# Atomic and Optical Physics

Fall 2011

Committee: Dave, Wolfgang, Martin

Starting point: you have a beam shining on an atom (or an ensemble) and detectors distributed over 4π space. What do you expect to see? Follow up questions: talk about the scattering photon spectroscopy under different conditions, explain (laser beam on/off resonance, different beam intensity...). For the monotriplet of off resonance case, one sideband is closer to atom resonance, is the intensity higher in this sideband than the other sideband? What sideband (of the monotriplet) do you see first? What are the correlations between the two sidebands as a function of delay time τ? Why? What if it is the single photon coming instead of a strong beam? What is the smallest step of tau you can get when you are collecting the g2 data? A question from Dave: you have a stationary atom to begin with. A photon comes from the left and is absorbed and then spontaneously emitted by this atom. You have a photon detector over 4π space. What is the velocity direction of this atom after this emission if you detect a photon at . . . direction? (pick several directions to talk about) Now a mirror is put on the right to reflect the photons, what is the field spatial distribution? Assume there is an atom sitting at the antinode, is there any way to tell which photon (from left or right) this atom absorbed? Your favorite atom: What atom are you working with? What is its structure? For example, in Cs: the primary transition we work on is the D2 line which couples 6P −6 S. What kind of coupling allows this transition? What is the analogous transition in hydrogen? How do those levels couple? How does the lifetime of the transition compare in hydrogen and cesium

Spring 2012

Committee: Dave, Wolfgang, Martin

First question assigned by Martin: Can you tell us about Bragg Scattering of atoms from interfering laser beams? I read up a lot on the topic of atomic Bragg scattering and atom interferometry and put together a pretty coherent presentation for ~30-40 minutes. They let me talk for 5-10 minutes before interrupting with follow-up questions. As soon as I drew the dispersion relation for free particles and indicated on it the 2-photon transition between momentum eigenstates (that’s Bragg scattering), Wolfgang interrupted and asked how Bragg scattering would proceed in a BEC. I did not know how to answer immediately and the discussion related to this question lasted for a good half of my exam. It included Bragg spectroscopy of trapped particles (where I was asked to show where the Lamb-Dicke parameter came from) and molecules. Here are a few points from the discussion: - For a trapped particle, momentum is not conserved because translational symmetry is broken, so you can only look at transitions between trap eigenstates. If the trap is included as part of the system, momentum is conserved again and the trap can recoil. - Now consider a 2-atom molecule. We can factorize into internal degrees of freedom, which has the character of harmonic motion in a trap, and external degrees of freedom, which is the center of mass motion of the trap. Consider the limit of very weak binding: the particles are almost free, so we can come back to the single particle dispersion relation. As we turn up the binding, each state splits into momentum eigenstates of the molecule and internal HO eigenstates. - Will Bragg scattering dissociate the molecule? If the binding energy is smaller than the recoil energy, we have single particle Bragg scattering and the wavefunctions of the two atoms loose overlap after a certain amount of time, so the molecule dissociates. If the binding energy is larger than the recoil energy, we can excite the molecule, but will not necessarily dissociate it. - Consider now a BEC, weakly and strongly interacting. In an ideal BEC with no interactions, we regain single particle physics like before. In the presence of interactions, the free-particle dispersion relation can be replaced by the phonon dispersion relation of the BEC. Unlike the molecule case, where the internal DOF are factored out and act like a HO oscillator with the binding frequency, there is no energy gap in a BEC: the lowest energy excitations are sound waves with a linear dispersion relation. (This question may sound scary to people who don’t work with BEC’s, but I think the committee really pushed me here for fun - Wolfgang told me himself later that he did not expect me to know about the low-energy excitations in a BEC a priori.) In the limit of very strong attractive interactions, the BEC center of mass motion may be considered as well and can recoil, but this effect is negligible because the total mass is so large (m_atom*10^6) and the recoil energy is tiny. Your favourite atom: This is an opportunity for them to see if you know atomic structure, and it seems that Dave asks everyone this question. He asked to write down the outer shell configurations and was particularly interested in hyperfine structure of each state. A follow up question was on how you can flip the electronic and nuclear spins with laser light (spin-orbit coupling and J*I, respectively, allow you to do that of course). I was talking about a 2-electron atom (neutral Yb). Note that a lot of the states have total J=0, so the hyperfine states are degenerate.

Fall 2012

Committee: Ike, Dave, Wolfgang

-topic: quantum nature of light, how does it arise in experimental atomic physics -You wrote down the vector potential as a plane wave solution, how do I picture this? what's a laser beam classically? (i.e. longitudinal and transverse intensity distributions) -how do you measure the wavelength of light? how does the size of the beam affect your measurement? -what is the meaning of hbar in the commutation relation for x,p? (came out of talking about Q.H.O) -can the vacuum field cause scattering off atoms? -What is the vacuum electric field (at T=0) inside this can of coke? -I'm making a cavity with my hands, what's the mean energy of the photons inside? -How is the fact that light comes as discrete energy packets observed experimentally? -What is the wavelength of a single photon? -Describe the interaction of light with atoms. What do each term in your hamiltonian represent. -Light coming through the window is refracted. How do I see this from this hamiltonian?