Historical research guide · 0555 · 1996
Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation
V. M. H. Ruutu · V. B. Eltsov · A. J. Gill · T. W. B. Kibble · M. Krusius · Yu. G. Makhlin · B. Plaçais · G. E. Volovik · Wen Xu
In one minute
Cosmology says the early universe cooled through phase transitions so fast that the new order could not agree with itself everywhere, and the disagreements froze in as defects. That is a hard idea to test on a universe you only get one of. The Helsinki group with Tom Kibble, Grisha Volovik and their colleagues built a version you can run all afternoon. They rotate a cylinder of superfluid helium-3 and fire thermal neutrons at it. Each neutron that lands splits a helium nucleus, and the fragments dump their energy as heat, boiling a cigar-shaped pocket back to ordinary liquid. The pocket recools through the superfluid transition in about a microsecond, and a tangle of quantized vortices freezes into it. Rings above a critical size then expand in the rotating flow and are counted one at a time by nuclear magnetic resonance, as steps on a chart. The count follows a clean cubic law in flow speed — the same law the frozen-tangle picture predicts.
Connection
Chapter 5 reads the vacuum as a quantum fluid, and this is where that reading stops being a metaphor: the same equations that describe defect freezing in the early universe are tested here on a liquid, one defect at a time. Chapter 13 needs experiments that connect condensed matter to cosmology, and this is the cleanest of them.
From the source
Absorbing a thermal neutron in superfluid helium-3 runs the reaction that turns a neutron and a helium-3 nucleus into a proton, a triton and 0.76 MeV, and the 573 keV proton and 191 keV triton lay down ionisation tracks 70 and 10 micrometres long whose recombination heats a cigar-shaped pocket of the liquid back above the superfluid transition temperature.Abstract; Introduction, third paragraph; Figure 1 caption, panels b and c
That pocket recools by quasiparticle diffusion in a characteristic time of about one microsecond, and the resulting rapid transition freezes in a random network of quantized vortices with an initial defect spacing of order one micrometre — the mechanism Kibble formulated and Zurek refined.Equations 1 and 2 and the two paragraphs following them
Vortex loops larger than a critical radius set by the superflow velocity expand under the Magnus force, reach the container wall as rectilinear lines and are counted individually by nuclear magnetic resonance, each absorption event appearing as a distinct step in the absorption record whose height is the number of lines nucleated.Paragraph beginning ’The number of the vortex lines is monitored with NMR’; Figure 2 insert caption
The nucleation rate vanishes below a threshold superflow velocity and above it follows a cubic law in the velocity normalised to that threshold, fitted at 1.37 plus or minus 0.03 vortex lines per minute in one data set and 1.46 plus or minus 0.12 in another, against a theoretical estimate of about 2.Figure 2 main frame caption; Figure 4 caption; Equation 5
The threshold velocity varies with temperature as the cube root of the reduced temperature, a different exponent from the fourth root followed by the spontaneous critical velocity measured without the neutron source, and once results are plotted against that threshold the dependence on temperature, pressure and magnetic field disappears into a single parameter.Equation 4 and the paragraph following it; Figure 3 caption; Figure 4 caption
The authors put the analogy plainly: many direct parallels and formal analogies connect superfluid helium-3 theory with the field theories used to describe the physical vacuum, gauge fields and fermionic elementary particles, and they suggest the vortex nucleation seen during the rapid cool-down is similar to defect formation during cosmological phase transitions in the early universe.Abstract, final sentence; Introduction, second paragraph, citing Volovik reference 7
The way in
https://doi.org/10.1038/382334a0How to cite it
V. M. H. Ruutu, V. B. Eltsov, A. J. Gill, T. W. B. Kibble, M. Krusius, Yu. G. Makhlin, B. Plaçais, G. E. Volovik, Wen Xu (1996) Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation doi:10.1038/382334a0