Double-resonance response of a superconducting quantum metamaterial: Manifestation of nonclassical states of photons
M. A. Iontsev, Sergei I. Mukhin, M. V. Fistul · Physical review. B./Physical review. B · 2016
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, ${T}^{\ensuremath{\star}}$, is determined by the energy splitting of two-level systems $\ensuremath{\delta}$, number of qubits in the array $N$, and the strength of the interaction $\ensuremath{\eta}$ between qubits and photons in the cavity. We obtain that the photon states manifest themselves by resonant drops in the frequency-dependent transmission $D(\ensuremath{\omega})$ of electromagnetic waves propagating through a transmission line weakly coupled to the SQM. At high temperatures the $D(\ensuremath{\omega})$ 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.