure 2F.

At first inspection, the experimental results on NCCO present a puzzle. On one hand, the elastic and inelastic signals appear to be linked since they occur at the same q C O wavevector, which was confirmed for two different dopings, each with distinct q C O . On the other hand, the elastic and inelastic signals appear in distinct polarization channels, σ - σ ′ and σ - π ′ , respectively. However, a resolution was proposed in (da Silva Neto et al., 2018), by noting that that temporal fluctuations of a CO pattern on top of underlying antiferromagnetic correlations require the transfer of charge between neighboring sites with alternating spins. Therefore, some dynamic charge order processes will necessarily involve spin flips.

The existence of dynamic correlations at the σ - π ′ channel at the same energy scale as J indicates a connection between strong correlation physics and charge order formation. With this rich and detailed phenomenology available, one may ask: what is the simplest Hamiltonian that describes this combined phenomenology? What is the effective Coulomb interaction in that Hamiltonian? A recent theoretical work based on an extended one-band Hubbard model successfully reproduced various aspects of the RIXS experiments on NCCO, including paramagnon dispersion, a plasmonic mode, charge order, the doping dependence of q C O , and a significant dynamic CO signal at paramagnon energy scales (Riegler et al., 2023), Figure 3. While model calculations often have to be modified to improve agreement with an experimental aspect at the expense of another, the model in (Riegler et al., 2023) shows excellent simultaneous agreement with all the above-mentioned experimental findings. A key ingredient necessary for this excellent agreement is the existence of a nearest-neighbor Coulomb repulsion V in addition to the onsite repulsion U . Within this model, it was found that a moderate V removes the propensity for phase separation with doping, leading to the formation of CO, and associated dynamic correlations, similar to the general mechanism discussed in Section 1. Crucially, the comprehensive and precise experimental RIXS studies provide extensive constraints on the model, naturally increasing confidence in the effective Coulomb interaction obtained from it.

To investigate the fingerprints of the effective Coulomb interaction in cuprates, studies of Bi-2212 adopted a new approach. Traditionally, RIXS experiments, constrained by limited synchrotron beam time, focus on the two high-symmetry directions of the 2D in-plane scattering Brillouin zone. However, the q x - q y structure of the Cu- L 3 RIXS cross-section contains signatures of the effective Coulomb interaction, which we review in this section. Before that discussion, however, we will discuss two notable EI-RXS studies that underscore the significance of full in-plane RIXS mapping.

The first study compared EI-RXS measurements of the q C O in Bi-2201 as a function of doping to calculations of the static Lindhard susceptibility (Comin et al., 2014). It was found that along the Cu-O bond direction, the doping dependence of q C O was consistent with the calculation when a pseudogap was included on the Fermi surface Figure 4A. Since the pseudogap itself may result from strong correlations stemming from the parent Mott state, these Lindhard calculations imply a similar origin for the CO. However, as we discuss below, the full 2D static Lindhard calculation shows much stronger intensity along a direction 45 ° away from the static charge order direction Figure 4B, casting doubt on the appropriateness of the Lindhard description.

The second study focused on T ′ − N d 2 C u O 4 thin films with low doping, extending EI-RXS to map the entire q x - q y plane. Those measurements revealed a quasi-circular ring-like feature, i.e., a nearly constant-radius in-plane pattern (Kang et al., 2019), Figure 4C. Based on a static Lindhard calculation, Figures 4D,E, those results were attributed to low-energy glassy charge modulations that reflect the Fermi surface topology. However, experimentally, EI-RXS could not resolve the energy structure of the scattering, leaving the origin the quasi-circular feature, elastic or inelastic, undetermined.

