No abstract

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.

Studies of perceptual learning have revealed a great deal of plasticity in adult humans. In this study, we systematically investigated the effects and mechanisms of several forms (trial-by-trial, block, and session rewards) and levels (no, low, high, subliminal) of monetary reward on the rate, magnitude, and generalizability of perceptual learning. We found that high monetary reward can greatly promote the rate and boost the magnitude of learning and enhance performance in untrained spatial frequencies and eye without changing interocular, interlocation, and interdirection transfer indices. High reward per se made unique contributions to the enhanced learning through improved internal noise reduction. Furthermore, the effects of high reward on perceptual learning occurred in a range of perceptual tasks. The results may have major implications for the understanding of the nature of the learning rule in perceptual learning and for the use of reward to enhance perceptual learning in practical applications.