Abstract
Chiral quantum optics is central to developing scalable quantum networks, yet existing approaches rely predominantly on linear single-photon regimes. It remains unclear how to generate directional multiphotons. Here we show that giant emitters coupled to nonlinear quantum optical baths enable tunable directional correlated photons, revealing a mechanism for multiphoton directional emission. We demonstrate that the propagation phases of correlated photons, together with the coupling phases of giant emitters, can generate destructive interference in one direction while enhancing emission in the opposite direction, making directionality fully tunable. Building on this mechanism, we introduce a nonlinear cascaded quantum network paradigm mediated by “correlated flying qubits”, providing a configurable building block enabling distinct many-body applications beyond linear unidirectional setups. These results reveal a rich landscape for engineering multiphoton propagation and correlations through interference in giant emitter-nonlinear bath architectures, offering pathways for quantum networks and strongly correlated light-matter platforms.
Similar content being viewed by others
Data availability
Supplementary data for all the figures are provided at https://doi.org/10.5281/zenodo.18409019. Additional data that support the findings of this study are available from the authors upon request.
Code availability
The codes used for the simulation and analysis of the data are available from the authors upon request.
References
Cirac, J. I., Zoller, P., Kimble, H. J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).
Mitsch, R., Sayrin, C., Albrecht, B., Schneeweiss, P. & Rauschenbeutel, A. Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide. Nat. Commun. 5, 5713 (2014).
Pichler, H., Ramos, T., Daley, A. J. & Zoller, P. Quantum optics of chiral spin networks. Phys. Rev. A 91, 042116 (2015).
Lodahl, P. et al. Chiral quantum optics. Nature 541, 473 (2017).
De Bernardis, D., Piccioli, F. S., Rabl, P. & Carusotto, I. Chiral quantum optics in the bulk of photonic quantum hall systems. PRX Quantum 4, 030306 (2023).
Guimond, P.-O. et al. A unidirectional on-chip photonic interface for superconducting circuits. npj Quantum Inf. 6, 32 (2020).
Kannan, B. et al. On-demand directional microwave photon emission using waveguide quantum electrodynamics. Nat. Phys. 19, 394 (2023).
Yao, W., Liu, R.-B. & Sham, L. J. Theory of control of the spin-photon interface for quantum networks. Phys. Rev. Lett. 95, 030504 (2005).
Stannigel, K., Rabl, P., Sørensen, A. S., Lukin, M. D. & Zoller, P. Optomechanical transducers for quantum-information processing. Phys. Rev. A 84, 042341 (2011).
Stannigel, K., Rabl, P. & Zoller, P. Driven-dissipative preparation of entangled states in cascaded quantum-optical networks. N. J. Phys. 14, 063014 (2012).
Vermersch, B., Guimond, P.-O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).
Xiang, Z.-L., Zhang, M., Jiang, L. & Rabl, P. Intracity quantum communication via thermal microwave networks. Phys. Rev. X 7, 011035 (2017).
Chang, D. E., Vuletic, V. & Lukin, M. D. Quantum nonlinear optics–photon by photon. Nat. Photonics 8, 685 (2014).
Mahmoodian, S. et al. Strongly correlated photon transport in waveguide quantum electrodynamics with weakly coupled emitters. Phys. Rev. Lett. 121, 143601 (2018).
Solano, P., Barberis-Blostein, P. & Sinha, K. Dissimilar collective decay and directional emission from two quantum emitters. Phys. Rev. A 107, 023723 (2023).
Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726 (2007).
Yuan, Z.-S. et al. Entangled photons and quantum communication. Phys. Rep. 497, 1–40 (2010).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photonics 5, 222 (2011).
Gatto Monticone, D. et al. Beating the abbe diffraction limit in confocal microscopy via nonclassical photon statistics. Phys. Rev. Lett. 113, 143602 (2014).
