The size of photon recoils, locking lasers to narrow optical cavities, and precise s-wave scattering measurements
I will discuss a two or three problems that are interesting for precision measurements, including atomic clocks. One question is how different is the photon recoil for a finite laser beam, as opposed to an infinite plane wave. The transverse momentum changes of atoms lead to frequency shifts with unusual dependences on the interrogation time and size of the atomic wave functions. These can be important for measurements of the photon recoil (for the fine structure constant) and also atomic clocks. A second topic is lock acquisition to very narrow optical cavities to stabilize lasers for optical clocks flywheels. This problem was first analyzed in the context of gravity wave detectors where the cavity sweeps through the resonance in less time than it takes for the light to build up in the cavity. For ultra-stable lasers, we show that lock can be robustly acquired directly to a narrow cavity. Finally, I will describe a novel experiment that juggles laser-cooled Cs atoms to directly measure the difference of s-wave scattering phase shifts.