Optomagnonic generation of entangled travelling fields with different polarizations

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.

💡 Research Summary

The manuscript presents a novel scheme for generating continuous‑variable entanglement between two travelling optical fields of orthogonal polarizations by exploiting the optomagnonic interaction in a yttrium‑iron‑garnet (YIG) sphere. The authors consider a hybrid system that supports both optical whisper‑gallery modes (WGMs) and a magnetostatic magnon mode. Two pairs of WGMs are used, each pair consisting of a transverse‑magnetic (TM) and a transverse‑electric (TE) mode whose frequency separation is tuned to match the magnon frequency ωₘ, thereby satisfying a triple‑resonance condition that maximizes Brillouin light scattering (BLS).

A strong laser pump drives the TM mode of the second pair (b₂) and the TE mode of the first pair (a₁). Pumping b₂ activates Stokes scattering, creating TE‑polarized Stokes photons in mode b₁ while simultaneously generating a magnon. Pumping a₁ activates anti‑Stokes scattering, annihilating a magnon and producing TM‑polarized anti‑Stokes photons in mode a₂. Because the same magnon mode participates in both processes, the Stokes and anti‑Stokes photons become correlated through the magnon as a quantum bus.

Treating the strongly driven modes a₁ and b₂ as classical amplitudes (α₁, β₂) linearizes the three‑wave interaction and yields an effective Hamiltonian

H_eff/ħ = G_a a₂ m† + G_a a₂† m + G_b b₁† m† + G_b b₁ m,

where G_a = g_a α₁ and G_b = g_b β₂ are pump‑enhanced optomagnonic coupling rates. The first term describes a beam‑splitter‑type state‑swap interaction between the magnon (m) and the anti‑Stokes mode a₂, while the second term is a two‑mode squeezing (TMS) interaction between the magnon and the Stokes mode b₁.

Including dissipation (κₘ, κ_{a₂}, κ_{b₁}) and thermal noise (mean occupation N_j) leads to a set of linear quantum Langevin equations. The output fields a_out₂(t) and b_out₁(t) are obtained via standard input‑output relations. Since the entanglement resides in the sideband photons, the authors introduce temporal filters with central frequencies Ω₁ = ω_{b₁} (Stokes) and Ω₂ = ω_{a₂} (anti‑Stokes) and duration τ. The filtered output operators A_out and B_out are defined by convolution with the filter functions, allowing the construction of a 4×4 covariance matrix V₄ for the two output modes.

Entanglement is quantified by the logarithmic negativity E_N = max