Generation of non-classical photon states in superconducting quantum metamaterials

TL;DR

This paper presents a theoretical analysis of how superconducting quantum metamaterials, specifically SQUID arrays in a resonant cavity, can exhibit phase transitions leading to non-classical photon states, with potential applications in quantum technologies.

Contribution

The study introduces a model predicting a phase transition in superconducting metamaterials that results in non-classical photon states, expanding understanding of quantum phase behavior in these systems.

Findings

Prediction of a second-order phase transition between incoherent and coherent photon states.

Identification of the order parameter as the photon field momentum minimizing the effective action.

Dependence of critical temperature on system parameters like energy splitting, number of SQUIDs, and interaction strength.

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.