Model-Independent Measurement of Excited State Fraction in a MOT

1. Model-Independent Measurement of Excited State Fraction in a MOT Mudessar H. Shah, Brett D. DePaola JRM. Labs, Department of Physics Kansas State University Manhattan, Kansas

2. Outline • Motivation • Introduction To a MOT • Theoretical Models • Experimental Setup • Experimental Results • Conclusion

3. Motivation • Absolute photo-ionization cross sections • Cold atom collisions cross sections • Photo-association spectroscopy • Total number of atoms in a MOT

4. Absorption. k I MF+1 E=ћω P=ћK J= ћ E=0 P=0 J= 0 E=ћω P=ћK J= ћ 2 MF0 MF-1 - + l 1 Detuning B-field Gradient Polarization I MOT has the combination of ground and excited states How MOT Works!

5. Photo Diode Monitor N = ext f N tot N = ext N tot f Total Number of Atoms in a MOT. For known Intensity and Detuning f iscalculated using simple Model

6. Approximations • Two level system • Electric dipole • Rotating wave Simple Model;Two level system Dilute Gas Laser Beam • A plane traveling wave • Linearly polarized • Intensity is low Polarization is parallel to dipole moment Ref: W. Demtröder, Laser Spectroscopy. (Springer, 2002)

7. -2 -1 0 1 2 MF 0 1 -1 Complex System 2 1 • System is multilevel • Standing wave • Circularly polarized • Intensity is not low

8. Modified Simple Model C1 and C2are the average Clebsh-Gordan coefficients (2- parameter Model) Ref: Phys. Rev. A 52, 1423 (1995)

9. Multi-level Model; An Ansatz Here “-1/2” and “β-1/2” are the CGCs, and Sr defines the low and High Intensities regimes for S << Sr, Ĩs = Is for S >> Sr, Ĩs = βIs Ref: J. Opt. Soc. Am. B 10, 572 (1992)

10. MF F / =3  -3 -2 -1 0 1 2 3 52P3/2 267MHz F / =2 52P1/2 Trapping Laser D2 MF 2 0 1 -1 -2 Re-pump Laser F =2 52S1/2 F =1 Rb87 , I=3/2 System Studied

11. Laser Locking setup RF Generator Energy and momentum Conservation between phonon and Photon Trapping laser Dumper AOM Polarization Setup Detuned Beam { Repump laser Laser Locking setup Generic MOT Setup

12. Laser Locking setup RF Generator Energy and momentum Conservation between phonon and Photon Trapping laser Dumper AOM Polarization Setup Detuned Beam { Repump laser Laser Locking setup Generic MOT Setup

13. Double Pass AOM

14. Experimental Setup (MOTRIMS) Ref: Nucl. Instrum. and Meth. Phys. Res. B 205, 191 (2003)

15. Difference of energy in final and initial state of electron Na + 7Kev Rb 87 What do Q-values tell us?

16. Ai = area under the peak ni = number of atoms in a peak i = Charge transfer cross section C = target thickness, acquisition time

17. How to deduce excited fraction?

18. Experimental Parameters

19. Intensity vs Detuning (Raw Data) A density plot of power and detuning Detuning in 16 equal steps Power in terms of ADC channels

20. Results: Intensity and Detuning Variation

21. Intensity Balance

22. B-field effects

23. Re-pump variation

24. Gensemer Absolute Photo-Ionization Data

25. Trap range Simple Model (1- Parameter Fit) • 1-Parameter fit • Is= 9.2 mW/cm2

26. 1-Parameter Residuals

27. Modified Simple Model (2-Parameter Fit) • 2-Parameters: • C1= 0.610 • C2= 0.645

28. 2-Parameter Residuals

29. Multi level model (3-Parameter Fit) No high and low intensity regimes so it is essentially the same as 1 or 2 parameter model!

30. Conclusions Thanks to DOE

31. Conclusions • First time excited state fraction is measured by model independent method. • Theory and experiment are in good agreement within the parameter space of a “good” trap. • Results are, at most, weakly dependent on other trap parameters. • Three parameter ansatz does not work very well • For two parameters: C1 = 0.610, C2= 0.645 • For one parameter : Is= 9.2 mW/cm2 Thanks to DOE

32. Special Thanks to MOTRIMS Team JRM Labs People! Thanks for your attention!

33. Special Thanks to MOTRIMS Team M. L. Trachy, G. Veshapidze, H. Camp Brett D. DePaola JRM Labs People Thanks for your attention!

34. Ai = area under the peak ni = number of atoms in a peak i = Charge transfer cross section C = target thickness, acquisition time

35. Relative Cross Section

40. Double Pass AOM

41. Complex System MF -2 0 1 -1 2 • Standing wave • Circularly polarized • Intensity is not low • System is multilevel 1 -1 0

42. MF Levels! • MF Levels! Rb 87 F=3 -3 -2 -1 0 +1 +2 +3 3-2 Co. 52P3/2 F=2 F=1 F=0 Re-pump Laser Trapping Laser F=2 -2 52S1/2 -1 0 +1 +2 F=1 System Studied

43. Simple Model;Two level system Approximations • A plane traveling wave • Linearly polarized • Intensity is low • Two level system • Electric dipole • Rotating wave Polarization is parallel to dipole moment Ref: W. Demtröder, Laser Spectroscopy. (Springer, 2002)

44. -3 -2 -1 0 1 2 3 2 0 1 -1 -2 Complex System • System is multilevel • Standing wave • Circularly polarized • Intensity is not low

45. Absorp. k E=ћω P=ћK J= ћ E=0 P=0 J= 0 E=ћω P=ћK J= ћ Two level system

46. Motivation • Formulae where it is being used

47. Experimental Setup (MOTRIMS) Ref: Nucl. Instrum. and Meth. Phys. Res. B 205, 191 (2003)

48. Na+ PSD Display TDC MOT Momentum spectrometer Experimental Setup (MOTRIMS) Ref: Nucl. Instrum. and Meth. Phys. Res. B 205, 191 (2003)