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Rare-earth ions are characterised by transitions with very narrow linewidths even in solid state crystals. Exceedingly long coherence times have been shown on both spin and optical transitions of rare-earth-ion doped crystals. A key factor, and generally the limitation, for such coherence times, is the effects of electronic and nuclear spins in the host crystal. Despite the attractive prospect, a low-strain, spin-free host crystal for rare-earth-ion dopants has not yet been demonstrated. The dopants experience the lowest strain when they substitute for another rare earth (including yttrium). However every stable isotope of the trivalent rare earth ions has either an electron spin, an nuclear spin, or both. The long optical coherence times reported here with erbium dopants in antiferromagnetically ordered gadolinium vanandate suggest an alternative method to achieve the quiet magnetic environment needed for long coherence times: use a magnetic host fully concentrated in electron spins and operate at temperatures low enough for these spins to be ordered. We also observe avoided crossings in the optical spectra, caused by strong coupling between the erbium ions and gadolinium magnons in the host crystal. This suggests the exciting prospect of microwave to optical quantum transduction using the rare-earth ions in these materials mediated by magnons of the host spins.

We report microwave to optical upconversion in isotopically purified erbium-doped yttrium orthosilicate in a Fabry-P\'erot resonator at millikelvin temperatures. This follows on from investigations made at higher temperatures and with natural isotopic ratios for the erbium dopants. In these previous investigations the highest efficiency was seen only for moderately strong microwave powers. The removal of the unwanted erbium-167 which has hyperfine structure and provides unwanted background optical absorption, and the lower temperatures has removed this problem. We now see efficiencies still increasing as the microwave power is decreased when we reach the smallest input powers for which we could measure an output. Efficiencies of $2\times10^{-6}$ were observed and we discuss potential improvements, including better optical cavity frequency stability and better thermalisation of the erbium spins., Comment: 8 Pages, 7 Figures

We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display intrinsic quality factors better than $10^8$ (linewidths less than 2 MHz), and coupling strengths to collective erbium transitions of up to 2$\pi\times$1.2 GHz - enough to reach the ensemble strong coupling regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition which is tuned by an external magnetic field. We show a modified optically detected magnetic resonance measurement that measures population transfer by a change in coupling strength rather than absorption coefficient. This modification was enabled by the strong coupling to our modes, and allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth. We contrast this measurement with electron paramagnetic resonance to experimentally show that our optical modes are confined in a region of large microwave magnetic field and we explore how such a geometry could be used for coherent microwave-optical transduction., Comment: 8 pages, 6 figures

Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region immediately above the semi-classical pumping threshold, where our numerical results differ significantly from semi-classical predictions. Regimes of measurable squeezing and bipartite entanglement are identified from steady-state spectra of the cavity output fields. We validate the truncated positive-P description against Monte Carlo wave function simulations, finding good agreement for low mode populations., Comment: 9 pages, 9 figures