Inelastic decay from integrability

TL;DR

This paper demonstrates that inelastic decay of microwave photons can occur in integrable boundary models within circuit QED, and provides exact analytical tools to describe this phenomenon, challenging the traditional view of purely elastic scattering in integrable systems.

Contribution

It reveals inelastic decay in integrable boundary models and develops exact analytical methods to quantify it, including energy-resolved spectra and response functions.

Findings

Inelastic decay observed in superconducting circuit models of integrable systems.

Exact expressions for inelastic decay rates and spectra derived using form factors.

Relation of theoretical results to recent photon splitting experiments and quantum phase transitions.

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.