Mukamel, S., Healion, D., Zhang, Y. & Biggs, J. D. Multidimensional attosecond resonant X-ray spectroscopy of molecules: lessons from the optical regime. Annu. Rev. Phys. Chem. 64, 101–127 (2013).
Leone, S. R. & Neumark, D. M. Probing matter with nonlinear spectroscopy. Science 379, 536–537 (2023).
Tanaka, S. & Mukamel, S. Coherent X-ray Raman spectroscopy: a nonlinear local probe for electronic excitations. Phys. Rev. Lett. 89, 043001 (2002).
Kraus, P. M., Zürch, M., Cushing, S. K., Neumark, D. M. & Leone, S. R. The ultrafast X-ray spectroscopic revolution in chemical dynamics. Nat. Rev. Chem. 2, 82–94 (2018).
Chergui, M., Beye, M., Mukamel, S., Svetina, C. & Masciovecchio, C. Progress and prospects in nonlinear extreme-ultraviolet and X-ray optics and spectroscopy. Nat. Rev. Phys. 5, 578–596 (2023).
Weninger, C. et al. Stimulated electronic X-ray Raman scattering. Phys. Rev. Lett. 111, 233902 (2013).
Mukamel, S. Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations. Annu. Rev. Phys. Chem. 51, 691–729 (2000).
Jonas, D. M. Two-dimensional femtosecond spectroscopy. Annu. Rev. Phys. Chem. 54, 425–463 (2003).
Jonas, D. M. Optical analogs of 2D NMR. Science 300, 1515–1517 (2003).
Engel, G. S. et al. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007).
Stone, K. W. et al. Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells. Science 324, 1169–1173 (2009).
Kolano, C., Helbing, J., Kozinski, M., Sander, W. & Hamm, P. Watching hydrogen-bond dynamics in a β-turn by transient two-dimensional infrared spectroscopy. Nature 444, 469–472 (2006).
Zumbusch, A., Holtom, G. R. & Xie, X. S. Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering. Phys. Rev. Lett. 82, 4142–4145 (1999).
Zhang, C., Zhang, D. & Cheng, J.-X. Coherent Raman scattering microscopy in biology and medicine. Annu. Rev. Biomed. Eng. 17, 415–445 (2015).
Marino, A. M., Pooser, R. C., Boyer, V. & Lett, P. D. Tunable delay of Einstein–Podolsky–Rosen entanglement. Nature 457, 859–862 (2009).
Camacho, R. M., Vudyasetu, P. K. & Howell, J. C. Four-wave-mixing stopped light in hot atomic rubidium vapour. Nat. Photonics 3, 103–106 (2009).
Dudovich, N., Oron, D. & Silberberg, Y. Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy. Nature 418, 512–514 (2002).
Ideguchi, T. et al. Coherent Raman spectro-imaging with laser frequency combs. Nature 502, 355–358 (2013).
Weber, T. et al. Complete photo-fragmentation of the deuterium molecule. Nature 431, 437–440 (2004).
Sansone, G., Pfeifer, T., Simeonidis, K. & Kuleff, A. I. Electron correlation in real time. ChemPhysChem 13, 661–680 (2011).
Bencivenga, F. et al. Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses. Sci. Adv. 5, eaaw5805 (2019).
Harrington, P. M., Mueller, E. J. & Murch, K. W. Engineered dissipation for quantum information science. Nat. Rev. Phys. 4, 660–671 (2022).
Avisar, D. & Tannor, D. J. Complete reconstruction of the wave function of a reacting molecule by four-wave mixing spectroscopy. Phys. Rev. Lett. 106, 170405 (2011).
Schwickert, D. et al. Electronic quantum coherence in glycine molecules probed with ultrashort X-ray pulses in real time. Sci. Adv. 8, eabn6848 (2022).
Fulde, P. Electron Correlations in Molecules and Solids (Springer, 2012).
Ossiander, M. et al. Attosecond correlation dynamics. Nat. Phys. 13, 280–285 (2017).
Wang, Y., Wu, H., McCandless, G. T., Chan, J. Y. & Ali, M. N. Quantum states and intertwining phases in kagome materials. Nat. Rev. Phys. 5, 635–658 (2023).
Ernst, R. R., Bodenhausen, G. & Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford Univ. Press, 1990).
Tanaka, S. & Mukamel, S. X-ray four-wave mixing in molecules. J. Chem. Phys. 116, 1877–1891 (2002).
Popmintchev, D. et al. Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua. Phys. Rev. Lett. 120, 093002 (2018).
Rouxel, J. R. et al. Hard X-ray transient grating spectroscopy on bismuth germanate. Nat. Photonics 15, 499–503 (2021).
Morillo-Candas, A. S. et al. Time resolved hard X-ray/optical transient grating spectroscopy on a liquid jet. In Proc. 2023 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) (IEEE, 2023).
Ferrari, E. et al. All hard X-ray transient grating spectroscopy. Commun. Phys. 8, 257 (2025).
Cavaletto, S. M., Keefer, D. & Mukamel, S. High temporal and spectral resolution of stimulated X-ray Raman signals with stochastic free-electron-laser pulses. Phys. Rev. X 11, 011029 (2021).