These two studies lead to an important consideration: Given the well-known Fermi surface in Bi-2212 and the results of the static Lindhard calculations, if a quasi-circular feature were to exist in Bi-2212, it would not originate from a Fermi surface instability, necessitating an alternative explanation. Indeed, RIXS measurements of Bi-2212 found a quasi-circular pattern in the q x - q y plane at finite inelastic energies, with the same wavevector magnitude, | q | = q C O as the static CO peak, q C O (Boschini et al., 2021; Scott et al., 2023), Figures 4F, 5. These dynamic correlations with the CO wavelength along all directions in the C u O 2 plane were termed quasi-circular dynamic correlations (QCDCs). In the original experiment, the RIXS scattering pattern was acquired using an instrument with a medium energy resolution of approximately 800 meV (Boschini et al., 2021), Figure 4F. The results suggested the presence of QCDCs that are broad over the mid-infrared range, approximately from 100 to 900 meV. Furthermore, since static probes like STM have never observed quasi-circles in the scattering patterns of Bi-2212 (Hoffman et al., 2002; Vershinin et al., 2004; Howald et al., 2003; da Silva Neto et al., 2014; Yazdani et al., 2016; Comin and Damascelli, 2016), the existence of a quasi-circle would imply that it is necessarily dynamic. Later, high energy resolution RIXS measurements (approximately 37 meV) tracking the q x - q y profile of the bond-stretching phonon softening concluded that a similar pattern exists at low energies also (below 70 meV), Figure 5. In Section 2.5 we discuss the phonon-tracking method and the connection between low-energy QCDCs to strange metal behavior (Scott et al., 2023). Before that, however, we discuss how the quasi-circular in-plane pattern provides insights into the origin of charge order and the effective Coulomb interaction (Boschini et al., 2021).

Given the quasi-circular pattern observed in the experiments, it is natural to ask what many-body description might produce it. Systematically going through different textbook approaches to calculating the charge susceptibility, it was first noted that a static Lindhard calculation strongly deviated from the observed quasi-circular pattern, Figure 4G. Next, to account for the finite energy resolution of the RIXS instruments, the experiments were compared to the dynamic Lindhard susceptibility integrated over an energy window comparable to the experimental resolution. Despite this adjustment, a strong qualitative disagreement persisted. It was further noted that the disagreement remained regardless of the inclusion of a pseudogap in the calculation.

Given the failure of the Lindhard (polarizability) function, directly reflecting the band structure geometry, to capture the most salient features of the experiment, the effective Coulomb interaction was considered. Within the random phase approximation (RPA) formalism, features in the susceptibility may emerge from either peaks in the Lindhard (polarizability) function or from minima in the effective Coulomb interaction. In the extreme case of a featureless polarizability function, as indicated by momentum-resolved electron energy loss spectrosocopy (MEELS) measurements of Bi-2212 (Mitrano et al., 2018; Husain et al., 2019), the RPA susceptibility is dominated by the form of the effective Coulomb interaction, V eff . Using known expressions and experimentally determined parameters (Drozdov et al., 2018; Hwang et al., 2007; Takayanagi et al., 2002), a V eff was calculated, incorporating both a short-range Hubbard-like component and a long-range potential derived from Poisson’s equation (Becca et al., 1996; Seibold et al., 2000; Caprara et al., 2017; Kivelson et al., 2003). While separately the short-range and long-range components are monotonic functions of | q | , with the former increasing and the latter decreasing, together they form a minimum at an intermediate value inside the scattering Brillouin zone. Remarkably, the minima of V eff , Figure 4H, form a quasi-circular pattern with a radius and shape that closely match the experimentally observed QCDCs (Boschini et al., 2021). In other words, the form of the Coulomb interaction described above captured the most salient aspect of the RIXS mapping—a quasi-circular scattering structure. It also indicated that the same long-range Coulomb interactions necessary to avoid phase separation were key to the appearance of quasi-circular minima in V eff .

A more detailed theoretical model that simultaneously reproduces various aspects of the RIXS on Bi-2212, similar to the one for NCCO, is still being developed. Nevertheless, following the first reports of QCDCs, theoretical works have also observed similar quasi-circular structures, using the same model that reproduced the RIXS measured plasmons in cuprates (Yamase et al., 2021; Bejas et al., 2022). Interestingly, these studies converge on an important conceptual point: the QCDCs are likely the consequence of an effective Coulomb potential that must include long-range interactions.

