DOUBLE-RESONANCE RESPONSE OF A SUPERCONDUCTING QUANTUM METAMATERIAL: MANIFESTATION OF NONCLASSICAL STATES OF PHOTONS

Physical Review B: Condensed Matter and Materials Physics. 2016. Vol. 94. No. 17. P. 174–510.

Iontsev M.A., Mukhin S. I., Fistul M. V.

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. 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.

Keywords: photons, QUANTUM METAMATERIAL, superconducting quantum metamaterials (SQMs), DOUBLE-RESONANCE RESPONSE