1. Measuring Polarizability with an Atom Interferometer Melissa Revelle

2. Overview The Importance of Atomic Polarizability Our Interferometer Modeling the Experiment Progress Future

3. Why Atomic Polarizability? Relates to Van der Waals forces Black body shifts for atomic clocks Depths of optical dipole traps for atoms Precision of α Na = 0.5% Precision of α K = 2%

4. Using Phase Shift to Find Polarizability Atom beam Detector 1G2G3G

5. Using Phase Shift to Find Polarizability Atom beam Detector 1G x 2G3G

6. Using Phase Shift to Find Polarizability Atom beam Detector 1G x 2G3G

7. Original Data Atom flux at each grating position is recorded Polarizability relates to this phase shift

8. Phase Shifts in an Atom Interferometer From the Schrödinger equation for an atom beam, we get: The total phase shift becomes:

9. The Electric Field Gradient Region x y Atom beams y x z

10. The Electric Field Gradient Region x y y x z

11. Finding the Equipotential Surfaces and Charge Density For an ideal wire and an image wire: g d y0y0 R y x z Atom beams

12. Creating the Model Integrate along a path in the x direction to get the phase shift. L=distance from 1G to gradient region a=grating period

13. Fitting the Data The model for the E-field and phase shift is used as a fit function Distance from Cylinder [mm] Phase Shift [rad] Data Fit Function

14. Summary We can precisely measure polarizability using atom interferometry. The electric field must be accurate. Velocity distribution is important

15. Current and Future Progress Improve precision polarizability of sodium and potassium to better than 1% Measure the polarizability tensor components of molecules.

16. References A.Salop, E. Pollack, and B. Bederson, Phys. Rev. 124, 1431 (1961) L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925) R. Molof, H. Schwartz, T. Miller, and B. Bederson, Phys. Rev. A 10, 1131 (1974)