Joe Vinen

1. Workshop on New Experimental Techniques for the Study of Quantum Turbulence, ICTP, Trieste, June 2005 Metastable He molecules and laser-induced fluorescence Dan McKinsey Yale University Joe Vinen Birmingham University

2. Introduction • The general idea of using spectroscopic detection of neutral molecules for the study of turbulence in a superfluid came from Dan McKinsey (nucl-ex/0503006). I have tried to develop it, in correspondence with Dan. This is a very preliminary and tentative report. Much of the report relates to proposals that have not yet been experimentally tested. • The techniques relate to what were first called neutral excitations in 4He, discovered by Surko & Reif in 1968, generated by an -particle source. Later it was discovered that they could also be produced by electron bombardment (eg a tritium source or electron beam). Mitchell and Rayfield showed that they travelled at velocities of typically 2 ms-1 at low temperatures. • Spectroscopic studies showed that electron bombardment produced He2excimer molecules, mostly in the states He2(A1u+) and He2(a3u+). • Production rates per Mev electron: 13000 triplet states; 19000 singlet states. • Both molecules decay by emission of 80 nm photons; lifetimes: singlet state 1ns; triplet state 13 s (decay requires spin flip). • Now known that the neutral excitations are formed from the triplet state molecules existing in a bubble state, radius 5.3Å.

3. Detection triplet molecules and simple experiments • In early experiments detection by: • production of electrons and ions at a free surface • production of electrons at a metal plate in the helium (a large voltage on the plate gives rise to current into plate) • Mitchell and Rayfield discovered how to gate their tritium source, and hence were able to measure the velocity of the molecular bubbles at low temperatures (no thermal excitations). At higher temperatures the bubbles ought to diffuse in the gas of thermal excitations, with a strongly temperature-dependent diffusion coefficient.

4. Possible use of triplet molecular bubbles for simple experiments on quantum turbulence • Presumably these bubbles will be trapped on vortex lines at a sufficiently low temperature. • Therefore they might be used in place of ions, in experiments similar to those to be described by Andre Golov for the study of turbulence in 4He at low temperatures: measure vortex line densities by observing the reduction in molecular current from trapping on vortex lines. • A first step would be to observe the reduction due to a known density of vortices in steadily rotating 4He, in order to measure capture cross-sections. • The molecular bubbles have a number of advantages over ions: • they move with smaller velocities, leading perhaps to larger capture cross-sections at low temps • they are not accelerated to large velocities in uncontrolled ways by small electric fields at low temps. • they move too slowly to create vortex rings at low temperatures.

5. Spectroscopic detection of triplet molecules • Ideally we want a way of detecting the molecules in the helium, with some spatial resolution. Dan McKinsey proposes a potentially powerful method. • Illuminate with pulsed i/r laser at 910 nm (modest power). • Immediately after, illuminate with pulsed i/r laser at 1040 nm. • Observe decay of d3+u to b3g with emission at 640 nm (lifetime 25 ns). • The b3g returns to a3 +u by non-radiative processes (may need to be accelerated by optical means) • Process recycles. •  ~ 4x107 photons/s at 640 nm.

6. Spectroscopic detection (cond) • Comments • Extremely sensitive. In appropriate cases it ought to be possible to detect individual molecules (return to later). • Only those molecules within the region of overlap of the two driving lasers will be detected. Hence some spatial resolution, even without any imaging. • Above ~ 1K, the molecules will diffuse in the helium to an extent that depends on the density of thermal excitations. Typically distance diffused in 10 s ~ 1 mm (1.5K). • Below ~ 1K, molecules will tend to move ballistically, perhaps with a velocity of order 2 ms-1, depending on the way they are produced? • Trapping of molecular bubbles on vortex lines: expect trapping below about 0.7K, if trapping cross-section is large enough. Trapped molecules move with vortex lines (more or less).

7. Applications of spectroscopic detection • Above 1K an injected bunch of molecules will move with the normal fluid (they are not trapped on vortex lines). We can observe the time taken for this bunch to reach the cross-over point of the two lasers. Hence we can measure normal-fluid velocity profiles (no trapping by vortex lines). A turbulent normal fluid would lead to extra “diffusion” of the molecules, from which we might deduce turbulent velocities. • Below ~0.7K we can hope that the molecules are trapped on vortex lines (even if trapping cross-section proves small we ought to get enough trapping if we inject enough molecules). Then we can find the extent of localized regions of turbulence, and any velocity with which these regions move. Decaying turbulence can be monitored by injecting at different times and observing how the fraction of trapped molecules changes. • A potentially exciting application is the use of the molecules as the “particles” in a PIV system (in principle they could be much better than conventional particles). Can a single molecule produce enough photons to produce two images in a CCD camera if it is illuminated by two sets of laser pulses each of length, say, 1 ms, separated by, say, 100 ms? A suitable system can probably be designed, although successful implementation may not be straightforward.

8. Conclusion Do these triplet molecules provide us with a really promising tool? Much development work required. Is it worthwhile?