Solid Helium

Freezing ⁴He in Vycor

Squeezing ⁴He in Vycor

At temperatures below 2.176 K, 4He enters a superfluid state and flows without friction. This perpetual motion makes superfluidity arguably the most dramatic manifestation of quantum mechanics on a macroscopic scale. Despite its appeal, and despite many searches for superfluidity in other systems, it remains an uncommon phenomenon. From 1938, when superfluidity was discovered, ⁴He was the only known example until 1972 when the phenomenon was seen, at much lower temperatures, in ³He. The temperature difference between the two isotopes' behaviour reflects the intimate connection of superfluidity to Bose-Einstein condensation (BEC). In 1995, advances in laser-cooling and magnetic-trapping techniques led to the achievement of BEC in rubidium vapour, adding to the list of superfluid systems, which now also includes other gases, such as spin-polarized hydrogen gas, and, most recently, molecular gases of paired fermions. Solids, with their atoms localized on a periodic lattice, are certainly the most unexpected phase of matter in which to find superfluid0like behaviour. However, the low atomic mass and the weak interatomic forces in solid helium make it very different from conventional solids. The quantum mechanical effect known as 'zero-point motion' dominates its properties, to the extent that it does not freeze at all unless external pressure (of at least 25 bar) is applied. At higher pressures helium does crystallize, but zero-point motion remains important and produces a very compressible low-density solid. In such a quantum solid, defects such as vacancies on the atomic lattice are easily created and can be very mobile. They might even exist in finite concentrations at absolute zero. Although such zero-point vacancies have not been directly observed, they would be expected to condense into a coherent state at low temperatures. And because mass flow accompanies the movement of vacancies, such a state could exhibit superfluid flow.

Freezing ⁴He in Vycor

In a recent torsional oscillator experiment¹, Eunseong Kim and Moses Chan, of Penn State University, observed an unexpected decoupling of ⁴He from a porous Vycor matrix, in a temperature and pressure range (below 175 mK and around 60 bar) where the helium was solid. The authors described the helium as a "supersolid" and speculated that its non-classical rotational inertia (NCRI) might be associated with a high vacancy concentration in the confined helium. The same authors have recently observed² similar behavior for bulk helium in an annulus, implying that supersolidity may be an intrinsic property of solid helium. Since mass can be transported in bulk crystals via the motion of extended defects like dislocations or grain boundaries, the Vycor results remain relevant; these defects would be immobilized in such small pores and so could not explain the observed NCRI. It is important to rule out alternative explanations of the NCRI in Vycor, such as the existence of a persistent liquid layer or a redistribution of mass due to some other transition in the confined helium that could mimic superfluid-like behaviour.

We have used a capacitive technique to directly monitor density changes for helium confined in Vycor at low temperature. We find that the ⁴He density in the pores increases by about 2.8% when it freezes. This is about half the corresponding change in bulk ⁴He but, if any liquid remains in the pores, then it must be very stable since the density change associated with freezing is independent of pressure. Measurements at temperatures as low as 30 mK showed no indication of a mass redistribution in the Vycor that could mimic supersolid decoupling.

1. E. Kim and M.H.W. Chan, Nature 427, 225 (2004).
2. E. Kim and M.H.W. Chan, Science 305, 1941 (2004).

Squeezing ⁴He in Vycor

Since our measurements rule out some of the most obvious alternative explanations of the decoupling observed for solid helium in Vycor, it becomes interesting to see whether solid helium exhibits any of the other unusual flow properties of a superfluid. In this experiment, by suddenly increasing the pressure in a cell containing the same Vycor sample, we were able to monitor the pressure induced flow of solid helium in the pores. Since thermally activated vacancies can transport mass in a pressure gradient, we do expect to see flow at temperatures near the melting point of the helium in the pores, but this flow rate should decrease rapidly with temperature.

We compressed the surrounding helium to study the pressure-induced flow of solid helium into the Vycor pores. Above about half the freezing temperature (T_F = 2.05 K), we observed a thermally activated flow which equilibrated the pressures inside and outside the pores in a time which ranged from seconds near T_F to hours near 1 K. Below about 700 mK this flow was too slow to be detected. We extended these measurements below 50 mK to look for evidence of mass flow in the range where supersolidity was observed, but saw no pressure-induced flow. Although our data are not systematic enough to provide a precise activation energy, the data between 1.1 and 1.8 K indicate a value around 9 K. Our measurements put an upper limit of about 0.001 mm/s on any supersolid flow in response to a pressure gradient.