Quantum dynamics of disordered arrays of interacting superconducting qubits: signatures of quantum collective states

TL;DR

This paper theoretically investigates how collective quantum states emerge in disordered arrays of superconducting qubits due to interactions, revealing signatures in their dynamic susceptibility and potential for quantum sensing.

Contribution

It demonstrates that weak interactions can overcome disorder to form collective states, observable via a large resonance in the dynamic susceptibility, and explores their detection through microwave transmission.

Findings

Weak interactions induce collective states despite disorder.

Collective states produce a large resonance in susceptibility.

Coupling to a transmission line enables experimental detection.

Abstract

We study theoretically the collective quantum dynamics occurring in various interacting superconducting qubits arrays (SQAs) in the presence of a spread of individual qubit frequencies. The interaction is provided by mutual inductive coupling between adjacent qubits (short-range Ising interaction) or inductive coupling to a low-dissipative resonator (long-range exchange interaction). In the absence of interaction the Fourier transform of temporal correlation function of the total polarization ($z$-projection of the total spin), i.e. the dynamic susceptibility $C(\omega)$, demonstrates a set of sharp small magnitude resonances corresponding to the transitions of individual superconducting qubits. We show that even a weak interaction between qubits can overcome the disorder with a simultaneous formation of the collective excited states. This collective behavior manifests itself by a single large resonance in $C(\omega)$. In the presence of a weak non-resonant microwave photon field in the low-dissipative resonator, the positions of dominant resonances depend on the number of photons, i.e. the collective ac Stark effect. Coupling of an SQA to the transmission line allows a straightforward experimental access of the collective states in microwave transmission experiments and, at the same time, to employ SQAs as sensitive single-photon detectors.