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We have obtained the superfluid fraction of 4 He and mixtures confined in channels 0.0185 μm ×1.08 μm ×∞ . We compare this with film data L×∞×∞, and data for channels 0.0483 μm ×3.0 μm ×∞ . The behavior of the data in the smallest channels is quite different from what one might expect for a planar film of a given thickness. The transition is shifted to a lower temperature than expected; and, the overall behavior of ρs does not follow the trend observed with other confined films. This suggests that the lateral dimension plays a significant role in the behavior. We believe our observations are consistent with the recent proposal of Sobnack and Kusmartsev about a new mechanism for vortex unbinding in 2D films.

We have measured the heat capacity of helium mixtures confined to lithographically created cylindrical boxes whose height, 1.08 μm , equals their diameter. The specific heat at constant concentration x, C px , is renormalized due to the 3 He impurity. Thus, in order to observe critical behavior, a conversion must be made to a specific heat at constant φ=μ 3 −μ 4 , C pφ . The confined system's specific heat, near it's maximum, has values which rise above the bulk system's specific heat at the same temperature. This is unexpected and is true for both Cpx and Cpφ. This enhancement, not observed with pure 4 He , becomes more dramatic as x and the correlation length increase. The shift of the maximum with x is much larger for the boxes than for 2D confined mixtures. These observations might be related to a “band structure” effect associated with the 18.5 nm channels which connect the cylinders.

We report measurements of the specific heat near the superfluid transition of 4 He confined to 1 μm 3 cylindrical boxes patterned in SiO2. This system crosses from a 3D behavior to a 0D behavior near the transition. This has a marked effect on the specific heat as seen by a pronounced rounding of the maximum and a shift to a temperature much lower than the transition of the bulk system (and systems with 2D or 1D crossover). We plot the data according to correlation-length scaling theory and compare this to a planar system with the same smallest confinement. Compared to our previous studies of planar systems, the 0D cell has 3× the surface to volume ratio as well as ∼750× as much edge length. We examine the regions where surface and edge effect contributions can be separated. We find that the data do not reach the expected value for the surface region. There is also evidence for a region where the term associated with edge contributions dominates.

We report new data for 4 He confined between two silicon wafers spaced 9869 A apart. This spacing complements a series of previous measurements which now span a factor of 20 between the smallest and largest confinements. These new data allow us to further check scaling predictions. We find, as reported with previous data, that the present data scale well except near the heat capacity maximum, and below into the superfluid region.

We have previously described a resonance involving the adiabatic motion of 4He from a superleak into a reservoir. We consider here the case of 3He–4He mixtures and show some preliminary results for ρs for confinement to a film with thickness L=0.0483 μm . We relate this to the behavior expected from correlation-length scaling.

Finite-size scaling theory predicts that uniformly small critical systems that have the same dimensionality and belong to the same universality class will scale as a function of the ratio of the spatial length L to the correlation length ζ. This should occur for all temperatures within the critical region. Measurements of the heat capacity of liquid 4He confined to a two-dimensional (2D) planar geometry agree well with this prediction when the 4He is normal but disagree near the specific heat maximum where the confined 4He becomes superfluid. Data for 4He confined to 1D structures show a similar behavior (however the lack of data collapse is not as dramatic). Recent measurements of the heat capacity from two 0D confinements, which differ by a factor of two in size, fail to scale at any temperature within the critical region. This lack of scaling may be due to the interaction of neighboring boxes through the shallow channels used to fill them. This is quite surprising since the liquid in the channels is not superfluid at the temperatures of interest for the helium in the boxes. Furthermore, measurements of the superfluid density of the helium within the channels reveal a critical temperature that is higher than expected suggesting that the normal fluid is affected by the already superfluid regions at each end of these channels. Both of these anomalies might be explained by a proximity effect analogous to what is seen when normal metals are sandwiched between two superconductors.

We report measurements of the specific heat of 3He-4He mixtures near the superfluid transition when confined to channels of 1 /tm square cross section. These data test the universality of finite-size scaling as function of 3He concentration for 1D crossover. The analysis of these data requires that data measured at fixed concentration be converted to a specific heat at constant chemical potential difference = μ3 - μ4. This is carried out according to a procedure performed for planar mixtures by Kimball and Gasparini. We find that, in the most self-consistent analysis of the data, the mixtures define a separate scaling locus from that of pure 4He, both above and below Tλ. An analysis whereby the exponent a is forced to have the same universal value—as opposed to the best-fit value—yields a good collapse of all the data. This is achieved, however, at a cost of self-consistency. These results mirror very closely those obtained for finite-size scaling of confined planar mixtures, i.e. for 2D crossover.

The Soft X-ray Spectrometer (SXS) is one of four instruments that will be flown on the Japanese Astro-H satellite, planned for launch in late 2015/early 2016. The SXS will perform imaging spectroscopy in the soft x-ray band using a 6x6 array of silicon microcalorimeters operated at 50 mK, cooled by an adiabatic demagnetization refrigerator (ADR). NASA/GSFC is providing the detector array and ADR, and Sumitomo Heavy Industries, Inc. is providing the remainder of the cryogenic system (superfluid helium dewar (