S. I. Mukhin

Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons

  1. M. A. Iontsev,
  2. S. I. Mukhin,
  3. and M. V. Fistul
We report a theoretical study of ac response of superconducting quantum metamaterials (SQMs), i.e. an array of qubits (two-levels system) embedded in the low-dissipative resonator.
By making use of a particular example of 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) states 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 \emph{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.
arxiv pdf

Generation of non-classical photon states in superconducting quantum metamaterials

  1. S. I. Mukhin,
  2. and M. V. Fistul
We report a theoretical study of diverse non-classical photon states that can be realized in superconducting quantum metamaterials. As a particular example of superconducting quantum
metamaterials an array of SQUIDs incorporated in a low-dissipative transmission line (resonant cavity) will be studied. This system will be modeled as a set of two-levels systems (qubits) strongly interacting with resonant cavity photons. We predict and analyze {a second(first)-order phase transition} between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) states of photons. In equilibrium state the partition function $Z$ of the electromagnetic field (EF) in the cavity is determined by the effective action $S_{eff}{P(tau)}$ that, in turn, depends on imaginary-time dependent momentum of photon field $P(tau)$. We show that the order parameter of this phase transition is the $P_{0}(tau)$ minimizing the effective action of a whole system. In the incoherent state the order parameter $P_{0}(tau)=0$ but at low temperatures we obtain various coherent states characterized by non-zero values of $P_{0}(tau)$. This phase transition in many aspects resembles the Peierls metal-insulator and the metal-superconductor phase transitions. The critical temperature of such phase transition $T^star$ is determined by the energy splitting of two-level systems $Delta$, a number of SQUIDs in the array $N$, and the strength of the interaction $eta$ between SQUIDs and photons in cavity.
arxiv pdf