Quantum phase transition and degeneracy of a circuit-QED vacuum
Résumé
We investigate theoretically the quantum vacuum properties of a transmission line resonator inductively coupled to a chain of $N$ superconducting qubits. We derive the quantum Hamiltonian for such circuit-QED system, showing that, due to the type and strength of the interaction, a quantum phase transition occurs in the limit of large $N$, with a twice degenerate quantum vacuum above a critical coupling. The phase diagram can be fully explored thanks to the controllable ultrastrong coupling of the qubits with the modes of the transmission line resonator. For finite values of $N$, an energy splitting occurs, which becomes exponentially small with increasing size and coupling.
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