Radiofrequncy Photon Wavefunction

[Frank Peters]

Radio waves are usually not viewed as streams of photons but according to quantum mechanics that is exactly what they are. But what does the wavefunction of an RF photon look like?

If we consider a dipole radiator, say of 10 Mhz, that emits a single photon, my guess is that the wavefunction of this photon would be identical to the classical dipole antenna pattern. The probablility of finding this photon in space would be described by this dipole pattern. However, once the photon was detected the wavefunction would collapse and the (very small) total energy would be located at that point.

Is this a correct assumption?

Also, if we a consider a directed antenna, such as a yagi, which is only a dipole with passive reflectors and
directors, that emits a single photon, would the wavefunction be "directed" as well? I would guess that it would not be "directed" because a yagi functions by interference and a single photon would not generate interference. But it is a very weak guess because the double-slit experiment shows that a single photon does interfere with itself.

Would there be a "directed" wavefunction with a yagi?

 

[Cryo]

Microwave cavity quantum electrodynamics is done using superconducting qubits. Here is a review (many others are available).

As far as I know, there is no real difference between optical and microwave non-classical states of light (apart from lower energies of course). More to the point of your question. What you do usually, is define the state of your electromagnetic field and then work with operators, such as operators of electric field, to extract experimentally observable quantities, e.g. power. A general rule of thumb, to the best of my knowledge, is that most of the things that work for classical electromagnetism, will also work for nonclassical light, but with much harder formalism. Where you do start seeing differences is in the second and higher-order coherence properties of light.

 

[Cryo]

The probablility of finding this photon in space would be described by this dipole pattern.

You would have state of your electromagnetic field $|\psi \rangle$ and the operators of your electric ($\hat{\vec{E}}$) and magnetic ($\hat{\vec{H}}$) fields, and the expectation value of this $\langle\psi |\hat{\vec{r}}.\left(\hat{\vec{E}}(\vec{r}, t)\times\hat{\vec{H}}(\vec{r}, t) \right)|\psi\rangle$ would follow the dipole pattern.

Is this a correct assumption?

This can all be calculated. No need to assume here.

 

[vanhees71]

Also let me just add that radiowaves are not "streams of photons" but rather coherent states of the quantized electromagnetic field.