Quantum synchronization in disordered superconducting metamaterials

TL;DR

This paper theoretically investigates how weak electromagnetic interactions can induce collective quantum synchronization in disordered superconducting metamaterials, overcoming disorder effects and leading to observable giant resonant features.

Contribution

It introduces a model showing how weak interactions cause synchronization in disordered SQMs, linking it to Anderson localization and aligning with recent experimental findings.

Findings

Weak electromagnetic interactions can synchronize qubits in disordered SQMs.

Synchronization results in giant resonant drops in transmission spectra.

The size of synchronized regions depends on interaction strength and disorder.

Abstract

I report a theoretical study of collective coherent quantum-mechanical oscillations in disordered superconducting quantum metamaterials (SQMs), i.e artificially fabricated arrays of interacting qubits (two-levels system). An unavoidable disorder in qubits parameters results in a substantial spread of qubits frequencies, and in the absence of electromagnetic interaction between qubits these individual quantum-mechanical oscillations of single qubits manifest themselves by a large number of small resonant drops in the frequency dependent transmission of electromagnetic waves propagating through disordered SQM, $D(\omega)$. We show that even a weak electromagnetic interaction between adjacent qubits can overcome the disorder and establish completely or partially \emph{synchronized} quantum-mechanical dynamic state in the disordered SQM. In such a state a large amount of qubits displays the collective quantum mechanical oscillations, and this collective behavior manifests itself by a few giant resonant drops in the $D(\omega)$ dependence. The size of a system $r_0$ showing the collective (synchronized) quantum-mechanical behavior is determined in the one-dimensional SQMs as $r_0 \simeq a [K/\delta \Delta]^2$, where $K$, $\delta \Delta$, $a$ are the energy of nearest-neighbor interaction, the spread of qubits energy splitting, and the distance between qubits, accordingly. We show that this phenomenon has an origin in the Anderson localization of spinon-type excitations arising in the SQM. Our analysis is also in a good accord with recent experiments on the electrodynamics of the disordered 1D SQMs.