Inelastic decay from integrability

Recent experiments in superconducting circuits have demonstrated the high probability splitting of single-photons [1,2], a phenomenon rarely observed in nature. This exotic effect is enabled by a high-impedance Josephson transmission line which increases the effective coupling of the microwave photons to an artificial atom, and provides a useful tool to probe fundamental phenomena in many-body systems.
I will discuss a collaboration with the Manucharyan and Kuzmin groups, in which we utilized single-photon splitting to observe the Schmid-Bulgadaev quantum phase transition [3], whose lack of clear evidence has sparked a recent debate. The experimental system realizes the boundary sine-Gordon model, which is known to be integrable and is characterized by purely elastic scattering of elementary excitations, that seems at odds with photon splitting. I will show that a nonlinear relation between these excitations and the photons not only allows for inelastic decay of the latter, but also that integrability provides powerful analytical tools yielding exact results for the total inelastic decay rate and the spectrum of the resulting photons [4]. Our results shed light on the Schmid-Bulgadaev transition, and compare nicely with experimental measurements.

References:

[1] R. Kuzmin, N. Grabon, N. Mehta, A. Burshtein, M. Goldstein, M. Houzet, L. I. Glazman, and V. E. Manucharyan, "Inelastic scattering of a photon by a quantum phase slip", PRL 126 197701 (2021)

[2] A. Burshtein, R. Kuzmin, V. E. Manucharyan, and M. Goldstein, "Photon-instanton collider implemented by a superconducting circuit", PRL 126 137701 (2021)

[3] R. Kuzmin, N. Mehta, N. Grabon, R. A. Mencia, A. Burshtein, M. Goldstein, and V. E. Manucharyan, "Observation of the Schmid-Bulgadaev dissipative quantum phase transition", arXiv:2304.05806, accepted to Nature Physics (2024)

[4] A. Burshtein and M. Goldstein, "Inelastic decay from integrability", PRX Quantum 5 020323 (2024)