Quantum synchronization in disordered superconducting metamaterials

I report a theoretical study of collective coherent quantum-mechanical oscillations in disordered superconducting quantum metamaterials (SQMs), i.e. artificial arrays of interacting qubits (twolevels 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 dips in the frequency dependent transmission of electromagnetic waves, |S21(ω)|. We show that even a weak electromagnetic interaction between adjacent qubits can overcome the disorder and establish completely or partially 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 dips in the |S21(ω)| dependence. The size of a system r0 showing the collective (synchronized) quantum-mechanical behavior is determined in the one-dimensional SQMs as r0 ≃ a [K/δΔ]2, where K, δΔ, a are the effective energy of nearest-neighbor interaction, the spread of qubits energy splitting, and the distance between qubits, accordingly. We show that this phenomenon is mapped to the Anderson localization of spinon-type excitations arising in the SQM.