Paulisch, V., Perarnau-Llobet, M., González-Tudela, A. & Cirac, J. I. Quantum metrology with one-dimensional superradiant photonic states. Phys. Rev. A 99, 043807 (2019).
Sheremet, A. S., Petrov, M. I., Iorsh, I. V., Poshakinskiy, A. V. & Poddubny, A. N. Waveguide quantum electrodynamics: collective radiance and photon-photon correlations. Rev. Mod. Phys. 95, 015002 (2023).
Mahmoodian, S., Calajó, G., Chang, D. E., Hammerer, K. & Sørensen, A. S. Dynamics of many-body photon bound states in chiral waveguide QED. Phys. Rev. X 10, 031011 (2020).
Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57 (2012).
Roy, D., Wilson, C. M. & Firstenberg, O. Colloquium: strongly interacting photons in one-dimensional continuum. Rev. Mod. Phys. 89, 021001 (2017).
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
Orell, T., Michailidis, A. A., Serbyn, M. & Silveri, M. Probing the many-body localization phase transition with superconducting circuits. Phys. Rev. B 100, 134504 (2019).
Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Gorshkov, A. V., Otterbach, J., Fleischhauer, M., Pohl, T. & Lukin, M. D. Photon-photon interactions via Rydberg blockade. Phys. Rev. Lett. 107, 133602 (2011).
Fedorov, G. P. et al. Photon transport in a Bose-Hubbard chain of superconducting artificial atoms. Phys. Rev. Lett. 126, 180503 (2021).
Karamlou, A. H. et al. Probing entanglement in a 2D hard-core Bose–Hubbard lattice. Nature 629, 561 (2024).
Castillo-Moreno, C. et al. Experimental observation of multimode quantum phase transitions in a superconducting Bose-Hubbard simulator. Preprint at arXiv https://doi.org/10.48550/arXiv.2508.20116 (2025).
Weckesser, P. et al. Realization of a Rydberg-dressed extended Bose-Hubbard model. Science 390, 849–853 (2025).
Winkler, K. et al. Repulsively bound atom pairs in an optical lattice. Nature 441, 853 (2006).
Piil, R. & Mølmer, K. Tunneling couplings in discrete lattices, single-particle band structure, and eigenstates of interacting atom pairs. Phys. Rev. A 76, 023607 (2007).
Valiente, M. & Petrosyan, D. Two-particle states in the Hubbard model. J. Phys. B 41, 161002 (2008).
Mansikkamäki, O., Laine, S., Piltonen, A. & Silveri, M. Beyond hard-core bosons in transmon arrays. PRX Quantum 3, 040314 (2022).
Wang, Z., Jaako, T., Kirton, P. & Rabl, P. Supercorrelated radiance in nonlinear photonic waveguides. Phys. Rev. Lett. 124, 213601 (2020).
Talukdar, J. & Blume, D. Two emitters coupled to a bath with Kerr-like nonlinearity: exponential decay, fractional populations, and Rabi oscillations. Phys. Rev. A 105, 063501 (2022).
Li, J.-Q. & Wang, X. Environmental quantum states trigger emission in nonlinear photonics. Commun. Phys. 8, 511 (2025).
Zhang, X., Guo, X., Zhang, Y., Wang, X. & Wang, Z. Quantum state preparation and transfer based on the bound state in the doublon continuum. Preprint at arXiv https://doi.org/10.48550/arXiv.2512.01339 (2025).
Rieck, W., Kockum, A. F. & Chen, G. Doublon bound states in the continuum through giant atoms. Preprint at arXiv https://doi.org/10.48550/arXiv.2511.18212 (2025).
Frisk Kockum, A., Delsing, P. & Johansson, G. Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom. Phys. Rev. A 90, 013837 (2014).
Frisk Kockum, A. Quantum Optics with Giant Atoms—the First Five Years, 125–146 (Springer Singapore, 2020). https://doi.org/10.1007/978-981-15-5191-8_12.
