Collective quantum coherent oscillations in a globally coupled array of superconducting qubits

Pavel A. Volkov; M. V. Fistul

doi:10.1103/PhysRevB.89.054507

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Collective quantum coherent oscillations in a globally coupled array of superconducting qubits

Pavel A. Volkov, M. V. Fistul

DOI 10.1103/PhysRevB.89.054507 · Physical Review B

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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 Δi and a spread of Δi is taken into account. Noninteracting qubits display coherent quantum beatings with N different frequencies, i.e., ωi=Δi/ℏ. 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 Ci(t) to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ω1=Δ¯/ℏ and ω2=ω̃R, where ω̃R is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ω1≃ω2. These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient D(ω) of electromagnetic field propagating in a transmission line coupled to the system.