Recent combined transport and RIXS studies revealed an unexpected link between linear-in-temperature resistivity, which characterizes the strange metal behavior, and charge order (CO) in YBCO (Wahlberg et al., 2021). The linear-in-temperature resistivity (Gurvitch and Fiory, 1987; Martin et al., 1990), often associated with an isotropic scattering rate that depends solely on temperature (i.e., ∝ k B T / ℏ , sometimes called the Planckian regime) (Grissonnanche et al., 2021; Varma et al., 1989; Aji and Varma, 2007; Patel et al., 2018; Patel and Sachdev, 2019; Phillips et al., 2022; Patel et al., 2023), has been suggested to result from low-energy dynamic CO leading to effective isotropic scattering (Seibold et al., 2021; Caprara et al., 2022). In this scenario, isotropic scattering occurs if collective modes, (i) low in energy and (ii) broad in momentum-space, are available to scatter electrons between any two points on the Fermi surface. Naturally, QCDCs occupying such a large momentum space manifold satisfy the second criterion. Demonstrating the first criterion, that they also exist at low energies, required a new approach based on a phonon-tracking methodology (Scott et al., 2023). This is based on the phenomenology revealed by RIXS measurements on various cuprates, which indicate a softening of the RIXS-measured bond-stretching (BS) phonon peak at q C O , i.e., along q x and q y (Chaix et al., 2017; Lee et al., 2021; Li et al., 2020; Miao et al., 2019; Lin J. Q. et al., 2020; Peng et al., 2020; Huang et al., 2021; Wang et al., 2021). By tracking the softening of the RIXS-measured BS phonon in the q x - q y plane, QCDCs were shown to exist at energies below approximately 70 meV (Scott et al., 2023), Figures 5A,B,D. Interestingly, the softening at azimuthal angles close to 45 ° contrasts with the absence of a static CO peak on the elastic line for azimuthal angles away from 0 ° , Figure 5C. Overall, these measurements demonstrated the dynamic, low-energy nature of the QCDCs, positioning them as a viable candidate to mediate the isotropic scattering in the strange metal phase.

Before addressing open questions and future directions, we briefly discuss the key instruments used to obtain the EI-RXS and RIXS results reviewed above, pointing out their key technical characteristics. This section is not intended as a comprehensive review of technical developments, but rather a brief mention of the beamlines from which these studies originated. For a more detailed and recent review of RIXS, we refer readers to (de Groot et al., 2024).

First, in the studies of charge order using EI-RXS in the soft x-rays, the UE-46 beamline at the BESSY II synchrotron (Weschke and Schierle, 2018) and the REIXS beamline at the Canadian Light Source (Hawthorn et al., 2011) were instrumental. At REIXS, measurements were conducted down to 20 K, with the capability to heat the sample stage up to 400 K. The ability to reach high temperatures was crucial for the temperature-dependent studies of electron-doped cuprate (da Silva Neto et al., 2015; 2016), such as the one presented in Figure 2B. Complementarily, the UE-46 beamline allowed access to lower temperatures, down to 10 K, and a second endstation at UE-46 enabled the application of magnetic fields at similar temperatures. These features were pivotal for studying the relationship between charge order and superconductivity (Blanco-Canosa et al., 2014), particularly in low- T c samples, such as electron-doped cuprates (da Silva Neto et al., 2016).

Second, the evolution of RIXS, as reflected in the results presented above, was driven by advancements in energy resolution at the Cu- L 3 edge. Before the developments at the ID32 beamline of the European Synchrotron Radiation Facility, which achieved better than 35 meV resolution (Brookes et al., 2018), the best energy resolution of 130 meV was achieved at the ADRESS beamline of the Swiss Light Source (Ghiringhelli et al., 2006; Strocov et al., 2010) (e.g., (Le Tacon et al., 2011)). Following this significant breakthrough, similar energy resolutions were achieved at the SIX beamline at the National Synchrotron Light Source II at Brookhaven National Laboratory (Dvorak et al., 2016; Jarrige et al., 2018) and the I21 beamline at the Diamond Light Source (Zhou et al., 2022). Additionally, the development of pol-RIXS capabilities at ID32 was crucial for the studies on NCCO shown in Figure 2F. Future application of pol-RIXS are discussed in the next section.

