Is a light pulse equivalent to a burst of photons

Question

Reading about photons you get all sorts of weird statements like "time is frozen for a photon", "the photon dies the instant it is born" and "the photon is everywhere and nowhere", etc. Probably these should be understood in the given context but for the layman it sounds like mumbo-jumbo.

In order to clear my understanding this leads me to ask for the umpteenth time about the wave/particle duality as follows : Assume we create a single picosecond light pulse, which is emitted in a certain direction towards the moon, propagating at speed $c$. The pulse length in that direction should then be about 300 micrometers. A few seconds later a detector on the moon should see the pulse and show a picosecond spike on a cathode ray screen.

Now my question is threefold:

1. Is the light pulse equivalent to a picosecond burst of photons?

2. If so, are the photons (or their probability density) concentrated within the pulse length?

3. Does the detector on the moon "see" the exact "same" photons as were created in the original bunch or is it impossible to thus individualize the photons?

In summary: I don't like photons but am perfectly happy with Maxwell. So why have them if they weren't necessary in order to fill some gap in the standard model?

Answer 1

The thing about photons is that their exact number within something that we would classically call a pulse or continuous wave is uncertain. For the fundamentals of characterizing photons as a bunch of separate particles you should get yourself familiar with the quantum harmonic oscillator and its Fock-state eigenbasis. As a short summary, the Hamiltonian of the harmonic oscillator for a single frequency $\omega$ is $$ \hat H = \hbar \omega \left(\hat n + \frac12\right) $$ where $\hat n$ is occupation number operator with the Fock-state $| n \rangle$ as eigenstate $(\hat n |n\rangle = n |n\rangle)$, which is labeled by the number of bosonic particles $n$ within the harmonic oscillator. Herein lies the problem of interpreting any form of classical light as just a bunch of photons. The only states with exactly n photons within them are the Fock-states, for any other form of light, which is not confined witihn an ideal harmonic oscillator, you usually get a superposition of Fock-states $$ |\gamma \rangle = \sum_n \gamma_n |n \rangle $$ which means that the number of photons within your pulse is somewhat uncertain. Therefore equivalent pulses of light may vary in the exact number of photons which are detected. Luckily this uncertainty goes down with increasing photon counts (see Poisson distribution), which is why high precision interferometers like LIGO use high powered lasers. This also fits with the classical limit of electromagnetic waves as light with a lot of photons, to the point where you can think of the discreteness as being 'smeared out' to behave like some continuous electromagnetic field.

To specifically answer your questions:

1. The light pulse is rather equivalent to a quantum state, that yields a statistical distribution of photons within that time frame
2. The photons are spatially concentrated within that distribution, while their exact number is not determined
3. It is impossible to 'individualize' the photons in the sense that quantum particles are indistinguishable (you can swap individual bosonic particles mathematically without affecting the state). Furthermore the number of photons usually changes during the time evolution of the state (e.g. see quantum beats in cavity quantum elector dynamics).