1. Spectroscopy of (He) N -Molecule Clusters: Tracing the Onset of Superfluidity Yunjie Xu and Wolfgang Jäger Department of Chemistry, University of Alberta, Edmonton, AB Canada Collaborations: Bob McKellar, Jiang Tang, NRC PN Roy, Nick Blinov, UofA

2. Overview Introduction Instrument and Technique Molecular Systems – He N – OCS – He N – N 2 O – He N – H-C≡C-C≡N

3. From the Molecular Regime to the Bulk Phase

4. A Case in Point: Superfluidity 4 He becomes superfluid below the λ-point (2.17 K). Frictionless flow, irrotationality, quantized vorticity, fountain effect … Andronikashvili experiment ‘Drag’ from normal fluid component causes increase of moment-of-inertia of disk stack. Confirmation of two–fluid model.

5. The Microscopic Andronikashvili Experiment Grebenev, Toennies, Vilesov, Science 279, 2083 (1998).

6. Helium Nanodroplet Isolation Spectroscopy Grebenev, Toennies, Vilesov, Science 279, 2083 (1998). Number of 4 He atoms 0 7 25 35 60 100 Relative Depletion [%] Wave Number Change [cm -1 ]

7. The Small Cluster Approach Tang, Xu, McKellar, Jäger, Science 297, 2030 (2002).

8. Rotational (microwave) spectra of He N -molecule clusters. Instrument: FT Microwave Spectrometer, 4 - 26 GHz (~0.1 - 1 cm -1 ). Clusters are produced in pulsed molecular expansion. Instrument and Technique

9. Fourier Transform Microwave Spectrometer Frequency range: 4 – 26 GHz (ca. 0.1 – 1 cm -1 )

10. microwave cavity nozzle Fourier Transform Microwave Spectrometer

11. A Real FTMW Experiment Example: Ne–Ar van der Waals complex @11652.3 MHz 10  s excitation pulse protective MW switch time detection period FT

12. Supersonic Molecular Expansion

13. 1. He N -OCS He N – Molecule Clusters

14. He 2 -OCS in its Principal Inertial Axes System

15. J KaKc =1 01 -0 00 Transitions of He 2 -OCS He 2 -OC 33 S He 2 - 17 OCS

16. Multidimensional Assignment Procedure a) infrared predictions b) sample conditions (pressure, temperature) c) double resonance experiments d) consistency of isotopic data e) spectral fits

17. Effect of Nozzle Cooling on Cluster Formation He 6 -OCS, J=3-2 at 11176.83 MHz, 0.01% OCS in He at 20.4 atm 100 averaging cycles nozzle at room temperature S/N ~ 2 nozzle at dry ice temperature (-78.5 C) S/N ~ 40

18. Double Resonance Spectrometer

20. Double Resonance Experiments on He 6 -OCS signal: J-3-2, 11176.83 MHz pump: J=2-1, 7588.75 MHz 20 averaging cycles pump power (continuous) off -3 dBm 3 dBm

21. Vibrational Frequency Shifts of He N -OCS Clusters experimental values, Tang et al., Science 297, 2030 (2002). values from Whaley and co-workers, JCP 115, 10225 (2001).

22. Moment-of-Inertia Shifts of Isotopomers )I / amuD 2 32.2 48.8 35.7 37.4 32.1 OCS O 13 CS OC 33 S O 13 C 33 S 17 O 13 CS 18 O 13 CS OC 34 S O 13 C 34 S

23. Proposed Structure of He 8 -OCS

24. Helium density in He 8 -OCS P. N. Roy, N. Blinov, private communication.

25. Spectroscopic Constants of He N -OCS Clusters MoleculeBD Free OCS6081.591.31x10 -5 He-OCS13208.57 5504.18 4582.80 3661.42 0.950 He 2 -OCS 5803.39 4546.34 3782.81 3019.28 --- He 3 -OCS 3104.575.11 He 4 -OCS2591.950.881 He 5 -OCS2225.150.234 He 6 -OCS1910.492.60 He 7 -OCS1682.981.29 He 8 -OCS1447.732.00 OCS in 4 He droplet (N~3,000) 2194.5(90)11.4(3)

26. Moment of Inertia I B I B = Σ m i * r i 2 m i : mass of atom i. r i : distance of atom i from rotational axis. Rotational Constant B B ~ 1 / I B

27. Rotational Constant vs. Number of He Atoms

28. … new Calculations … S. Baroni and coworkers, Phys. Rev. Lett. 90, 143401 (2003). B. Whaley and coworkers, Phys. Rev. Lett. 90, 073401 (2003).

29. … and very recent Calculations. N. Blinov, X. Song, P. N. Roy, JCP 120, 5916 (2004). S. Moroni et al., Phys. Rev. Lett. 90, 143401 (2003).

30. Helium Density Profiles in He N -OCS N. Blinov, X. Song, P. N. Roy, JCP 120, 5916 (2004). N=5 N=7 N=9 N=6 N=8 N=10

31. 2. He N -N 2 O He N – Molecule Clusters

32. Potential Energy Surface of He-N 2 O level of theory: CCSD(T) basis set: aug-cc-pVTZ bond functions: 3s, 3p, 2d, 1f, 1g Energies in cm -1 X. Song, P. N. Roy, Y. Xu, and W. Jäger, JCP, accepted.

33. Bound State Calculations for He-N 2 O

34. Wavefunction of Ground State

35. Wavefunctions of 1 st and 2 nd Excited States

36. He 6 -N 2 O in its Principal Inertial Axes System

37. Xu, Jäger, Tang, McKellar, Phys. Rev. Lett. 91, 163401 (2003). Selected for presentation on Physical Review Focus. He 12 –N 2 O

38. J=1-0 Rotational Transition Intensity Frequency / MHz He 7 - 14 N 15 NO He 5 - 14 N 15 NO Intensity He 12 - 14 N 15 NO 6792.0 6793.5 5471.5 5473.0 6194.5 6195.5

39. Rotational Constant vs.Number of He Atoms S. Moroni, N. Blinov, P. N. Roy, JCP 121, 3577 (2004). Helium droplet value Nauta, Miller, JCP 115, 10254 (2001.)

40. Helium Density Distributions in He N -N 2 O N=5 N=9 N=14 N=6 N=10 N=15

41. $$$ Acknowledgements Acknowledgements Dr. Dominik Bremm Dr. Rudolf Lehnig Dr. Chakree Tanjaroon Dean Court Dr. Kai Brendel Dr. Yaqian Liu Dr. Silas Ngari Dr. Hans Osthoff Dr. Jennifer van Wijngaarden Jen Landry Julie Michaud Wendy Topic Qing Wen Kyle Green Kristine Liao James Song Ling Tang Bilkiss Issack Dr. Nick Blinov Dr. Bob McKellar Dr. PN Roy Chemistry Design and Manufacturing Facility NSERC ASRA, ISRIP CIPI Faculty of Science Canada Foundation for Innovation