Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment

TL;DR

This paper investigates the stability of bound states of interacting microwave photons in a Google Quantum AI experiment, showing they persist in finite systems but become unstable as system size grows, indicating eventual decay.

Contribution

It provides a detailed spectral analysis and physical interpretation of bound state stability, revealing their finite-size persistence and thermodynamic instability.

Findings

Bound states are observable in the spectrum for large but finite systems.

Eigenstate localization suggests bound states become unstable in the thermodynamic limit.

Perturbative estimates align with the predicted decay of bound states at large sizes.

Abstract

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multi-magnon bound states in the celebrated XXZ spin chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan et al., Nature 612, 240 (2022)] realizing the Floquet model demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic non-integrable systems. We here study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes.