Optical measurements on 3He-B

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Optical measurements on ³He-B

In these experiments, which are the first optical studies of superfluid ³He, we extended the temperature range of direct observation to 0.7 mK, from about 10 mK previously. Instead of windows, we employ optical fibers to communicate between the cold parts of the cryostat and the video camera at room temperature.

Light from a 5-mW He-Ne laser, guided through a single-mode optical fiber, is reflected from the bottom window of the optical cell and from the surface of the ³He sample. The interference pattern is transmitted to a video camera at room temperature via a coherent bundle of 30,000 optical fibers. The sample is typically illuminated by 50-ms pulses every 2 s.

In the superfluid state, the viscosity of ³He is so low that the free surface remains perpendicular to gravity while the slightly tilted cryostat is rotated slowly, at 1 rad/s. This means that in the coordinate system of the video camera, which rotates with the cryostat, the liquid surface and, consequently, the light beam that is reflected by it are precessing. When the sample is warmed up to the normal state while still rotating, precession suddenly stops at the transition temperature. Normal liquid, which is very viscous near T_c, is forced to follow the walls of the optical cell. The transition is shown very clearly in a video film which we have produced. When the liquid is warmed further, the viscosity becomes finally so low that precession resumes.

The free meniscus z(r) = ${\it\Omega}$ ²r²/2g of a rotating classical liquid or of a superfluid with an equilibrium number of vortices acts as a parabolic mirror with a focal length f = g/2 ${\it\Omega}$ ². In a vortex-free state, discussed in the previous section, the superfluid component $\rho$ _s/ $\rho$ stays at rest and only the normal fraction $\rho$ _n/ $\rho$ rotates with the container. The surface profile, z(r) = ( $\rho$ _n/ $\rho$ ) $\Omega$ ²r²/2g, is then a flatter paraboloid and f = ( $\rho$ / $\rho$ _n)g/2 $\Omega$ ² is longer. The curvature is scaled by the temperature-dependent fraction of the normal fluid component, $\rho$ _n/ $\rho$ , so that at very low temperatures the surface is almost flat. An even more exotic meniscus should be produced by a vortex bundle (see Fig. 6b).

Both in the normal liquid and in the superfluid state, down to the minimum experimental temperature T/T_c = 0.75, focusing of reflected light occurred at the same angular velocity, ${\it \Omega}$ _foc = 2.25 ± 0.10 rad/s. This means that the superfluid surface had the same parabolic shape as the surface of the normal liquid at this speed of rotation, i.e., that the equilibrium number of vortices was present in the superfluid.

Optical interference under continuous illumination made possible elegant observations of the classical fountain effect on a thin layer of superfluid ³He. During these experiments the cryostat was at rest, so that the liquid surface was originally flat. A special superleak was not necessary: the viscous normal component of the thin sample was immobile on the bottom of the experimental chamber. Interference rings were formed because of the slightly curved bottom window of the optical cell.

The series of pictures in Fig. 3 were taken at 20-ms intervals. The frames show shrinking of the interference rings towards the center, which means that the thickness of the superfluid layer increases. This was due to the fact that in the superfluid state the rings moved under continuous illumination towards their heated center, where the curved reference surface had its highest point. The amount of liquid in the heated beam area increased, owing to the fountain effect. Counting the number of rings that shrank into the center, one can calculate that the thickness of the liquid layer increased as much as 10 µm in a few seconds. The superfluid component thus rushed into the illuminated region, trying to reduce the temperature differences in the ³He sample. When the liquid had warmed into the normal state, the surface started to flatten.

In the ROTA1 experiments described earlier it was possible to prepare a vortex-free state of ³He-B or even a situation with a vortex bundle in the center of the cell. The ROTA2 group tried to see these configurations as well. For reasons that probably have to do with the availability of suitable nucleation centers at the walls and with the large radius of the optical cell, a state with the equilibrium number of vortices was always observed by the ROTA2 group.