# In quantum optics if you measure the energy of a thermal state does it collapse to a Fock state (Photon number state)?

As I understand it a thermal state is a state of light such that the light is in a superposition of many Fock states (Photon number states) with the probability of the light being found in a particular Fock state (i.e. having a certain photon number) following a Boltzmann distribution.

So surely if you had light in a thermal state in an experiment and measured it, it would collapse into a single Fock state, is this correct?

I understand creating Fock states experimentally is of some interest at the moment and it seems like it would be trivial if this was the case.

## 1 Answer

Perhaps the question is, how do you measure an arbitrary number of photons without destroying the system? It's certainly the case that somehow measuring the number of photons in the cavity would collapse the state into a Fock state, but it's not obvious how to do that without actively destroying the system in some way; there has been some work done in non-destructively measuring single photons within a cavity (c.f. Reiserer, et al. 2013) but little with directly measuring arbitrary ensembles non-destructively, which appears impossible with the method introduced in the paper.

It should be noted that the current approaches to creating Fock states involve the strong coupling of an atom or quantum dot with a cavity and passing some squeezed state $a|\alpha\rangle = \alpha |\alpha\rangle$ into the system; here, the nonlinearities introduced by the atom-cavity interactions reject states that aren't particular Fock states. This is often taught in a first course in cavity QED as an application of strong interactions between a two-level system coupled with a cavity, but there has been some recent work in applications of these systems (c.f. Vuckovic, et al 2007.) to other problems.

Overall, while measuring the number of photons in a system without destroying it would certainly collapse it into a particular Fock state, there are easier methods---not to mention that you'd probably be awarded a Nobel prize for being able to non-destructively do so.

• @Guillermo_Angeris Ahh, OK, that makes sense, thanks. You can't produce a Fock state from a thermal state by measuring it, because by measuring it your destroying it, e.g. counting the photons by absorption means you know what state it collapsed to, but you absorbed all the photons so they're not there anymore in that state. What about decoherence due to interaction with the environment? Why does this not cause the system to collapse into a certain Fock state? (albeit an unknown Fock state) – SomeRandomPhysicist May 6 '16 at 12:35
• @SomeRandomPhysicist That is correct, which is why production of Fock states has been such an active research topic in several fields (e.g. for quantum computing). To answer the latter two questions: interactions with the environment are often just losses which still do not yield complete information about the system (e.g. through radiative losses) and we cannot know the exact Fock state unless we've measured all photons---I should probably be a little more careful when I write this, but that's the gist of it. – Guillermo Angeris May 6 '16 at 12:39