Du, L., Zhang, Y., Wu, J.-H., Kockum, A. F. & Li, Y. Giant atoms in a synthetic frequency dimension. Phys. Rev. Lett. 128, 223602 (2022).
Terradas-Briansó, S., González-Gutiérrez, C. A., Nori, F., Martín-Moreno, L. & Zueco, D. Ultrastrong waveguide QED with giant atoms. Phys. Rev. A 106, 063717 (2022).
Qiu, Q.-Y., Wu, Y. & Lü, X.-Y. Collective radiance of giant atoms in non-Markovian regime. Sci. China Phys. Mech. https://doi.org/10.1007/s11433-022-1990-x (2023).
Gustafsson, M. V. et al. Propagating phonons coupled to an artificial atom. Science 346, 207 (2014).
Aref, T. et al. Quantum acoustics with surface acoustic waves. In (eds Hadfield, R. H. & Johansson, G.) Superconducting Devices in Quantum Optics (Springer, 2016).
Guo, L., Grimsmo, A., Kockum, A. F., Pletyukhov, M. & Johansson, G. Giant acoustic atom: a single quantum system with a deterministic time delay. Phys. Rev. A 95, 053821 (2017).
Andersson, G., Suri, B., Guo, L., Aref, T. & Delsing, P. Non-exponential decay of a giant artificial atom. Nat. Phys. 15, 1123 (2019).
Vadiraj, A. M. et al. Engineering the level structure of a giant artificial atom in waveguide quantum electrodynamics. Phys. Rev. A 103, 023710 (2021).
Wang, X. & Li, H.-R. Chiral quantum network with giant atoms. Quantum Sci. Technol. 7, 035007 (2022).
Wang, Z.-Q. et al. Giant spin ensembles in waveguide magnonics. Nat. Commun. 13, 7580 (2022).
Kockum, A. F., Johansson, G. & Nori, F. Decoherence-free interaction between giant atoms in waveguide quantum electrodynamics. Phys. Rev. Lett. 120, 140404 (2018).
Kannan, B. et al. Waveguide quantum electrodynamics with superconducting artificial giant atoms. Nature 583, 775 (2020).
Carollo, A., Cilluffo, D. & Ciccarello, F. Mechanism of decoherence-free coupling between giant atoms. Phys. Rev. Res. 2, 043184 (2020).
Soro, A., Muñoz, C. S. & Kockum, A. F. Interaction between giant atoms in a one-dimensional structured environment. Phys. Rev. A 107, 013710 (2023).
Guo, L., Kockum, A. F., Marquardt, F. & Johansson, G. Oscillating bound states for a giant atom. Phys. Rev. Res. 2, 043014 (2020).
Noachtar, D. D., Knörzer, J. & Jonsson, R. H. Nonperturbative treatment of giant atoms using chain transformations. Phys. Rev. A 106, 013702 (2022).
Lim, K. H., Mok, W. K. & Kwek, L. C. Oscillating bound states in non-Markovian photonic lattices. Phys. Rev. A 107, 023716 (2023).
Zhao, W. & Wang, Z. Single-photon scattering and bound states in an atom-waveguide system with two or multiple coupling points. Phys. Rev. A 101, 053855 (2020).
González-Tudela, A., Muñoz, C. S. & Cirac, J. I. Engineering and harnessing giant atoms in high-dimensional baths: a proposal for implementation with cold atoms. Phys. Rev. Lett. 122, 203603 (2019).
Wang, X., Liu, T., Kockum, A. F., Li, H.-R. & Nori, F. Tunable chiral bound states with giant atoms. Phys. Rev. Lett. 126, 043602 (2021).
Joshi, C., Yang, F. & Mirhosseini, M. Resonance fluorescence of a chiral artificial atom. Phys. Rev. X 13, 021039 (2023).
Scully, M. O. & Zubairy, M. S. Quantum Optics (Cambridge University Press, 1997).
