Model-Independent Measurement of

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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
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Outline

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

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Motivation

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

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How MOT Works!
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Total Number of Atoms in a MOT.
For known Intensity and Detuning f is
calculated using simple Model
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Simple ModelTwo 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)
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Complex System
2
1

• System is multilevel
• Standing wave
• Circularly polarized
• Intensity is not low

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Modified Simple Model
C1 and C2 are the average Clebsh-Gordan
coefficients (2- parameter Model)
Ref Phys. Rev. A 52, 1423 (1995)
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Multi-level Model An Ansatz
Here ?-1/2 and ß-1/2 are the CGCs, and Sr
defines the low and High Intensities regimes for
S ltlt Sr, Is ?Is for S gtgt Sr,
Is ßIs
Phase MMT ? ß Sr
0 1.712 3.321 1.541
Random 1.259 1.620 1.045
Ref J. Opt. Soc. Am. B 10, 572 (1992)
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System Studied
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Generic MOT Setup
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Generic MOT Setup
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Double Pass AOM
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Experimental Setup
(MOTRIMS)
Ref Nucl. Instrum. and Meth. Phys. Res. B 205,
191 (2003)
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What do Q-values tell us?
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How to deduce excited fraction?
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Experimental Parameters
B-Field 12.5, 7.22 G/cm
Trap Intensity Balance 25.3 36.1 30.7 mW/cm2
Trap Intensity Balance 17.2 30.2 40.7 mW/cm2
Re-Pump 3.26, 1.37, 0.85 mW/cm2
Total intensities 36-134 mW/cm2
Detuning Range 4.9??/??1.57
MOT temperature 130 µ Kelvin
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Intensity vs Detuning (Raw Data)
A density plot of power and detuning Detuning in
16 equal steps Power in terms of ADC channels
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Results Intensity and Detuning Variation
Re-Pump 3.26 mW/cm2
Total intensities 36-134 mW/cm2
B-Field 12.5 G/cm
Intensity Balance 25.3 36.1 30.7 mW/cm2
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Intensity Balance
Trap Intensity Balance 17.2 30.2 40.7 mW/cm2
Re-Pump 3.26mW/cm2
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B-field effects
B-Field 7.22 G/cm
Trap Intensity Balance 25.3 36.1 30.7 mW/cm2
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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
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Gensemer Absolute Photo-Ionization Data
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Simple Model (1- Parameter Fit)
1-Parameter fit Is 9.2 mW/cm2
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1-Parameter Residuals
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Modified Simple Model (2-Parameter Fit)
2-Parameters C1 0.610 C2 0.645
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2-Parameter Residuals
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Multi level model (3-Parameter Fit)
No high and low intensity regimes so it is
essentially the same as 1 or 2 parameter model!
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Conclusions
Thanks to DOE
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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
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Special Thanks to
MOTRIMS Team
JRM Labs People! Thanks for your attention!
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Special Thanks to
MOTRIMS Team M. L. Trachy, G. Veshapidze, H.
Camp Brett D. DePaola JRM Labs People Thanks
for your attention!
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Ai area under the peak ni number of atoms
in a peak ?i Charge transfer cross section C
target thickness, acquisition time
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Relative Cross Section
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Double Pass AOM
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Complex System
MF
0
1
-1
-2
2

• Standing wave
• Circularly polarized
• Intensity is not low
• System is multilevel

1
-1
0
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System Studied
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Simple ModelTwo 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)
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Complex System

• System is multilevel
• Standing wave
• Circularly polarized
• Intensity is not low

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Two level system
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Motivation

• Formulae where it is being used

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