Superfluid effects in para-H 2 clusters probed by CO 2 rotation-vibration transitions Hui Li, Robert J. LeRoy, Pierre-Nicolas Roy Department of Chemistry University of Waterloo A.R.W. McKellar Steacie Institute for Molecular Sciences National Research Council of Canada

Apparatus Direct IR absorption in a supersonic jet Pulsed supersonic jet expansion –Slit or pinhole nozzle (General Valve) –Repetition rate: 0.5 to 5 Hz –Backing pressures up to ~45 atm –Cooled nozzle (down to ~100 K) –Two 10” diffusion pumps (Varian VHS-10) –Moderately skimmed jet Rapid-scan tunable diode laser probe –Pb-salt IR diode laser at 20 – 100 K –Toroidal mirrors give >100 traversals of laser through jet –5 MHz digitization during each millisecond laser sweep –Signal averaging with background subtraction (jet on minus jet off) –Wavelength calibration using reference gas and etalon –Laser is boxcar-stabilized to a reference line to minimize drift during signal averaging, giving sharper lines

Boxcar stabilizer system TDL controller L5830 TDL jet controller G.V. Iota One JET IR detector IR detector IR detector ref. gas etalon NI DAQ card Gage Compuscope 1250 card multiplexer Gas supply ref. gas signal etalon signal ref. or etalon signal multiplex control signal laser sweep trigger jet trigger jet pulse jet signal laser scan settings feedback signal to stabilize laser

highly reflective surface

cooling gas supply cooling gas return expansion gas supply solenoid current supply skimmer spider jet valve

Hydrogen clusters Compared to He, H 2 is lighter (more quantum) but also stickier (less quantum) ortho-H 2 is much stickier, so observation of para clusters requires high purity para-H 2 sample para-H 2 is a (composite) boson; calculations indicate it might be superfluid below about 6 K However, hydrogen solidifies at 13.8 K

para-hydrogen resultant nuclear spin, I = 0 rotational angular momentum, J = 0, 2, 4,... at low temp, all pH 2 is in the J = 0 level (J = 2 lies at 509 K) J remains a very good quantum number: J = 0 pH 2 is (almost) spherical, so pH 2 is a light spin- zero boson, “just like 4 He” we can prepare paraH 2 in the lab ortho-hydrogen resultant nuclear spin, I = 1 rotational angular momentum, J = 1, 3, 5,... at low temp, all oH 2 is in the J = 1 level normal-hydrogen at room temperature is 25% para and 75% ortho For clusters containing CO 2, half the rotational levels are missing. We observe R(0), P(2), R(2),... transitions, but not P(1), R(1),... Most of this work is on (pH 2 ) N - 13 C 16 O 2 and especially (pH 2 ) N - 13 C 18 O 2

increasing clustering effective cluster rotational temperatures are ~0.5 K (pH 2 ) N - 13 C 16 O 2

assignment was difficult for N >5

(pH 2 ) N - 13 C 16 O 2 larger clusters are present, but how can we assign them??

paraH 2 -CO 2 cluster spectra observed reliably up to N  6 Intriguing series of possible R(0) lines up to N  15 Reliable calculations of the vibrational shifts would be useful for H 2 -CO (requires very good difference potential surface) Hydrogen clusters my conclusions from Columbus 2008

This is exactly what we needed!!

(pH 2 ) N - 13 C 16 O 2

CO 2 R(0)CO 2 P(2)CO 2 P(4) the R(0) lines are shown here (pH 2 ) N - 13 C 18 O 2

N

Superfluid fraction N = 5 and 12 are “magic” (in different ways)

N = 5 and 12 are “magic”

We have an “experimental” measurement of the superfluid fraction for small para-H 2 clusters, using CO 2 rotation as a probe Good agreement between experiment and theory Significant superfluid fraction is observed in the range N = 9 to 17 (as large as ~0.9 for N = 12) What does ‘superfluidity’ mean in a small cluster? The best experimental probe seems to be observation of a nonclassical (larger than expected) B-value for coherent rotation of a probe molecule like CO 2 Conclusions