Entangled dark state mediated by a dielectric cavity within epsilon-near-zero materials.

Two emitters can be entangled by manipulating them through optical fields within a photonic cavity. However, maintaining entanglement for a long time is challenging due to the decoherence of the entangled qubits, primarily caused by cavity loss and atomic decay. Here, we found the entangled dark state between two emitters mediated by a dielectric cavity within epsilon-near-zero (ENZ) materials, ensuring entanglement maintenance over an extended period. To obtain the entangled dark state, we derived an effective model with degenerate mode modulation. In the dielectric cavities within ENZ materials, the decay rate of emitters can be regarded as 0, which is the key to achieving the entangled dark state. Meanwhile, the dark state immune to cavity loss exists when two emitters are in symmetric positions in the dielectric cavity. Additionally, by adjusting the emitters to specific asymmetric positions, it is possible to achieve transient entanglement with higher concurrence. By overcoming the decoherence of the entangled qubits, this study demonstrates stable, long-term entanglement with ENZ materials, holding significant importance for applications such as nanodevice design for quantum communication and quantum information processing.