Enhancing macroscopic multimode entanglement through many-body interactions in cavity magnomechanics

Coherent control of many-body interactions allows the possibility of generating complex quantum states for future quantum technology. Specifically, the quantum states of the center-of-mass motion of a trapped macroscopic particle, being highly isolated from the environment, in hybrid systems is a potential platform for testing macroscopic quantum mechanics. We present a many-body interaction platform to enhance multimode Gaussian entanglement where the center-of-mass motion is coupled to a magnon through a microwave field. The strong and ultrastrong cavity-magnon couplings allow the generation of simultaneous entanglement in all bipartitions, without any pairwise entanglement, through numerical optimization of parameters, akin to quantum phase transitions in spin systems. Moreover, the ultrastrong coupling facilitates the generation of such multimode entanglement for a low-frequency oscillator in the unresolved sideband. This scheme provides a potential platform to explore the quantum effects in a large massive oscillator and paves the way for creating complex states for quantum simulation, sensing, exploring exotic quantum phases, and quantum computing.