Quasi-Superradiant Soliton State of Matter in Quantum Metamaterials

Strong interaction of a system of quantum emitters (e.g., two-level atoms) with electromagnetic field induces specific correlations in the system accompanied by a drastic insrease of emitted radiation (superradiation or superfluorescence). Despite the fact that since its prediction this phenomenon was subject to a vigorous experimental and theoretical research, there remain open question, in particular, concerning the possibility of a first order phase transition to the superradiant state from the vacuum state. In systems of natural and charge-based artificial atome this transition is prohibited by "no-go" theorems. Here we demonstrate numerically a similar transition in a one-dimensional quantum metamaterial - a chain of artificial atoms (qubits) strongly interacting with classical electromagnetic fields in a transmission line. The system switches from vacuum state with zero classical electromagnetic fields and all qubits being in the ground state to the quasi-superradiant (QS) phase with one or several magnetic solitons and finite average occupation of qubit excited states along the transmission line. A quantum metamaterial in the QS phase circumvents the "no-go" restrictions by considerably decreasing its total energy relative to the vacuum state by exciting nonlinear electromagnetic solitons with many nonlinearly coupled electromagnetic modes in the presence of external magnetic field.