Ramos, T., Vermersch, B., Hauke, P., Pichler, H. & Zoller, P. Non-Markovian dynamics in chiral quantum networks with spins and photons. Phys. Rev. A 93, 062104 (2016).
Wang, X., Zhu, H.-B., Liu, T. & Nori, F. Realizing quantum optics in structured environments with giant atoms. Phys. Rev. Res. 6, 013279 (2024).
Gao, Z.-M., Li, J.-Q., Wu, Y.-H., Liu, W.-X. & Wang, X. Harnessing spontaneous emission of correlated photon pairs from ladder-type giant atoms. Phys. Rev. A 110, 053706 (2024).
Wang, D.-W., Zhu, S.-Y., Evers, J. & Scully, M. O. High-frequency light reflector via low-frequency light control. Phys. Rev. A 91, 011801 (2015).
Zhong, Y. et al. Deterministic multi-qubit entanglement in a quantum network. Nature 590, 571–575 (2021).
Strand, H. U. R., Eckstein, M. & Werner, P. Beyond the Hubbard bands in strongly correlated lattice bosons. Phys. Rev. A 92, 063602 (2015).
Sajna, A. S. Effects of higher-order energy bands and temperature on the bosonic Mott insulator in a periodically modulated lattice. Phys. Rev. A 94, 043612 (2016).
Chang, C. W. S. et al. Observation of three-photon spontaneous parametric down-conversion in a superconducting parametric cavity. Phys. Rev. X 10, 011011 (2020).
Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y.-X. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718-719, 1 (2017).
Krantz, P. et al. A quantum engineer’s guide to superconducting qubits. Appl. Phys. Rev. 6, 021318 (2019).
Hacohen-Gourgy, S., Ramasesh, V. V., De Grandi, C., Siddiqi, I. & Girvin, S. M. Cooling and autonomous feedback in a Bose-Hubbard chain with attractive interactions. Phys. Rev. Lett. 115, 240501 (2015).
Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).
Kim, E. et al. Quantum electrodynamics in a topological waveguide. Phys. Rev. X 11, 011015 (2021).
Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146 (2017).
Krinner, S. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669 (2022).
Place, A. P. M. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021).
Johansson, J. R., Nation, P. D. & Nori, F. QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 183, 1760 (2012).
Johansson, J. R., Nation, P. D. & Nori, F. QuTiP 2: a Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234 (2013).
Acknowledgements
X.W. is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 12174303). Z.H.W. acknowledges the support from the National Natural Science Foundation of China (Grant No. 12375010). T.L. acknowledges the support from Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2505004), National Natural Science Foundation of China (Grant No. 12274142), and the Introduced Innovative Team Project of Guangdong Pearl River Talents Program (Grant No. 2021ZT09Z109). A.F.K. acknowledges support from the Swedish Research Council (grant number 2019-03696), the Swedish Foundation for Strategic Research (grants numbers FFL21-0279 and FUS21-0063), the Horizon Europe program HORIZON-CL4-2022-QUANTUM-01-SGA via the project 101113946 OpenSuperQPlus100, and from the Knut and Alice Wallenberg Foundation through the Wallenberg Centre for Quantum Technology (WACQT). F.N. is supported in part by the Japan Science and Technology Agency (JST) [via the CREST Quantum Frontiers program Grant No. JPMJCR24I2, the Quantum Leap Flagship Program (Q-LEAP), the Moonshot R&D Grant Number JPMJMS256E, and the ASPIRE program (Grant Number JPMJAP2513).
Author information
Authors and Affiliations
Contributions
X.W. and T.L. conceived the original idea. J.Q.L. did the analytical and numerical analysis under the supervision of X.W. and T.L. Z.H.W., A.F.K., L.D., and F.N. provided very useful insights and guidance. All authors contributed to and approved the final version of the paper.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Communications Physics thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Wang, X., Li, JQ., Wang, Z. et al. Nonlinear cascaded quantum network with giant emitters. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02618-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s42005-026-02618-3


