Inelastic decay from integrability

Abstract

A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this work, we show that inelastic decay can nevertheless be observed in circuit QED realizations of integrable boundary models. We consider the scattering of microwave photons off impurities in superconducting circuits implementing the boundary sine-Gordon and Kondo models, which are both integrable. We show that not only inelastic decay is possible for the microwave photons, in spite of integrability, and thanks to a nonlinear relation between them and the elastically-scattered excitations, but also that integrability in fact provides powerful analytical tools allowing to obtain exact expressions for response functions describing the inelastic decay. Using the framework of form factors, we calculate the total inelastic decay rate and elastic phase shift of the microwave photons, extracted from a 2-point response function. We then go beyond linear response and obtain the exact energy-resolved inelastic decay spectrum, using a novel method to evaluate form factor expansions of 3-point response functions, which could prove useful in other applications of integrable quantum field theories. We relate our results to several recent photon splitting experiments, and in particular to recent experimental data that provides evidence for the elusive Schmid-Bulgadaev dissipative quantum phase transition.

Close to published version

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Experimental Observation of a Generalized Gibbs Ensemble
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Form factor expansion for thermal correlators
• Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array
• Scaling of the low temperature dephasing rate in Kondo systems
• Theory of inelastic scattering from quantum impurities
• Finite-Temperature Form Factors: a Review
• Quantum Effects in Small-Capacitance Single Josephson Junctions
• Critical fluorescence of a transmon at the Schmid transition
• Microwave spectroscopy of a weakly-pinned charge density wave in a superinductor

Cited by in corpus (8)

• Direct detection of down-converted photons spontaneously produced at a single Josephson junction
• Limitations of Caldeira-Leggett model for description of phase transitions in superconducting circuits
• Bloch oscillations in a transmon embedded in a resonant electromagnetic environment
• Nonlinear response theory for lossy superconducting quantum circuits
• Resilience of the quantum critical line in the Schmid transition
• Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities
• Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime
• Revisiting dissipation-driven phase transition in a Josephson junction