Magneto-Optic Modulator with Unit Quantum Efficiency

We propose a device for the reversible and quiet conversion of microwave photons to optical sideband photons that can reach 100% quantum efficiency. The device is based on an erbium-doped crystal placed in both an optical and microwave resonator. We show that efficient conversion can be achieved so long as the product of the optical and microwave cooperativity factors can be made large. We argue that achieving this regime is feasible with current technology and we discuss a possible implementation.

Figure 1

An outline of a device of the type we consider. An erbium-doped crystal acts as an ensemble of $\mathrm{\Lambda }$ systems and is coupled to a microwave resonator, an optical resonator, and a coherent driving field. To enable phase matching the coherent driving field will be applied using another mode of the optical resonator separated by one free spectral range.

Figure 2

Energy level diagram of an erbium atom showing driven transitions. The microwave resonator is coupled to a spin transition. The optical resonator and coherent driving field drive the atoms from these two spin levels to a common excited state.

Figure 3

Two optical cavities that are coupled by sharing a partially transmissive end mirror. If the reflectivity of this end face mirror is tuned appropriately then, on resonance, the three mirrors will have 100% transmission.

Figure 4

Diagrams showing proposed (a) microwave (to scale), (b) optical resonator (not to scale) geometry, and (c) microwave field distributions, on the left viewed from in front, on the right viewed from above. The 5-mm-diameter crystal sits in the middle of the loop-gap resonator. The optical resonator would be hemilithic, with the antireflection coated face of the crystal to improve the stability of the large mode diameter optical resonator.

Figure 5

Contour plot of $R$ versus the filling factor $F$ and the quality factor product $Q_a{Q}_b$. Complete photon conversion is achievable in the red region, where $R>1$. The horizontal dashed line shows the filling factor for the geometry shown in Fig. 4 and the vertical dashed line corresponds to quality factors of $Q_a=10^7$ and $Q_b=2000$. The intersection of these lines gives a realistically achievable $R$ value of 1.7 (solid black disk) and therefore our resonator design is theoretically capable of achieving complete photon conversion.