Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Multimode photon blockade


Interactions are essential for the creation of correlated quantum many-body states. Although two-body interactions underlie most natural phenomena, three- and four-body interactions are important for the physics of nuclei1, exotic few-body states in ultracold quantum gases2, the fractional quantum Hall effect3, quantum error correction4 and holography5,6. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm and require building up multibody interactions by combining two-body forces. Here we implement a scheme to create a higher-order interaction between photons stored in multiple electromagnetic modes of a microwave cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point the photons interact strongly. In our demonstration, we create interactions involving up to three bodies and across up to five modes. We harness the interaction to prepare single-mode Fock states and multimode W states, which we verify by introducing a multimode Wigner tomography method.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Schematic of the experimental system.
Fig. 2: Universal control of a qudit using optimal control.
Fig. 3: Generating multimode N-body interactions via photon blockade.
Fig. 4: Multimode Wigner tomography.

Similar content being viewed by others

Data availability

The source data for Figs. 14 are available at

Code availability

The analysis code is available at The control pulses used in this work were generated using the optimal control package developed elsewhere40 and also available at


  1. Loiseau, B. & Nogami, Y. Three-nucleon force. Nucl. Phys. B 2, 470–478 (1967).

    Article  ADS  Google Scholar 

  2. Hammer, H.-W., Nogga, A. & Schwenk, A. Colloquium: three-body forces: from cold atoms to nuclei. Rev. Mod. Phys. 85, 197 (2013).

    Article  ADS  Google Scholar 

  3. Wójs, A., Tőke, C. & Jain, J. K. Global phase diagram of the fractional quantum Hall effect arising from repulsive three-body interactions. Phys. Rev. Lett. 105, 196801 (2010).

    Article  ADS  Google Scholar 

  4. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339 (1993).

    Article  ADS  Google Scholar 

  6. Maldacena, J. & Stanford, D. Remarks on the Sachdev-Ye-Kitaev model. Phys. Rev. D 94, 106002 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  7. Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).

  8. Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).

    Article  ADS  Google Scholar 

  9. Kollár, A. J., Fitzpatrick, M. & Houck, A. A. Hyperbolic lattices in circuit quantum electrodynamics. Nature 571, 45–50 (2019).

    Article  ADS  Google Scholar 

  10. Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

    Article  ADS  Google Scholar 

  11. Romanenko, A. et al. Three-dimensional superconducting resonators at T < 20 mK with photon lifetimes up to τ = 2 s. Phys. Rev. Appl. 13, 034032 (2020).

    Article  ADS  Google Scholar 

  12. Rosenblum, S. et al. A CNOT gate between multiphoton qubits encoded in two cavities. Nat. Commun. 9, 652 (2018).

    Article  ADS  Google Scholar 

  13. Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368–373 (2018).

    Article  ADS  Google Scholar 

  14. Gao, Y. Y. et al. Entanglement of bosonic modes through an engineered exchange interaction. Nature 566, 509–512 (2019).

    Article  ADS  Google Scholar 

  15. Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

    Article  ADS  Google Scholar 

  16. Hu, L. et al. Quantum error correction and universal gate set operation on a binomial bosonic logical qubit. Nat. Phys. 15, 503–508 (2019).

    Article  Google Scholar 

  17. Campagne-Ibarcq, P. et al. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368–372 (2020).

    Article  Google Scholar 

  18. Owens, C. et al. Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array. Phys. Rev. A 97, 013818 (2018).

    Article  ADS  Google Scholar 

  19. Naik, R. et al. Random access quantum information processors using multimode circuit quantum electrodynamics. Nat. Commun. 8, 1904 (2017).

    Article  ADS  Google Scholar 

  20. Sundaresan, N. M. et al. Beyond strong coupling in a multimode cavity. Phys. Rev. X 5, 021035 (2015).

    Google Scholar 

  21. Pechal, M., Arrangoiz-Arriola, P. & Safavi-Naeini, A. H. Superconducting circuit quantum computing with nanomechanical resonators as storage. Quantum Sci. Technol. 4, 015006 (2018).

    Article  ADS  Google Scholar 

  22. Sletten, L. R., Moores, B. A., Viennot, J. J. & Lehnert, K. W. Resolving phonon Fock states in a multimode cavity with a double-slit qubit. Phys. Rev. X 9, 021056 (2019).

    Google Scholar 

  23. Bretheau, L., Campagne-Ibarcq, P., Flurin, E., Mallet, F. & Huard, B. Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 348, 776–779 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Vrajitoarea, A., Huang, Z., Groszkowski, P., Koch, J. & Houck, A. A. Quantum control of an oscillator using a stimulated Josephson nonlinearity. Nat. Phys. 16, 211–217 (2020).

    Article  Google Scholar 

  25. Facchi, P., Gorini, V., Marmo, G., Pascazio, S. & Sudarshan, E. Quantum Zeno dynamics. Phys. Lett. A 275, 12–19 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Facchi, P. & Pascazio, S. Quantum Zeno dynamics: mathematical and physical aspects. J. Phys. A Math. Theor. 41, 493001 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  27. Raimond, J.-M. et al. Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics. Phys. Rev. Lett. 105, 213601 (2010).

    Article  ADS  Google Scholar 

  28. Raimond, J.-M. et al. Quantum Zeno dynamics of a field in a cavity. Phys. Rev. A 86, 032120 (2012).

    Article  ADS  Google Scholar 

  29. Burgarth, D. K. et al. Exponential rise of dynamical complexity in quantum computing through projections. Nat. Commun. 5, 5173 (2014).

