Traveling-wave electro-optics for microwave-to-optical quantum transduction

High-efficiency microwave-to-optical quantum transduction is crucial for quantum networks and distributed quantum computing. Cavity-based electro-optic transducers have been widely explored due to their cavity-enhanced conversion efficiency, albeit at the compromise of limited transduction bandwidth and strict frequency alignment requirements between microwave and optical modes. A recent advancement in meter-long superconducting electro-optic modulators (SEOM) has demonstrated conversion efficiency approaching that of the cavity-based transducers on a traveling-wave structure while maintaining a broad bandwidth of tens of gigahertz. This paper provides a further theoretical investigation into the dynamics of the microwave-to-optical conversion process in a traveling-wave geometry. Based on this analysis, we propose a traveling-wave electro-optic transducer design featuring near-unity conversion efficiency and tunable conversion frequency.

Figure 1

(a) and (b) Schematic illustration of cavity electro-optics and traveling-wave electro-optics. (c) Material stack and the optical waveguide-electrode design of the traveling-wave electro-optics. (d) (i) Intraband electro-optic conversion dispersion. There is only one optical mode branch. Optical pump is set at point p and scattered into multiple sidebands. (d) (ii) Interband electro-optic conversion dispersion. There are two optical mode branches with mode crossing. The pump is set at $k_p$ of mode branch a. The phase-matched microwave with wave vector $k_m$ is converted into optical mode branch b.

Figure 2

(a) Cross section of optical waveguide and microwave transmission line. The x-cut lithium niobate film is on silicon dioxide on silicon. The mode profile of TE and TM mode are shown on the right side. (b) Optical mode dispersion of the TE and TM modes. In this simulation, the lithium niobate film thickness is 615 nm, $h=315\mathrm{nm}, w=2\mu \mathrm{m}$, and $m=1.5\mu \mathrm{m}$. (c) Microwave impedance and velocity. In this simulation, the signal electrode width $s=0.5\mu \mathrm{m}, \mathrm{gap}=6\mu \mathrm{m}$, and the NbN film thickness $t$ is varied to tune the microwave velocity and impedance. We use 50-pH/square kinetic inductance for the 10-nm-thick NbN film. The normalized microwave speed is normalized by the speed of light in vacuum.

Figure 3

Conversion efficiency with different microwave velocity and impedance. With a high impedance of 2500 $\mathrm{\Omega }$, the highest conversion efficiency of about 80% is achieved with only 0.6 meter-long modulation length.