Microwave-to-Optical Quantum Transduction (2D)

Coupling Rates

Electromechanical cooperativity C_e 4.0

Optomechanical cooperativity C_o 4.0

Microwave port efficiency η_e 90%

Optical port efficiency η_o 85%

Live Readouts

η_total0.0%

Impedance match M

0.0%

Converted photons/s

0.0

Photons lost to mechanical bath (rate)

0.0

How it works

A quantum "ecosystem" only works if platforms speaking different languages can exchange quanta. Superconducting qubits operate at ~5 GHz microwave frequencies; long-distance fiber networks carry ~193 THz telecom photons. An electro-optomechanical transducer bridges them through a single shared phonon mode of a nanomechanical or piezo-optomechanical resonator, coherently swapping one microwave photon for one optical photon.

C_e = 4g_e² / (κ_e κ_m)   electromechanical cooperativity
C_o = 4g_o² / (κ_o κ_m)   optomechanical cooperativity

η_total = η_e · η_o · 4C_e·C_o / (1 + C_e + C_o)²

C_e, C_o — how strongly each port (microwave, optical) is coupled to the shared mechanical mode relative to its own linewidth and the phonon linewidth κ_m.
Impedance match M = 4C_e·C_o/(1+C_e+C_o)² — this term alone caps at 100% exactly when C_e = C_o: an unbalanced transducer wastes energy driving the mechanical mode without extracting it on the other side. That's why the Impedance-Match button and the heatmap's diagonal ridge are the single biggest efficiency lever.
η_e, η_o — the fraction of each port's decay that actually couples to a usable external line (antenna/waveguide) rather than internal material loss.
Particles that fail to convert are shown scattering off the drum — genuine phonon-bath loss, not just a visual placeholder.
The lower panel is a live heatmap of M(C_e, C_o) over the whole slider range — drag anywhere on it to set both cooperativities at once and watch the schematic above respond instantly.

Real-world relevance: this is the working principle behind piezo-optomechanical and electro-opto-mechanical transducers (e.g. GaAs/AlN membrane and bulk-acoustic-wave devices) being built to link superconducting quantum processors into a fiber-based quantum internet — the literal infrastructure layer of a "quantum ecosystem".

Microwave photon (5 GHz) Phonon (mechanical mode) Optical photon (193 THz) Lost to phonon bath

drag to set C_e / C_o