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

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, pp286 2014; New J. Phys.17 pp035014 2015) “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, 015007 (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.

Motivation/Background (cont.) Rate eq. model for SrF (Mike Tarbutt, New J. Phys 17, 015007 (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.

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. 1200 lines fit to 0.007 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 .

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%)

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

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

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

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

Observations: Zeeman of low-J PQ12 & P1 features of (0,0) A2P1/2 –X2S+ Next Slide Obs. 5296 G, Parallel. Pol. Predicted 0 G to 5300 G, Parallel. Pol.

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 .

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

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

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

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

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 2.002 & 1.000). The gl & gl’ are small terms introduced to account for mixing with other electronic states. Curl relationships (after Bob Curl)

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)

Results (cont): A2P and B2S+ g-factors Curl Rel. values a) X2S+ parameters fixed to gS=2.002 and gl=-0.00194= -g/2B. Curl Rel. values -0.0653 0.0653 Mike’s predicted acceleration curves B2S+–X2S+ A2P1/2–X2S+ bigger smaller Laser power,mW

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 !