We show that parity-time (PT ) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the PT -broken phase, magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of environment, in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybridized system. As a comparison, neither PT -symmetry broken nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open a novel window to utilize magnonphoton entanglement as a resource for quantum technologies.

Magnon-photon coupling has been experimentally realized inside a cavity and the emerging field known as cavity spintronics has attracted significant attention for its potential docking with quantum information science. However, one seldom knows whether this coupling implies an entanglement state among magnons and photons or not, which is crucial for its usage in quantum information.Here we study the entanglement properties among magnons and photons in an antiferromagnet-light system and find that the entanglement between magnon and photon is nearly zero while the magnonmagnon entanglement is very strong and it can be even further enhanced through the coupling with the cavity photons. The maximum enhancement occurs when the antiferromagnet reaches resonant with the light. The essential physics can be well understood within the picture of cavity induced cooling of magnon-magnon state near its joint vacuum with stronger entanglement. Our results are significant to extend the cavity spintronics to quantum manipulation and further provide an alternate to manipulate the deep strong correlations of continuous variable entanglement with a generic stable condition and easy tunability.Introduction.-Antiferromagnetic (AFM) spintronics emerges for its better stability and fast dynamics over its ferromagnetic counterpart [1,2]. Of particular interest are antiferromagnetic spin waves (magnons) that show much richer physics than ferromagnets, such as the spin pumping at the interface of an AFM/normal metal bilayer [3], magnon spin current enhancement through an AFM layer [4][5][6][7], long-distance magnon transport [8][9][10], and magnon-driven magnetic structure motion [11][12][13]. It has recently been theoretically proposed [14] and experimentally verified [15] that antiferromagnetic magnons can be strongly coupled to the light by placing an AFM element into a cavity, which serves a promising candidate to realize coherent information transfer between magnons and photons for its superb stability and tunability of magnons properties through external knobs. One promising application of the hybridized magnonphoton polariton is to connect it with the quantum information science [16,17], similar to the cavity electrodynamics that rose 20 years ago and has found its role in the implementation of quantum qubits and quantum computing circuits [18]. To push the development of cavity spintronics along this line, it is crucial to have a clear insight into the quantum correlations among magnons and photons, especially their entanglement properties, which are central resources for quantum computing and quantum technologies.

No abstract