1. Photoassociation Spectroscopy of Ytterbium Atoms with Dipole-allowed and Intercombination Transitions K. Enomoto, M. Kitagawa, K. Kasa, S. Tojo, T. Fukuhara, A. Yamaguchi, S. Uetake, Y. Takasu, and Y. Takahashi, Kyoto University Ultracold Group II atoms: Theory and Applications 06/Sep/18 ITAMP についての COE 報告会

2. Ytterbium Group II

3. Workshop on ultracold group II atoms 2000 Cold Alkaline-Earth Atoms (in ITAMP) 2003 Cold Alkaline-Earth Atoms (in Copenhagen) 2006 Sep/18-20 Ultracold Group II Atoms (in ITAMP) Atomic clock Number of invited speakers ExperimentTheory Photoassociation Novel species/mixtures Others 4 1 45 51 35

4. Next generation atomic clock 1 S 0 - 3 P 0 atomic transition has extremely narrow linewidth (  <0.1 Hz), and is inert to a magnetic field. The atoms trapped in an optical lattice with the magic wavelength are free from the Doppler broadening and the collisional shift. Frequency standard with  / ~ 10 -17 Precise frequency measurements of Sr and Yb in 1D lattice have been presented (NIST, JILA, SYRTE, PTB groups). The precision is about 5Hz.

5. R gg Photoassociation (PA) Ultracold atoms has narrow thermal distribution, so free-bound transitions (photoassociation) are observed with high resolution. This photoassociation is a powerful tool for probing rovibrational levels near the threshold and scattering states. Such parameters are determined for Sr, Ca, and Yb. Atomic parameters such as radiative lifetimes and scattering lengths are determined precisely. Theory for optical control of collision, PA in low dimensions

6. Novel species/mixtures Magneto-optical trap (MOT) of Ra (radium,  =15day) Measurement of nuclear EDM MOT of Li-K-Sr mixture Novel cooper pair (heteronuclear, FFLO, etc.)

7. Summary of my talk

8. Level Diagram of Yb (6s6p) 1 P 1 (6s 2 ) 1 S 0 intercombination transition 556 nm,  =874ns (Linewidth=182kHz) (6s6p) 3P23P2 3P13P1 3P03P0 clock transition dipole allowed, 399 nm  =5.5ns (Linewidth=29MHz) Mass number Nuclear spin i Abundance(%) 168 0 0.13 170 0 3.05 171 1/2 14.3 172 0 21.9 173 5/2 16.2 174 0 31.8 176 0 12.7  =15s  ~ 

9. Outline 1. Experimental procedure 2. Determination of scattering length of 174 Yb 3. Two-color PAS 4. Intercombination PAS of 4 isotopes 5. Optical Feshbach resonance

10. atomic beam Zeeman slower Experimental procedure 399 nm Zeeman slowing laser ( ～ 40 mW) anti-Helmholtz coils 556 nm MOT laser ( ～ 30 mW each) slower MOT horiz. FORT vertical FORT PA probe ～ 10s ～ 6s ～ 100ms Typical time chart

11. Experimental procedure CCD camera absorption image 532 nm FORT laser (7→0.2 W,  0 = 12  m) (7 W  0 = 80  m) 399 nm probe laser ( ～ 0.01W/cm 2 ) 556 nm PA laser ( ～ 0.1W/cm 2 ) slower MOT horiz. FORT vertical FORT PA probe ～ 10s ～ 6s ～ 100ms Typical time chart Off resonance 240  m 1.0 0.0 transmission On resonance N ~10 5 n ~10 14 cm -3

12. Determination of scattering length of 174 Yb using dipole-allowed PAS

13. Spectra of dipole-allowed PAS PAS of 1 S 0 - 1 P 1 transition at ~1  K

14. Ground-state wavefunction Wavefunction obtained from PA rates to various vibrational states Scattering length a of 174 Yb is 5.53  0.11 nm C 6 potential coefficient is 2300  250 a.u. (with taking account of other sources of error.)