Finally, despite the advancements in energy resolution for Cu- L 3 RIXS, achieving these high resolutions comes at the cost of reduced flux, leading to longer measurement times. For some applications, however, a lower energy resolution may suffice for initial measurements. For instance, the first detection of QCDCs (Boschini et al., 2021) was achieved with an energy resolution of 0.8 eV at the qRIXS beamline of the Advanced Light Source at Lawrence Berkeley National Laboratory (Chuang et al., 2022). The balance between energy resolution and flux there allowed for a full in-plane mapping within 12–24 h, whereas at high-resolution beamlines, this time frame typically applies to q-mapping at a single ϕ . Thus, there remains significant potential for discovery with instruments operating at resolutions on the order of hundreds of meV.

One of the main advantages of the soft x-ray RIXS cross-section is its sensitivity to various degrees of freedom (Ament et al., 2011; Devereaux et al., 2016), but this also presents complications. Despite the success of the phonon-tracking method, the energy profile of the QCDCs, i.e., their energy spectrum, has not been resolved. Thus, although high-energy and low-energy QCDCs appear at the same momenta, it remains possible that they have different origins. Resolving this question requires the ability to decompose the rich RIXS spectrum into its different components. For this, pol-RIXS may be the most effective technique to determine the contributions to the MIR energy scale, as demonstrated in NCCO. However, these experiments are extremely challenging. The most mature state-of-the-art polarimeter, available at the ID32 beamline of the European Synchrotron Radiation Facility, uses a mirror with an average reflection coefficient of about 0.1 (Brookes et al., 2018; Braicovich et al., 2014). Recently, pol-RIXS is also being developed at the I21 beamline at Diamond Light Source, with a similar average reflection coefficient at the Ni- L 3 edge already demonstrated Chen et al. (2024). As a result of the low reflection coefficient, polarimetric RIXS requires acquisition times over ten times longer than standard RIXS to achieve comparable statistics. To fit these measurements within a typical five-day beam time, either energy resolution is sacrificed to allow for momentum mapping, as in NCCO da Silva Neto et al. (2018), or momentum mapping is abandoned to obtain high-resolution polarimetric spectra, as demonstrated in the resolution of the 2-phonon mode (Scott et al., 2024). Furthermore, the actual spectral decomposition is not performed directly by the instrument but requires nuanced data processing. Still, there are plenty of cuprate families, doping values, electronic phases and regions of momentum space that remain to be explored with pol-RIXS. Therefore, we believe that one of the most significant future directions for advancements in soft x-ray RIXS instruments will be the development of fast and reliable polarimetry capabilities.

It is still unclear if QCDCs exist in other cuprate families. One approach to investigate this would be to use the phonon tracking method to map the q x - q y plane. However, this method may be affected by varying degrees of coupling between QCDCs and the bond-stretching phonon across different families and it would not probe the high-energy sector. Following a Brazovskii framework (Boschini et al., 2021), the effective Coulomb interaction allows charge order domains to appear along any in-plane direction, while the lattice structure and phonon spectrum determine the direction of static charge order. Thus, manipulating the lattice, for example, with uniaxial strain, should compress spectral weight from the QCDC manifold into the more localized static CO peaks. This differential measurement approach could be used to detect QCDCs in other cuprates. On the other hand, a recent study combining uniaxial strain and RIXS on L a 2 − x S r x C u O 4 finds that, while the relative intensity of static CO peaks along q x and q y is sensitive to uniaxial strain, the energy and intensity of dynamic CO correlations, as well as the softening of the BS mode, remain equal along q x and q y Martinelli et al. (2024). This latest result in L a 2 − x S r x C u O 4 further indicates a non-trivial relation between static and dynamic CO correlations, similar to the findings in Scott et al. (2023), which highlight different behaviors of static and dynamic CO correlations with ϕ , Figure 5.

