Engineering and control of the entanglement for four Magnon modes inside two microwave cavities

We present a model for investigating the entanglement features of four magnon modes in four yttrium-iron-garnet spheres dispersed in two microwave cavities (each cavity containing two spheres), which are driven by a squeezed field under actual experimental conditions. Each two-magnon mode inside each cavity is coupled via a beam splitter. We solve the covariance matrix associated with the four magnons, taking into account the relevant physical parameters. To quantify the degree of entanglement, we use the logarithmic negativity measure. Our study focuses on two parts. First, we study the entanglement properties between magnon modes by modifying the system parameters, and comparing the results with those obtained when we use a single magnon in each cavity, i.e. when one of the two magnons is not coupled to the cavity. In the second part, we give a new method for enhancing and controlling entanglement between magnon modes. We analyze the case where one of the two magnons is not coupled to the cavity, which can result a significant entanglement. Indeed, this goal is met in our situation by including an effective magnon–magnon coupling into both cavities. However, at high temperatures, the entanglement is almost completely broken. It can withstand temperatures of up to hundreds of millikelvin when using an experimentally accessible two-mode squeezed source.