15. Two-color PAS

16. Two-color PA spectra of 174 Yb Raman transition Recently, we succeeded in observing two-color PAS spectra for 174 Yb at ~1  K. 1 2 174 Yb 1 S 0 - 1 P 1 Frequency difference (MHz) Last bound state level 10.63 MHz Lightshift Expected shift (MHz)

17. Two-color PA spectra of 174 Yb Next-to-the-last state level 268.6 MHz 1 2 Frequency difference (MHz) Dark state ( 1 is scanned) Autler-Townes spectroscopy ( 2 is scanned) These two-color PAS results determine C 6 and a more precisely.

18. Scattering length of other isotopes Gribakin et al., PRA 48, 546 (1993). The scattering length a can be described with the phase . Two-color PA spectroscopy of some isotopes will reveal the scattering lengths of all the isotopes and their combinations. Scattering length pos.6 nm small neg. ? small small? large ? +10 - 5 Mass number 168 170171 172173 174176 ~54 Å Scattering length ~54 Å ? Å Mass number 168 170171 172173 174176 ? Å

19. Intercombination PAS of bosonic (i=0) isotopes ( 174 Yb, 176 Yb )

20. PA spectrum of 174 Yb v’ = 8 v’ = 9 v’ = 10 v’ = 7 T ~ 4  K At a low temperature of ~4  K, only transition from s-wave scattering state was observed. Even the vibrational level at 3 MHz from the disso- ciation limit was resolved. v ’ : vibrational number counted from the dissociation limit.

21. PA spectra of 174 Yb & 176 Yb (T~25  K) 174 Yb J e = 1 J e = 3 v ’ = 16 v ’ = 14 v ’ = 10 R C =6.5 nm R C =8.6 nm R C =17.4 nm J e = 1 J e = 3 J e = 1 J e = 3 v ’ = 16 v ’ = 13 v ’ = 10 R C = 6.0 nm R C = 9.0 nm R C =15.1 nm 176 Yb Large difference in signal intensity

22. Difference between 174 Yb & 176 Yb The PA efficiency for J e =3 line of 174 Yb is large inside the centri- fugal potential barrier. This is due to shape resonance. wavefunction near shape resonance d-wave potential wavefunction far from shape resonance

23. Intercombination PAS of fermionic (i  0) isotopes ( 171 Yb, 173 Yb ) L S JaJa I F T  hyperfine coupling  coupling to molecular axis

24. Potential calculation, :transition dipole, a :hyperfine coupling constant 171 Yb ( 3 P 1 ) ‥ i =1/2, j =1 1 S 0, f 1 =1/2 3 P 1, f 2 =3/2,1/2 basis sym. : basis antisym. :,  i and  are projection of and to molecular axis, respectively., i i j f ( 1 S 0 ) ‥ i =1/2, j =0

25. Pair potential of 171 Yb 2 [ 1 S 0 + 3 P 1 (f=3/2)] Hyperfine-induced purely long-range states exist. F = 1,  = 0  = 2  = 1 F = 2,  = 0 state sym.: state antisym.: s,d-wavep,f-wave f=3/2

26. PA spectrum of 171 Yb p wave s wave T=1 T=2 T=3 T=1 p s purely long-range state -4000-1000-200 -800-600 f =3/2 (MHz) -1060MHz ~ -160MHz Temperature ~20  K p

27. Conclusion PAS with the intercombination transition d-wave shape resonance is inferred for 174 Yb. Hyperfine-induced purely long-range state was observed. PAS with the dipole-allowed transition a = 5.53 ± 0.11 nm, C 6 = 2300 ± 250 nm for 174 Yb Two-color PAS of 174 Yb Bound levels at 10.6 MHz and 268.6 MHz were found. Optical Feshbach resonance with the intercombination line The asymmetric spectrum implies the change of a. 3 P 2 state atoms are trapped in the optical trap with high density. Quantum degenerate gases have been achieved for 5 isotopes.