Despite the recent successful examples of integrating soft x-ray RXS with uniaxial strain (Boyle et al., 2021; Kim et al., 2021; Wang et al., 2022; Gupta et al., 2023; Martinelli et al., 2024), we note that these measurements are extremely challenging for several reasons: (i) technical challenges associated with the integration of the strain devices into the ultra-high-vacuum chambers of the existing RIXS setups, (ii) a high-rate of broken samples upon stress application and (iii) difficulty in precisely determining the effective strain on the sample during the RIXS study. Barring advances in methods for applying uniaxial strain, more efficient RIXS would greatly benefit these studies by allowing for faster cycling of samples. Relatedly, epitaxial strain (Bluschke et al., 2018) and chemical pressure (Ruiz et al., 2022) have been shown to have significant impact on the out-of-plane coupling of the CO in YBCO. How this translates to the in-plane structure of the dynamic charge correlations remains an open question.

In recent years, the advent of free-electron lasers (FELs) has enabled the extension of EI-RXS and RIXS into the time domain, providing new insights into the light-induced dynamics and melting of CO in cuprates (Mitrano et al., 2019; Mitrano and Wang, 2020; Bluschke et al., 2024). In particular, two recent time-resolved EI-RXS studies have reported the dynamic competition between superconductivity and CO in YBCO (Wandel et al., 2022; Jang et al., 2022). Both studies show that quenching the superconducting phase with near-infrared (near-IR) light results in a transient non-thermal enhancement of the static CO coherence length and peak intensity. These results provided evidence that superconductivity is intimately intertwined with CO, disrupting its spatial coherence (Wandel et al., 2022), and that the light-driven non-thermal state of cuprates shares close similarity with that reached under the magnetic field (Jang et al., 2022). Regarding the response of CO above T c , it has been shown that the near-IR light excitation further suppresses the CO peak intensity (Wandel et al., 2022). Therefore, while these pioneering studies demonstrate that studying the transient evolution of CO correlations as an exciting new direction, they could not resolve the possibly different behaviors of the static and dynamic contributions at q C O . To gain access into the transient evolution of dynamic CO correlations, time-resolved RIXS (TR-RIXS) becomes necessary.

Building up on the recent report of the ultrafast renormalization of the on-site Coulomb interaction in cuprates via time-resolved X-ray absorption (Baykusheva et al., 2022), we highlight the potential of TR-RIXS to investigate V eff by noting that visible/near-IR light excitations in the normal state of cuprates can transiently change the screening via the generation of hot carriers. Consequently, a change in the screening should affect the local minimum of the effective Coulomb interaction V e f f discussed in Section 2.4, thus potentially transiently altering the QCDCs manifold in the q x - q y plane–this could be detected with TR-RIXS. And while the current energy resolution of the time-resolved RIXS endstations at the Cu- L 3 edge ( ∼ 100 meV) may not allow tracking the transient evolution of the phonon softening described in Section 2.5, it is certainly sufficient to separate the quasi-static CO peak from the high-energy CO correlations and other underlying collective excitations. Furthermore, the proposed studies would benefit from complementary time- and angle-resolved photoemission spectroscopy (TR-ARPES) experiments. TR-ARPES, which can access light-induced changes in the low-energy electronic band structure with momentum resolution (Boschini et al., 2024), allows the simultaneous measurement of transient changes in the band structure. A combined TR-RIXS and TR-ARPES study would thus allow us to assess the effects of the Lindhard polarizability on the transient response of CO correlations, ultimately determining how much it may contribute to the RIXS signal and/or the emergence of QCDCs.

The experimental strategy discussed above relies on the combination of two experimental probes to obtain direct insights into the momentum transfer q (RIXS) and the electronic state momentum k (ARPES) with energy resolution. However, by combining these two momentum-resolved techniques, we would still not be able to identify exactly which electronic states k are correlated by q C O . In this context, the recently proposed development of two-electron coincidence techniques, such as 2e-ARPES (Trützschler et al., 2017; Mahmood et al., 2022) and noise correlation ARPES (Stahl and Eckstein, 2019; Su and Zhang, 2020; Devereaux et al., 2023), may provide direct access to the static and dynamic correlations between two electronic states for the first time. Looking ahead, the successful demonstration and development of these techniques would offer a direct way to quantitatively estimate which electronic states play a role in the emergence of charge correlations in cuprates and in quantum materials in general.