Generation of non-classical photon states in superconducting quantum metamaterials

Abstract

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.

7 pages, 2 figures, special focus issue of the Superconductor Science and Technology

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• Wide-Band Tuneability, Nonlinear Transmission, and Dynamic Multistability in SQUID Metamaterials
• From Josephson junction metamaterials to tunable pseudo-cavities
• First order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction
• Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons
• Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top
• Anomalous Loss Reduction Below Two-Level System Saturation in Aluminum Superconducting Resonators
• Qubit-Photon Bound States in Superconducting Metamaterials