Enhancement via the Kittel mode of a magnet of the microwave to optical quantum transduction in a rare-earth-doped crystal*

The highly localized 4$f$ electrons of rare-earth-doped materials provide a simple atom-like level structure with a spin-photon interface, telecom-wavelength optical transitions, potential for long spin and optical coherence times, and the ability to realize high-density doping. Initial quantum operations (transduction, quantum information storage, sensing) using commercial rare-earth doped materials have shown the promise of rare-earth quantum information science, however current coupling strengths, linewidths and coherence times remain far away from those required to achieve highly efficient, low noise and high bandwidth quantum operations. Proposals for quantum transduction using rare-earth ions rely on spin-flip transitions from microwaves that couple to inter-4$f$ transitions (such as the $J=15/2$ to $J=13/2$ optical transition at telecom wavelengths of the Er$^{3+}$ ion in a solid host).  The oscillator strengths of the microwave excitations are particularly weak leading to poor transduction efficiencies.

We describe an approach to dramatically enhance the microwave coupling without diminishing the optical oscillator strength for Er$^{3+}$ ions. The microwave excitation is coupled to the Kittel mode of a magnetic material in which the Er$^{3+}$ ions are embedded, such as yttrium iron garnet (YIG). We predict that the iron sublattices of the YIG host have a strong antiferromagnetic exchange coupling to the  Er$^{3+}$ ions that dramatically exceeds the dipolar coupling they would experience to the direct microwave excitation. We analyze this situation using a formalism similar to Ref. [PRL 113, 203601 (2014)] and estimate the conversion efficiency to be enhanced by several orders of magnitude.