Decay of a particle into more particles is a ubiquitous phenomenon to interacting quantum systems, taking place in colliders, nuclear reactors or solids. In a nonlinear medium, even a single photon would decay by down-converting (splitting) into lower-frequency photons with the same total energy1, at a rate given by Fermi’s golden rule. However, the energy-conservation condition cannot be matched precisely if the medium is finite and only supports quantized modes. In this case, the fate of the photon becomes the long-standing question of many-body localization, originally formulated as a gedanken experiment for the lifetime of a single Fermi-liquid quasiparticle confined to a quantum dot2. Here we implement such an experiment using a superconducting multimode cavity, the nonlinearity of which was tailored to strongly violate the photon-number conservation. The resulting interaction attempts to convert a single photon excitation into a shower of low-energy photons but fails owing to the many-body localization mechanism, which manifests as a striking spectral fine structure of multiparticle resonances at the standing-wave-mode frequencies of the cavity. Each resonance was identified as a many-body state of radiation composed of photons from a broad frequency range and not obeying Fermi’s golden rule theory. Our result introduces a new platform to explore the fundamentals of many-body localization without having to control many atoms or qubits3,4,5,6,7,8,9.
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The raw data collected in this study are available from the corresponding author on reasonable request.
The code used to analyse the data reported in this study is available from the corresponding author on reasonable request.
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We acknowledge support from DOE Early Career Award (DE-SC0020160), US ARO MURI programme ‘Exotic states of light in superconducting circuits’ (W911NF-15-1-0397) and Google Faculty Research Award. C.C. acknowledges financial support from FET FLAGSHIP Project PhoQuS (grant agreement no. 820392) and from the French agency ANR through the project NOMOS (ANR-18-CE24-0026) and TRIANGLE (ANR-20-CE47-0011).
The authors declare no competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Non-interacting spectra.
Left column, excitation frequency versus the applied flux bias for the single-particle eigenstates (solid black lines). The filled black dots are the experimental data used for the fitting procedure described in the text. Middle column, energy of the uncoupled two-particle states added (red lines). Right column, energy of the uncoupled thee-particle states added (green lines). Note that at a frequency of around 8 GHz and above, the three-particle spectrum is almost uniformly spread in energy, as if the system has a natural disorder in the single-particle spectrum.
Extended Data Fig. 2 Dispersion characterization.
Measured standing-wave-mode frequency spacing fk+1 − fk versus frequency fk (k = 1, 2,…) at φext = 0 (black circles) and at φext/2π = 0.5 (red circles). The dispersion varies the mode spacing from 165 to 195 MHz in the frequency range of interest. The non-dispersive mode spacing is extracted to be Δ = v/2ℓ ≈ 197 MHz. The hybridization window width Γ ≈ 1 GHz and the low-frequency cutoff corresponding to j0 = 20 are indicated.
Extended Data Fig. 3 Interaction parameters.
a, Photon–photon interaction frequency scale g as a function of the external flux. b, Colour plot of the matrix elements Ak,k′ versus the mode indices k,k′ when the qubit frequency is tuned to feg = 7.2 GHz (around mode index 39) at φext/2π = 0.36. Note that the width of the local maximum in Ak,k′ is given by Γ/Δ.
Extended Data Fig. 4 Photon loss characterization.
Internal (blue circles) and external (red triangles) quality factors of the bare Fabry–Pérot modes as a function of mode frequency measured at the flux bias φext = 0. For this flux value, the qubit coupling is negligible.
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Mehta, N., Kuzmin, R., Ciuti, C. et al. Down-conversion of a single photon as a probe of many-body localization. Nature 613, 650–655 (2023). https://doi.org/10.1038/s41586-022-05615-y
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