Atomic, Molecular, Optical Science

A Single-Photon Collider Implemented by a Superconducting Circuit: From Photon-Instanton Scattering to the Bulgadaev-Schmid Transition

How would our world look like if the fine structure constant were of order unity? While in our world of small fine structure constant, $\alpha \approx 1/137$, an atom excited to the first excited state has negligible probability of decaying to the ground state while emitting more than a single photon, such processes are important in a large $\alpha$ world, making photon frequency conversion effective in the regime of a single incoming photon. We show how such behavior can be realized in a superconducting circuit quantum electrodynamics system, where a transmon qubit, which serves as an artificial atom, is galvanically coupled to a high-impedance transmission line (whose impedance is of the order of the quantum of resistance, $h/(2e)^2 \approx 6.5$ k$\Omega$), realized by an array of large Josephson junctions. The array acts as a waveguide for microwave photons with a high effective $\alpha$. For small transmon charging energy, instantons (phase slips) that occur in the transmon interact with the microwave photons, and lead to inelastic scattering probabilities which approach unity and greatly exceed the effect of the quartic anharmoncity of the Josephson potential [1]. The instanton-photon cross section is calculated using a novel formalism, which allows to directly observe the dynamical properties of the instantons, and should be useful in other quantum field theoretical contexts. The calculated inelastic decay rates compare well with recent measurements by the Manucharyan group at Maryland [2,3]. Turning to the case of large transmon charging energy, we show how photon splitting can be used to shed a single-photon light on the Bulgadaev-Schmid superconductor-to-insulator quantum phase transition in the transmon (as function of the array impedance) [4], which has been the center of a recent controversy. Interestingly, the system becomes integrable in that limit, which does not prohibit inelastic photon scattering, but, on the contrary, allows an exact calculation of the corresponding cross section [5]. Moreover, such setups are ideal for studying the intriguing microscopic-to-macroscopic crossover, and reveal how inelastic processes involving different numbers of photons can serve as effective baths for each other, and usher in the emergence of the Fermi golden rule [6].
[1] A. Burshtein, R. Kuzmin, V. E. Manucharyan, and M. Goldstein, Photon-instanton collider implemented by a superconducting circuit, Phys. Rev. Lett. 126, 137701 (2021).
[2] R. Kuzmin, N. Grabon, N. Mehta, A. Burshtein, M. Goldstein, M. Houzet, L. I. Glazman, and V. E. Manucharyan, Photon decay in circuit quantum electrodynamics, Phys. Rev. Lett. 126, 197701, (2021).
[3] A. Burshtein, D. Shuliutsky, R. Kuzmin, V. Manucharyan, and M. Goldstein, Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime, Phys. Rev. B 112, 054514 (2025).
[4] 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, Nature Phys. 21, 132 (2025).
[5] A. Burshtein and M. Goldstein, Inelastic decay from integrability, PRX Quantum 5, 020323 (2024).
[6] Burshtein, A., and M. Goldstein, Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities, Phys. Rev. B 111, 174303 (2025).