A highly readable book I picked up a few years ago is Principles of Quantum Electronics by Dietrich Marcuse. One of the fun parts about this book is that it beigins discussion of quantizing electronmagnetism by starting with the quantization of simple LC circuits. Of course, Marcuse, writes
It is true that the quantum theory of the LC circuit must be regarded as more correct than the classical theory, but the difference between the results of classical and quantum theory are unobservable by experiments with LC circuits.
This was written in 1970. What is interesting, of course, in our modern day of cool quantum experiments, is whether this is true today. In many ways, it does remain true, but there is a notable exception and that is in superconducing circuits. Very interesting, and readable works on this (with a focus on decoherence) are cond-mat/0308025 and cond-math/0408588 (works by Guido Burkard, Roger Koch, and David DiVincenzo.) So if a quantized theory of quantum circuits can be used to describe some superconducting quantum systems can we also do things like couple these to electromagnetic fields which are themselves quantized?
Well the answer is yes! And a group at Yale has been doing some excellent experiments in this direction. Here is a Nature paper just published about coupling superconducting circuits to microwaves transmission lines (Nature 445, 515-518, “Resolving photon number states in a superconducting circuit”, D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf) Previos work had shown how to get this coupling into the “strong coupling regime” where a single photon can be absorbed and emitted multiple times, whereas in this work they show how to get into a “strongly disapative regime” where the a single photon can have a large effect on the superconducting circuit without ever being absorbed. This allows the authors to perform experiments where they measure the photon number of the microwave field. Pretty cool! They call experiments like this circuit quantum electrodynamics. A new field is born.
So what consequences are there for quantum computerists? Well certainly this gives a possible method for a bus in some of the superconducting quantum systems. It should also allow for the preparation on nonclassical states of the microwave field, something which might have potential impact on quantum communication like protocols for quantum computing. But this is all in the future. Right now it’s just cool to sit back and read about the experiment!