  30. Signoles, A. et al. Confined quantum Zeno dynamics of a watched atomic arrow. Nat. Phys. 10, 715–719 (2014).

    Article  Google Scholar 

  31. Schäfer, F. et al. Experimental realization of quantum Zeno dynamics. Nat. Commun. 5, 3194 (2014).

    Article  ADS  Google Scholar 

  32. Barontini, G., Hohmann, L., Haas, F., Estève, J. & Reichel, J. Deterministic generation of multiparticle entanglement by quantum Zeno dynamics. Science 349, 1317–1321 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Patil, Y., Chakram, S. & Vengalattore, M. Measurement-induced localization of an ultracold lattice gas. Phys. Rev. Lett. 115, 140402 (2015).

    Article  ADS  Google Scholar 

  34. Schirmer, S. G., Fu, H. & Solomon, A. I. Complete controllability of quantum systems. Phys. Rev. A 63, 063410 (2001).

    Article  ADS  Google Scholar 

  35. Chakram, S. et al. Seamless high-Q microwave cavities for multimode circuit quantum electrodynamics. Phys. Rev. Lett. 127, 107701 (2021).

    Article  ADS  Google Scholar 

  36. Schuster, D. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

    Article  ADS  Google Scholar 

  37. Heeres, R. W. et al. Cavity state manipulation using photon-number selective phase gates. Phys. Rev. Lett. 115, 137002 (2015).

    Article  ADS  Google Scholar 

  38. Heeres, R. W. et al. Implementing a universal gate set on a logical qubit encoded in an oscillator. Nat. Commun. 8, 94 (2017).

    Article  ADS  Google Scholar 

  39. Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005).

    Article  ADS  Google Scholar 

  40. Leung, N., Abdelhafez, M., Koch, J. & Schuster, D. Speedup for quantum optimal control from automatic differentiation based on graphics processing units. Phys. Rev. A 95, 042318 (2017).

    Article  ADS  Google Scholar 

  41. Ma, Y. et al. Error-transparent operations on a logical qubit protected by quantum error correction. Nat. Phys. 16, 827–831 (2020).

    Article  Google Scholar 

  42. Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  43. Larrouy, A. et al. Fast navigation in a large Hilbert space using quantum optimal control. Phys. Rev. X 10, 021058 (2020).

    Google Scholar 

  44. Wang, C. et al. A Schrödinger cat living in two boxes. Science 352, 1087–1091 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Rosenblum, S. et al. Fault-tolerant detection of a quantum error. Science 361, 266–270 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. Leung, N. et al. Deterministic bidirectional communication and remote entanglement generation between superconducting qubits. npj Quantum Inf. 5, 18 (2019).

    Article  ADS  Google Scholar 

  47. Monroe, C. R., Schoelkopf, R. J. & Lukin, M. D. Quantum connections. Sci. Am. 314, 50–57 (2016).

    Article  ADS  Google Scholar 

Download references


We thank T. Propson, Y. Lu, A. Agrawal, T. Roy and J. Simon for useful discussions. We acknowledge support from the Samsung Advanced Institute of Technology Global Research Partnership. This work was also supported by ARO Grants W911NF-15-1-0397 and W911NF-18-1-0212, ARO MURI grant W911NF-16-1-0349, AFOSR MURI grant FA9550-19-1-0399 and the Packard Foundation (2013-39273). This work is funded in part by EPiQC, a National Science Foundation (NSF) Expedition in Computing, under grant CCF-1730449. We acknowledge the support provided by the Heising-Simons Foundation. D.I.S. acknowledges support from the David and Lucile Packard Foundation. This work was partially supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the NSF under award no. DMR-1420709. The devices were fabricated in the Pritzker Nanofabrication Facility at the University of Chicago, which receives support from Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205), a node of the NSF’s National Nanotechnology Coordinated Infrastructure.

Author information

Authors and Affiliations



L.J., D.I.S., and S.C. conceived the experiment. S.C. designed the device and fabricated the cavity, with help from A.E.O., R.K.N. and A.V.D. K.H. fabricated the transmon, with assistance from A.V.D. K.H. and S.C. performed the experiment and analysed the data, with assistance from H.K. N.L. developed the optimal control package, and wrote the framework for the experimental control software. W.-L.M. and L.J. provided theoretical support and guidance throughout the experiment, and D.I.S. supervised all the aspects of the project. S.C., K.H. and D.I.S. wrote the manuscript, with input from all the authors.

Corresponding author

Correspondence to David I. Schuster.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Luyan Sun and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12, Discussion and Table 1.

Supplementary Video 1

Measured Wigner functions and photon-number-resolved spectroscopy over time for an optimal control pulse that prepares Fock state 1 with a blockade of Fock state 3.

Supplementary Video 2

Measured Wigner functions and photon-number-resolved spectroscopy over time for an optimal control pulse that prepares Fock state 2 with a blockade of Fock state 3.

Supplementary Video 3

Wigner tomography over time for the two-mode W-state preparation sequence, showing each of the six possible two-dimensional phase space slices.

Supplementary Video 4

Density matrix over time for two-mode W-state preparation.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chakram, S., He, K., Dixit, A.V. et al. Multimode photon blockade. Nat. Phys. 18, 879–884 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing