1. Optical Zeeman Spectroscopy of Calcium Fluoride, CaF
Timothy C. Steimle and Damian Kokkin
Dept. Chem. & BioChem., Arizona State University, Tempe, AZ,USA
Michael Tarbutt and Jack Delvin
Centre for Cold Matter, Imperial College, London UK,
The 70th International Symposium on Molecular Spectroscopy, June 2015
U. Illinois, Champagne-Urbana
A2P1/2
A2P3/2
X2S+
B2S+
16490 cm-1
16560 cm-1
18835 cm-1
LIF
Funded by: NSF

2. Goals
a)ASU: Determination of properties in preparation for magneto optical trapping
(MOT) of CaF.
b)Imperial College: Model diatomic MOT & demonstrate MOT for CaF
Background
SrF MOT :(DeMille’s group, Nature 512, pp ; New J. Phys.17
pp )
“There appears to be no widely accepted understanding of the mechanisms responsible for generating a restoring force in type-II MOTs”
Energy levels assoc. with SrF MOT
(DeMille’s Nature paper) type-II MOT
A2P1/2
X2S+
Rate eq. model developed by Mike Tarbutt, New J. Phys 17, (2015).
It was shown that the correct choice of laser polarization depends upon the sign of the upper state magnetic g-factor, gu, and that there is no trapping force if gu is zero. In cases where gu is much smaller than the lower state g-factor, gl, the trapping forces are weak.
In Hund’s case (a) limit g-factor for 2P1/2  0.

3. Motivation/Background (cont.)
Rate eq. model for SrF (Mike Tarbutt, New J. Phys 17, (2015).
Ideal arrangement of laser freq. & polarizations
Proposed arrangement of laser freq. & polarizations
Actual arrangement of laser freq. & polarizations
for original MOT
Mike’s predicted acceleration curves
A similar scheme for CaF will most likely not work because the g-factor for A2P1/2 (CaF) << g-factor for A2P1/2 (SrF).
Alternative: use the B2S+ -X2S+ transition.

4. Most Relevant Previous Spectroscopic Studies:
Microwave spectra of X2S+ state: Anderson et al ApJ 424 (1994)
Field-free parameters X2S+ are well determined
Rf-spectra of X2S+ state: Childs et al. JMS 86 (1981)
Field-free parameters A2P & B2S+ are reasonably well determined
De-perturbation of the A2P and B2S+ states based upon Doppler-limited (0,0) A2P-X2S+ & B2S+-X2S+ spectra: Field’s group JMS 197, (1999)
Fourier transform emission of Kr+ laser pumped lines fit to cm-1 : Verges et al. J. Phys. B 26, 279–284 (1993).
No previous comprehensive molecular beam study of the A2P-X2S+ & B2S+-X2S systems .
No previous Zeeman studies of the A2P-X2S+ & B2S+-X2S systems .

5. Molecular beam production
11/23/2018
Ablation laser
Generation via laser ablation/supersonic expansion
Supersonic expansion
Pulsed valve
0.5’’ Ca rod
Production of CaF: Ablated Ca + Ar(98%)/SF6(2%)

6. Optical Zeeman Spectroscopy
High-resolution Molecular Beam spectrometer
Helmholtz coils or magnet
Optical Zeeman Spectroscopy
PMT
Gated photon counter
LIF
skimmer
Ablation laser
Reagent
&
Carrier
Single freq. tunable laser radiation
Metal target
Pulse
valve
Well collimated
molecular beam
Rot.Temp.<10 K

7. Rare earth magnets: up to 8.6 kG
CW dye laser
Molecular
beam

8. Observations: Field-Free (0,0) A2P1/2 –X2S+ & A2P3/2 –X2S+
FWHM30 MHZ
X2S+ Spin-rot. split
19F Splitting
“Pred.” = predicted spectrum obtained using our optimized parameters

9. Observations: Field Free (0,0) B2S+–X2S+C D E
Hyperfine induced transition. Needs to be addresses in pumping scheme.

10. Observations: Zeeman of low-J PQ12 & P1 features of (0,0) A2P1/2 –X2S+
Next Slide
Obs G,
Parallel. Pol.
Predicted 0 G to 5300 G,
Parallel. Pol.

11. In the Hund’s case (a) limit these levels would not tune.
Magnetic tuning of energy levels associated with the PQ12 & P1(3) lines
In the Hund’s case (a) limit these levels would not tune.
A large parity dependence due to interaction with the B2S+ state.
Splitting very nearly equal to that expected for a “free” electron : 2BBz where B is the Bohr magneton=1.399 MHz/G .

12. Observations: Zeeman low-J RQ21 & R2 features of (0,0) A2P3/2 –X2S+
Next Slide C D
Obs G,
Perpendicular Pol.
Predicted 0 G to 3163 G,
Perp. Pol.

13. Magnetic tuning of energy levels associated with the RQ21 & R2(1) lines
There is a slight non-linearity in tuning due to magnetic-field-induced interaction with the J=5/2 levels
Rapid tuning
Negligible (<1 MHz) -Doubling

14. Observations: Zeeman low-J PQ12, P1,& P2 branch features of (0,0) B2S+–X2S+
A-F next slide
Saturation
Obs G,
Parallel Pol.
Predicted 0 G to 3163 G,
Par. Pol.

15. Magnetic tuning of energy levels associated with the RQ21 & R2(1) lines
Approx. good quantum #
Electron spin de-couples from rotation at a relatively large magnetic field.
Weaker MS=1 seen at higher laser power (saturation).
The strong transitions are the MS=0

16. Modelling the Spectra(PGOPHER not required- a “teachable moment” )
Effective Hamiltonian
Needed for the 19F hyperfine in X2S+ state
Zeeman terms
gS and gL’ need to be viewed as variables (i.e. allowed to vary from their nominal values of & 1.000).
The gl & gl’ are small terms introduced to account for mixing with other electronic states.
Curl relationships (after Bob Curl)

17. A2P and B2S+ field-free parameters (in cm-1):
Results:
Field-Free Fits
Band
# of lines
Std. dev.
A2Pr–X2S+
106
30 MHz
B2S+–X2S+ 68
24 MHz
Zeeman Fits
Band
# of lines
Std. dev.
A2Pr–X2S+
309
58 MHz
B2S+–X2S+
266
39 MHz
A2P and B2S+ field-free parameters (in cm-1):
a) X2S+ parameters fixed microwave data.
J. Vergès, C. Effantin, A. Bernard, A. Topouzkhanian, A. R. Allouche, J. d’Incan, and R. F. Barrow, J. Phys. B 26, 279–284 (1993). d)

18. Results (cont): A2P and B2S+ g-factors Curl Rel. values
a) X2S+ parameters fixed to gS=2.002 and gl= = -g/2B.
Curl Rel. values
0.0653
Mike’s predicted acceleration curves
B2S+–X2S+
A2P1/2–X2S+
bigger
smaller
Laser power,mW

19. Summary
The transition wavelengths and magnetic tuning of the low-J lines of the B2S+-X2S+ and A2P-X2S+ states that will be used in the MOT experiment have been measured
The g-factors and field-free parameters have been precisely determined.
Using the newly determines spectroscopic data. Prof. Mike Tarbutt (Imperial College) has modelled the CaF MOT.
Thank you !