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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.

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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.

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


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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.

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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.

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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.

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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.

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

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