Oka, T. & Kitamura, S. Floquet engineering of quantum materials. Annu. Rev. Condens. Matter Phys. 10, 387–408 (2019).

Article 

Google Scholar
 

de la Torre, A. et al. Colloquium: Nonthermal pathways to ultrafast control in quantum materials. Rev. Mod. Phys. 93, 041002 (2021).

Article 
CAS 

Google Scholar
 

Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet–Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).

Article 
CAS 
PubMed 

Google Scholar
 

Ito, S. et al. Build-up and dephasing of Floquet–Bloch bands on subcycle timescales. Nature 616, 696–701 (2023).

Article 
CAS 
PubMed 

Google Scholar
 

Choi, D. et al. Observation of Floquet–Bloch states in monolayer graphene. Nat. Phys. 21, 1100–1105 (2025).

Merboldt, M. et al. Observation of Floquet states in graphene. Nat. Phys. 21, 1093–1099 (2025).

Aeschlimann, S. et al. Survival of Floquet–Bloch states in the presence of scattering. Nano Lett. 21, 5028–5035 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Zhou, S. et al. Pseudospin-selective Floquet band engineering in black phosphorus. Nature 614, 75–80 (2023).

Article 
CAS 
PubMed 

Google Scholar
 

Bielinski, N. et al. Floquet–Bloch manipulation of the Dirac gap in a topological antiferromagnet. Nat. Phys. 21, 458–463 (2025).

Article 
CAS 

Google Scholar
 

Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).

Article 
CAS 
PubMed 

Google Scholar
 

Sie, E. J. et al. Large, valley-exclusive Bloch–Siegert shift in monolayer WS2. Science 355, 1066–1069 (2017).

Article 
CAS 
PubMed 

Google Scholar
 

McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

Shan, J.-Y. et al. Giant modulation of optical nonlinearity by Floquet engineering. Nature 600, 235–239 (2021).

Article 
CAS 
PubMed 

Google Scholar
 

Kobayashi, Y. et al. Floquet engineering of strongly driven excitons in monolayer tungsten disulfide. Nat. Phys. 19, 171–176 (2023).

CAS 

Google Scholar
 

Zhang, X. et al. Light-induced electronic polarization in antiferromagnetic Cr2O3. Nat. Mater. 23, 790–795 (2024).

Article 
CAS 
PubMed 

Google Scholar
 

Bloch, J., Cavalleri, A., Galitski, V., Hafezi, M. & Rubio, A. Strongly correlated electron–photon systems. Nature 606, 41–48 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Mentink, J. H., Balzer, K. & Eckstein, M. Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 6708 (2015).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Valmispild, V. N. et al. Dynamically induced doublon repulsion in the Fermi–Hubbard model probed by a single-particle density of states. Phys. Rev. B 102, 220301 (2020).

Article 
CAS 

Google Scholar
 

Claassen, M., Jiang, H.-C., Moritz, B. & Devereaux, T. P. Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators. Nat. Commun. 8, 1192 (2017).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Lee, C. H., Ho, W. W., Yang, B., Gong, J. & Papić, Z. Floquet mechanism for non-Abelian fractional quantum Hall states. Phys. Rev. Lett. 121, 237401 (2018).

Article 
CAS 
PubMed 

Google Scholar
 

Peronaci, F., Parcollet, O. & Schiró, M. Enhancement of local pairing correlations in periodically driven Mott insulators. Phys. Rev. B 101, 161101 (2020).

Article 
CAS 

Google Scholar
 

Clarke, D. G. Particle-hole bound states in Mott-Hubbard insulators. Phys. Rev. B 48, 7520 (1993).

Article 
CAS 

Google Scholar
 

Essler, F. H. L., Gebhard, F. & Jeckelmann, E. Excitons in one-dimensional Mott insulators. Phys. Rev. B 64, 125119 (2001).

Article 

Google Scholar
 

Kishida, H. et al. Gigantic optical nonlinearity in one-dimensional Mott–Hubbard insulators. Nature 405, 929–932 (2000).

Article 
CAS 
PubMed 

Google Scholar
 

Ono, M. et al. Linear and nonlinear optical properties of one-dimensional Mott insulators consisting of Ni-halogen chain and CuO-chain compounds. Phys. Rev. B 70, 085101 (2004).

Article 

Google Scholar
 

Motoyama, N., Eisaki, H. & Uchida, S. Magnetic susceptibility of ideal spin 1/2 Heisenberg antiferromagnetic chain systems, Sr2CuO3 and SrCuO2. Phys. Rev. Lett. 76, 3212 (1996).

Article 
CAS 
PubMed 

Google Scholar
 

Walters, A. C. et al. Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds. Nat. Phys. 5, 867–872 (2009).

Article 
CAS 

Google Scholar
 

Schlappa, J. et al. Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3. Nature 485, 82–85 (2012).

