Double-resonance response of a superconducting quantum metamaterial: Manifestation of nonclassical states of photons

Abstract

We report a theoretical study of the ac response of superconducting quantum metamaterials (SQMs), i.e., an array of qubits (two-level systems) embedded in a low-dissipative resonator. By making use of a particular example of a SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) state of photons. This phase transition in many aspects resembles the paramagnetic-ferromagnetic phase transition. The critical temperature of the phase transition, T☆, is determined by the energy splitting of two-level systems δ, number of qubits in the array N, and the strength of the interaction η between qubits and photons in the cavity. We obtain that the photon states manifest themselves by resonant drops in the frequency-dependent transmission D(ω) of electromagnetic waves propagating through a transmission line weakly coupled to the SQM. At high temperatures the D(ω) displays a single resonant drop, and at low temperatures a peculiar double-resonance response has to be observed. The physical origin of such a resonant splitting is the quantum oscillations between two coherent states of photons of different polarizations.

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