Optomagnonic generation of entangled travelling fields with different polarizations

Abstract

The optomagnonic coupling between magnons and optical photons is an essential component for building remote quantum networks based on magnonics. Here we show that such a coupling, manifested as the magnon-induced Brillouin light scattering, can be exploited to entangle two propagating optical fields. The protocol employs two pairs of the whispering gallery modes coupled to the same magnon mode in a YIG sphere. In each pair a strong pump field is applied to activate either Stokes or anti-Stokes scattering. Due to the magnon mode involving in the two scattering processes and as a mediation, Stokes and anti-Stokes photons of different polarizations get entangled. The entanglement can be extracted by filtering the travelling output fields centered at the Stokes and anti-Stokes sidebands. Optimal conditions are identified under which strong output entanglement can be achieved.

Figures (3)

• Figure 1: (a) Schematic of the protocol for generating entangled travelling fields. A YIG sphere, placed in a uniform bias magnetic field, supports a magnetostatic magnon mode ($m$) and two pairs of WGMs ($a_{1,2}$ and $b_{1,2}$). In each pair, the optomagnonic interaction is manifested as the magnon-induced BLS. Two strong laser fields are used to drive the TM- and TE-polarized WGMs $b_{2}$ and $a_{1}$, via nanofibers coupled to the resonator, to simultaneously activate the Stokes and anti-Stokes scatterings. The generated Stokes and anti-Stokes photons are then coupled to and propagating in the fibers, and subsequently extracted from pump photons by two filters. (b) Frequencies relation of the magnon mode, two pairs of WGMs, and two pump fields. The TM-polarized WGM $b_{2}$ is resonantly pumped to activate the Stokes scattering, creating entangled magnons and TE-polarized Stokes photons entering the WGM $b_{1}$. Similarly, the TE-polarized WGM $a_{1}$ is resonantly driven to activate the anti-Stokes scattering, producing TM-polarized anti-Stokes photons (via annihilating magnons) entering the WGM $a_{2}$. The two vertical lines with arrows denote two pump fields.
• Figure 2: (a) Stationary entanglement $E_{N}$ of two output modes versus effective optomagnonic coupling rates $G_{a}$ and $G_{b}$. (b) Optimal coupling $G_{b}$ for different magnon decay rates: $\kappa_{m}/2\pi=0.5,1,1.5,2$ MHz, for a fixed $G_{a}/2\pi=10$ MHz. The numbers around the stars denote the maximum entanglement $E_{N}$ achieved with the given values of $\kappa_{m}$ and $G_b$. The other parameters are provided in the text.
• Figure 3: Stationary output entanglement $E_{N}$ versus (a) filter time duration $\tau$; and (b) the bath temperature $T$ (logarithmic scale). In both plots, we take $G_{a}/2\pi=10$ MHz and $G_{b}/2\pi=6.5$ MHz, and in (b) the solid (dashed) line is for $\tau=10$$\mu$s (1 $\mu$s). The other parameters are the same as in Fig. \ref{['fig2']}(a).