Belabas, N. & Jonas, D. M. Three-dimensional view of signal propagation in femtosecond four-wave mixing with application to the boxcars geometry. J. Opt. Soc. Am. B 22, 655–674 (2005).
Müller, A. et al. Photoionization of Ne atoms and Ne+ ions near the K edge: precision spectroscopy and absolute cross-sections. Astrophys. J. 836, 166 (2017).
Williams, S., Rohlfing, E. A., Rahn, L. A. & Zare, R. N. Two-color resonant four-wave mixing: analytical expressions for signal intensity. J. Chem. Phys. 106, 3090–3102 (1997).
Gel’mukhanov, F., Sałek, P., Privalov, T. & Ågren, H. Duration of x-ray Raman scattering. Phys. Rev. A 59, 380–389 (1999).
Rohringer, N. et al. Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser. Nature 481, 488–491 (2012).
Li, K., Labeye, M., Ho, P. J., Gaarde, M. B. & Young, L. Resonant propagation of x rays from the linear to the nonlinear regime. Phys. Rev. A 102, 053113 (2020).
Frasinski, L. et al. Dynamics of hollow atom formation in intense X-ray pulses probed by partial covariance mapping. Phys. Rev. Lett. 111, 073002 (2013).
Hennies, F. et al. Resonant inelastic scattering spectra of free molecules with vibrational resolution. Phys. Rev. Lett. 104, 193002 (2010).
Lundberg, M. & Wernet, P. Resonant Inelastic X-ray Scattering (RIXS) Studies in Chemistry: Present and Future, 1–52 (Springer, 2019).
Ament, L. J. P., van Veenendaal, M., Devereaux, T. P., Hill, J. P. & van den Brink, J. Resonant inelastic x-ray scattering studies of elementary excitations. Rev. Mod. Phys. 83, 705–767 (2011).
de Groot, F. M. et al. Resonant inelastic X-ray scattering. Nat. Rev. Methods Primers 4, 45 (2024).
Guo, Z. et al. Experimental demonstration of attosecond pump–probe spectroscopy with an X-ray free-electron laser. Nat. Photonics 18, 691–697 (2024).
Li, S. et al. Attosecond-pump attosecond-probe x-ray spectroscopy of liquid water. Science 383, 1118–1122 (2024).
Meier, T., Schulze, A., Thomas, P., Vaupel, H. & Maschke, K. Signatures of Fano resonances in four-wave-mixing experiments. Phys. Rev. B 51, 13977–13986 (1995).
Ott, C. et al. Lorentz meets Fano in spectral line shapes: a universal phase and its laser control. Science 340, 716–720 (2013).
Li, K. et al. Super-resolution stimulated X-ray Raman spectroscopy. Nature 643, 662–668 (2025).
Eckbreth, A. C. BOXCARS: crossed-beam phase-matched cars generation in gases. Appl. Phys. Lett. 32, 421–423 (1978).
Prior, Y. Three-dimensional phase matching in four-wave mixing. Appl. Opt. 19, 1741–1743 (1980).
Vdovin, G. & van Goor, F. LightPipes for Python. Github https://opticspy.github.io/lightpipes/ (2023).
Prat, E. et al. An X-ray free-electron laser with a highly configurable undulator and integrated chicanes for tailored pulse properties. Nat. Commun. 14, 5069 (2023).
Pradervand, C. et al. A compact gas attenuator for the SwissFEL ATHOS beamline realized using additive manufacturing. J. Synchrotron Radiat. 30, 717–722 (2023).
Al Haddad, A. et al. High magnification optical imaging systems for the characterization of soft X-ray focii. J. Synchrotron Radiat. 32, 1479–1490 (2025).
Boyd, R. W., Gaeta, A. L. & Giese, E. in Springer Handbook of Atomic, Molecular, and Optical Physics, 1097–1110 (Springer, 2023).
Lutman, A. et al. Fresh-slice multicolour X-ray free-electron lasers. Nat. Photonics 10, 745–750 (2016).
Reiche, S. & Prat, E. Two-color operation of a free-electron laser with a tilted beam. J. Synchrotron Radiat. 23, 869–873 (2016).
Prat, E. et al. Widely tunable two-color X-ray free-electron laser pulses. Phys. Rev. Res. 4, L022025 (2022).
Wang, G., Dijkstal, P., Reiche, S., Schnorr, K. & Prat, E. Millijoule femtosecond X-ray pulses from an efficient fresh-slice multistage free-electron laser. Phys. Rev. Lett. 132, 035002 (2024).
Prior, Y. & Ben-Reuven, A. Nonimpact theory of four-wave mixing and intracollisional dynamics. Phys. Rev. A 33, 2362–2377 (1986).
Rohringer, N. & London, R. Atomic inner-shell X-ray laser pumped by an X-ray free-electron laser. Phys. Rev. A 80, 013809 (2009).
Pfeifer, T., Jiang, Y., Düsterer, S., Moshammer, R. & Ullrich, J. Partial-coherence method to model experimental free-electron laser pulse statistics. Opt. Lett. 35, 3441–3443 (2010).
Frasinski, L. J., Codling, K. & Hatherly, P. A. Covariance mapping: a correlation method applied to multiphoton multiple ionization. Science 246, 1029–1031 (1989).