Thermodynamic entanglement of magnonic condensates

Abstract

Over the last decade, significant progresses have been achieved to create Bose-Einstein condensates (BEC) of magnetic excitations, i.e., magnons, at the room temperature, which is a novel quantum many-body system with a strong spin-spin correlation, and contains potential applications in magnonic spintronics. For quantum information science, the magnonic condensates can become an attractive source of quantum entanglement, which plays a central role in most of the quantum information processing tasks. Here we theoretically study the entanglement properties of a magnon gas above and below the condensation temperature. We show that the thermodynamic entanglement of the magnons is a manifestation of the off-diagonal long-range order; the entanglement of the condensate does not vanish, even if the spins are separated by an infinitely large distance, which is fundamentally distinct from the normal magnetic ordering below the Curie temperature. In addition, the phase transition point occurs when the derivative of the entanglement changes abruptly. Furthermore, the spin-spin entanglement can be experimentally accessed with the current technology. These results provide a theoretical foundation for a future experimental investigation of the magnon BEC in terms of quantum entanglement.