Article 
CAS 
PubMed 

Google Scholar
 

Kim, K. W., Gu, G. D., Homes, C. C. & Noh, T. W. Bound excitons in Sr2CuO3. Phys. Rev. Lett. 101, 177404 (2008).

Article 
CAS 
PubMed 

Google Scholar
 

Kim, K. W. & Gu, G. D. Optical excitations in Sr2CuO3. Phys. Rev. B 79, 085121 (2009).

Article 

Google Scholar
 

Ogasawara, T. et al. Ultrafast optical nonlinearity in the quasi-one-dimensional Mott insulator Sr2CuO3. Phys. Rev. Lett. 85, 2204 (2000).

Article 
CAS 
PubMed 

Google Scholar
 

Mizuno, Y., Tsutsui, K., Tohyama, T. & Maekawa, S. Nonlinear optical response and spin-charge separation in one-dimensional Mott insulators. Phys. Rev. B 62, R4769 (2000).

Article 
CAS 

Google Scholar
 

Jeckelmann, E. Optical excitations in a one-dimensional Mott insulator. Phys. Rev. B 67, 075106 (2003).

Article 

Google Scholar
 

Kishida, H. et al. Large third-order optical nonlinearity of Cu–O chains investigated by third-harmonic generation spectroscopy. Phys. Rev. Lett. 87, 177401 (2001).

Article 
CAS 
PubMed 

Google Scholar
 

Maeda, A. et al. Third-order nonlinear susceptibility spectra of CuO chain compounds investigated by the Z-scan method. Phys. Rev. B 70, 125117 (2004).

Article 

Google Scholar
 

Cundiff, S. T. et al. Rabi flopping in semiconductors. Phys. Rev. Lett. 73, 1178 (1994).

Article 
CAS 
PubMed 

Google Scholar
 

Cole, B. E., Williams, J. B., King, B. T., Sherwin, M. S. & Stanley, C. R. Coherent manipulation of semiconductor quantum bits with terahertz radiation. Nature 410, 60–63 (2001).

Article 
CAS 
PubMed 

Google Scholar
 

Press, D., Ladd, T. D., Zhang, B. & Yamamoto, Y. Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008).

Article 
CAS 
PubMed 

Google Scholar
 

Berezovsky, J., Mikkelsen, M. H., Stoltz, N. G., Coldren, L. A. & Awschalom, D. D. Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science 320, 349–352 (2008).

Article 
CAS 
PubMed 

Google Scholar
 

Rabitz, H. A., Hsieh, M. M. & Rosenthal, C. M. Quantum optimally controlled transition landscapes. Science 303, 1998–2001 (2004).

Article 
CAS 
PubMed 

Google Scholar
 

Kaindl, R. A. et al. Generation, shaping, and characterization of intense femtosecond pulses tunable from 3 to 20 μm. J. Opt. Soc. Am. B 17, 2086–2094 (2000).

Article 
CAS 

Google Scholar
 

Cartella, A. et al. Pulse shaping in the mid-infrared by a deformable mirror. Opt. Lett. 39, 1485–1488 (2014).

Article 
PubMed 

Google Scholar
 

Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037 (2005).

Article 

Google Scholar
 

Choi, J. et al. Robust dynamic Hamiltonian engineering of many-body spin systems. Phys. Rev. X 10, 031002 (2020).

CAS 

Google Scholar
 

Kim, J. et al. Excitonic quasiparticles in a spin–orbit Mott insulator. Nat. Commun. 5, 4453 (2014).

Article 
CAS 
PubMed 

Google Scholar
 

Kuneš, J. Excitonic condensation in systems of strongly correlated electrons. J. Phys. Condens. Matter 27, 333201 (2015).

Article 
PubMed 

Google Scholar
 

Xia, Z. et al. Optical readout of the chemical potential of two-dimensional electrons. Nat. Photon. 18, 344–349 (2024).

Article 
CAS 

Google Scholar
 

Kazimierczuk, T., Fröhlich, D., Scheel, S., Stolz, H. & Bayer, M. Giant Rydberg excitons in the copper oxide Cu2O. Nature 514, 343–347 (2014).

Article 
CAS 
PubMed 

Google Scholar
 

Kang, S. et al. Coherent many-body exciton in van der Waals antiferromagnet NiPS3. Nature 583, 785–789 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

Bae, Y. J. et al. Exciton-coupled coherent magnons in a 2D semiconductor. Nature 609, 282–286 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Mitrano, M. Source data for quantum control of Hubbard excitons. Figshare https://doi.org/10.6084/m9.figshare.31146367 (2026).

Jülich Supercomputing Centre. JURECA: data centric and booster modules implementing the modular supercomputing architecture at Jülich Supercomputing Centre. J. Large-Scale Res. Facil. https://doi.org/10.17815/jlsrf-7-182 (2021).