Collective bosonic effects in an array of transmon devices

TL;DR

This paper investigates collective effects in arrays of transmon devices modeled as bosonic oscillators, revealing unique superradiance and dark state phenomena that differ from two-level systems, with implications for waveguide QED experiments.

Contribution

It demonstrates the importance of modeling transmons as bosonic multilevel systems to accurately capture collective effects in arrays, highlighting differences from two-level approximations.

Findings

Bosonic decay rate of superradiant states increases linearly with filling factor.

Dark states form at each filling factor in bosonic systems.

Transmon arrays exhibit distinct collective behaviors compared to two-level systems.

Abstract

Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in M. Zanner et al., arXiv.2106.05623 (2021), and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.