Collective quantum coherent oscillations in a globally coupled array of qubits

Abstract

We report a theoretical study of coherent collective quantum dynamic effects in an array of N qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences ${\Delta }_i$ and we take into account a spread of parameters ${\Delta }_i$. Non-interacting qubits display coherent quantum beatings with N different frequencies, i.e. ${\omega }_i={\Delta }_i/\hslash$ . Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits $C_i(t)$ to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ${\omega }_1=\bar{\Delta }/\hslash$ and ${\omega }_2={\tilde{\omega }}_R$, where ${\tilde{\omega }}_R$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ${\omega }_1\simeq {\omega }_2$.

5 pages, 3 figures

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• Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons
• Spectral features of polaronic excitations in a superconducting analog simulator
• Synchronization of qubit ensemble under optimized $\pi$-pulse driving
• Anomalous Loss Reduction Below Two-Level System Saturation in Aluminum Superconducting Resonators
• Spectral Magnetization Ratchets with Discrete Time Quantum Walks
• Electromagnetic waves propagation through an array of superconducting qubits: manifestations of non-equilibrium steady states of qubits
• Role of qubit-cavity entanglement for switching dynamics of quantum interfaces in superconductor metamaterials
• Quantum synchronization in disordered superconducting metamaterials