8.422  Atomic & Optical Physics II

A quick - and unfortunately late - reminder that we'll have an extra lecture today at 1pm, as announced in class.

There's no class on Monday, a holiday. Next class is Wednesday 22nd.
Homework 8 is about, due that Wed 22nd. Have a quick look at the wiki to learn what Lindblad operators are. We encountered them when writing down the Master equation for the two-level atom.
https://cua-admin.mit.edu/apwiki/wiki/Optical_Bloch_equations

We will hold a make-up lecture this Friday, April 3rd, usual time&place: 4-163, 1pm-2:30pm
The new homework HW6 is online and will be due next Wednesday, April 8th.
Solutions to HW4 have been posted.

Tomorrow's class (Monday 3/30) is cancelled - MZ caught a virus that literally left him speechless.
We will have a make-up lecture this Friday April 3rd - room to be announced (likely the usual).

Next week is spring break, no classes. I strongly recommend reading Atom-Photon Interactions by Cohen-Tannoudji et al., especially as background for today's discussion Complement C-I, pp. 49-66, where a nice model system is treated of a discrete state coupled to a broad continuum.
We didn't get to Van der Waals interactions in class, so for background for the homework #5, you may enjoy reading API 118-126 and some additional notes (by Dan Kleppner) and a physics today paper that I put online at cua.mit.edu/8.422.
Today's lecture notes, including scattering and van der Waals interactions, are online, if you want to have a preview.

One clarification on today's perturbative calculation of the probability to stay in the initial state. We saw that the scattering matrix goes like S_ii = 1 - Gamma/2 T - i Delta T/hbar, with the decay rate Gamma and the level shift Delta. This is the short time limit of the full non-perturbative result that S_ii = exp(- Gamma T/2)exp(-i Delta T/hbar). From the latter, it is clear that the *probability* P_ii will go like exp(-Gamma T) and have no contribution from the level shift Delta. In the perturbative calculation, we ended up with P_ii = 1 - Gamma T, plus terms in T^2 that included Delta. Those T^2 terms involving Delta will cancel when including even higher-order contributions, i.e. at each order we will find that Delta does not come into the probability P_ii, as it should be for an energy shift which is purely a phase factor in S_ii. We will cover the non-perturbative calculation in one of the forthcoming lectures.