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

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

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

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

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

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)

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

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)

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)

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

{ 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

{ 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

Double Pass AOM

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

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

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

How to deduce excited fraction?

Experimental Parameters B-Field 12.5, 7.22 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 36-134 mW/cm2 Detuning Range 4.9/1.57 MOT temperature 130 µ Kelvin

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

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 36-134 mW/cm2

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

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

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

Gensemer Absolute Photo-Ionization Data

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

1-Parameter Residuals

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

2-Parameter Residuals

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

Conclusions Thanks to DOE

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

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

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

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

Relative Cross Section

Double Pass AOM

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

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

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)

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

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

Formulae where it is being used Motivation Formulae where it is being used

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

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