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

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

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

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

6. Simple Model; Two level system
Dilute Gas
Two level system
Electric dipole
Rotating wave
Approximations
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. Complex System System is multilevel Standing wave Circularly polarized2 MF -1 1 2 -2 1
System is multilevel
Standing wave
Circularly polarized
Intensity is not low

8. Clebsh-Gordan coefficients (2- parameter Model)
Modified Simple Model
C1 and C2 are 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
Phase
MMT  β Sr
1.712
3.321
1.541
Random
1.259
1.620
1.045
Ref: J. Opt. Soc. Am. B 10, 572 (1992)

10. System Studied MF  52P3/2 52P1/2 D2 52S1/2 Rb 87 , I=3/2 F / =3-1 1 2 3 -2 -3
52P3/2
52S1/2
F =2
Trapping Laser
F / =3
Re-pump Laser 
F / =2
F =1
267MHz D2
Rb 87
, I=3/2 MF
52P1/2

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

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

13. Double Pass AOM

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

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

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
B-Field
12.5, G/cm
Trap Intensity Balance
25.3: 36.1: 30.7 mW/cm2
17.2: 30.2: 40.7 mW/cm2
Re-Pump
3.26, 1.37, 0.85 mW/cm2
Total intensities
mW/cm2
Detuning Range
4.9/1.57
MOT temperature
130 µ Kelvin

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
B-Field
12.5 G/cm
Intensity Balance
25.3: 36.1: 30.7 mW/cm2
Re-Pump
3.26 mW/cm2
Total intensities
mW/cm2

21. Intensity Balance Trap Intensity Balance 17.2: 30.2: 40.7 mW/cm2
Re-Pump
3.26mW/cm2

22. B-field effects B-Field 7.22 G/cm Trap Intensity Balance 25.3: 36.1:
30.7 mW/cm2

23. Re-pump variation B-Field 12.5 G/cm Trap Intensity Balance
25.3: 36.1: 30.7 mW/cm2
Re-Pump
3.26, 1.37, 0.85 mW

24. Gensemer Absolute Photo-Ionization Data

25. Simple Model (1- Parameter Fit)
Trap range
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 Standing wave Circularly polarized Intensity is not lowMF -2 -1 1 2
Standing wave
Circularly polarized
Intensity is not low
System is multilevel -1 1

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

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

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

46. Formulae where it is being used
Motivation
Formulae where it is being used

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

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