# Quantum impedance conversion

Communication between electronic logic devices over wires has a basic physical problem: while the devices themselves can have very low capacitances and operate with very high impedances (so, requiring very little current for a given voltage), wires always have high capacitances per unit length (e.g., ~ 2 pF/cm) and/or have low impedances (e.g., 50 ohms). [1] [2]. These capacitances and impedances are quite intrinsic to wires, and there is little we can do to change them; impedances and capacitances per unit length only depend ~ logarithmically on the ratio of conductor sizes to conductor separations once the wires are separated by distances of the order of their dimensions. This means that the energy practically to send signals over wires is much larger than the energy of logic operations. (Indeed, even at the size scales of individual gates, the capacitance of the wire to communicate to the next gate over is comparable to the transistor capacitance.) Hence, for example, operating with logic voltages of the order of a fraction of a volt, leads to energies of the scale of picojoules for communicating even over the centimeter distances between chips. In contrast, the logic energies themselves are in the scale of femtojoules or even smaller [2].

Electrical lines have high capacitance per unit length and/or low impedance, but logic devices have small capacitances and high impedances, creating energy and drive problems for connecting with electrical lines, especially over long distances

Optics, however, has a solution to this problem, and it is one that comes from the quantum mechanical nature of light and photons. Suppose we shine a weak light beam – for example, with a power of 1 nanowatt – into a photodiode. The classical voltage in a 1 nanowatt light beam is about 600 microvolts (this is a simple consequence of the impedance of free space being ~ 377 ohms). But, if we connect the photodiode to a large load resistance, such as 1 gigaohm, we will be able to generate a good fraction of a volt in the photodetector.

A 1 nW light beam would have only ~ 600 microvolts of classical voltage, but, with 1 eV photons, it could generate ~ 1 V signal in a 1 gigaohm load on a photodetector because of “quantum impedance conversion”

The reason for this is that optical beams are generated and detected quantum mechanically – that is, with photons. A simple photodetector works by counting photons, e.g., with one electron of photocurrent for each absorbed photon. Essentially what we are seeing is a consequence of the same physics that gives rise to the photoelectric effect. We can call this effective ability to convert between high impedance devices and the low impedance communications medium “quantum impedance conversion” [1]. This is a fundamental advantage of optics for interconnection that can allow us to reduce the energy. Also in optics the energy required is essentially independent of distance, certainly over distances inside machines, and also possibly much longer distances.

So, once we get to the point that the optoelectronic devices take less energy to run than the energy to charge up a corresponding length of electrical wire, optics takes less energy. Practically, this leads to a “break-even” distance for optical interconnects. As technology gets better, giving lower energy optoelectronic devices and lower capacitance integration of optoelectronics with electronics, this “break-even” distance can even be smaller than the chip size.

[1] D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Optics Lett. **14**, 146‑148 (1989).

[2] D. A. B. Miller, “Attojoule Optoelectronics for Low-Energy Information Processing and Communications: a Tutorial Review,” IEEE/OSA J. Lightwave Technology **35** (3), 343-393 (2017) https://doi.org/10.1109/JLT.2017.2647779; http://ieeexplore.ieee.org/document/7805240/