We propose to use quantum coherence as ultimate proof of quantum nature in the radiation that appears by means of the Dynamical Casimir Effect in experiments with superconducting microwave waveguides. We show that, unlike previously considered measurements such as entanglement and discord, quantum coherence does not require a threshold value of the external pump amplitude and is highly robust to thermal noise. *
The rainbow state denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, γ, and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for 0 ≤ γ ≤ 1, while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime the entanglement entropy satisfies a volume law, derived from CFT in curved spacetime, with an effective central charge that depends on the inhomogeneity parameter and γ. In all regimes we have found that the entanglement properties are invariant under the transformation γ ←→ 1 − γ, whose fixed point γ = 1 2 corresponds to the usual rainbow model. Finally, we study the robustness of non trivial topological phases in the presence of the defect.
It has been shown recently that inhomogenous spin chains can exhibit exotic phenomena such as the breaking of the area law of the entanglement entropy. An example is given by the rainbow model where the exchange coupling constants decrease from the center of the chain. Here we show that by folding the chain around its center, the long-range entanglement becomes short-range which can lead to topological phases protected by symmetries (SPT). The phases are trivial for bond-centered foldings, and non trivial for site-centered ones. In the latter case, the folded spin 1/2 chain with U (1) symmetry belongs to the Su-Schrieer-Heeger class, while the folded chain with SU (2) symmetry is in the Haldane phase. Finally, we extend these results to higher spin chains where we find a correspondence between the symmetry protection of gapped and gapless phases.
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