The abbreviation here has a double meaning– both “Open Access” and “Operator Algebra.” In my Quantum Optics class yesterday, I was talking about how to describe “coherent states” in the photon number state formalism. Coherent states are the best quantum description of a classical light field– something like a laser, which behaves very much as if it were a smoothly oscillating electromagnetic field with a well-defined frequency and phase.
Mathematically, one of the important features of a coherent state is that it is unchanged by the photon annihilation operator (in formal terms, it’s an “eigenstate” of that operator). That is, if you have a coherent state with an average of five photons in it, and you subtract one photon from it (say, by detecting that photon), you end up with… a coherent state with an average of five photons in it. It’s not that the photon subtraction makes a negligible change in the state of the light, it makes absolutely no change at all.
This is kind of odd, and at least 16.7% of the class was bothered by this. So, even though I hadn’t planned for it as part of the class, I remembered a recent experimental paper that did just this measurement (I wrote it up for ResearchBlogging earlier this year). And because it’s an Open Access journal (New Journal of Physics), it was easy to Google up the paper and show it to the class. so, rather than talking about Hanbury Brown and Twiss type experiments in the photon number formalism, we spent the last tfifteen or so mintues of the class talking about the experimental demonstration.
So, hooray for OA. Both types.
The relevant lecture notes are below the fold, for those who care:
- Lecture12-13.pdf: Coherent states and squeezed states in the phasor picture, experimental generation and detection of squeezed states.
- Lecture14.pdf: The simple harmonic oscillator using ladder operators; photon creation and annihilation operators.
- Lecture15-16.pdf: Coherent states as eigenstates of the annihilation operator, Hanbury Brown and Twiss experiments in the number-state formalism.