Coupling of Confined Superfluid Helium
نویسندگان
چکیده
Early measurements of the specific heat of liquid helium confined in all three spatial dimensions suggest a coupling of individual regions of superfluid via connecting channels. Preliminary measurements have been made to investigate this apparent coupling. Although more data need to be collected before anything conclusive can be said, the available data support the idea that behavior of helium confined in larger boxes is indeed modified by being in contact with the helium connecting the boxes through the narrow filling channels. Summary of Research: There is an intrinsic length scale associated with liquid helium called the correlation length. This is the distance over which fluctuations in the system are correlated. As one approaches the superfluid transition temperature, the correlation length diverges and becomes macroscopic. This means that if one brings a system of liquid helium close enough to the transition temperature, the correlation length can become comparable to the spatial extent of the system. Since the correlation length determines the thermodynamic responses, when it is no longer free to diverge due to the finite size of the system, the thermodynamics are altered. These effects are referred to as finite-size effects. This is the focus of our studies. By confining helium to small homogeneous structures we are able to measure finite-size effects in a controlled manner. We etch various geometries into silicon dioxide thermally grown on a silicon substrate. We use directwafer bonding to bond another wafer to this patterned structure to form an enclosure. The enclosure can be planar, linear, or box-like representing 2-dimensional (2D), 1-dimensional (1D) and 0-dimensional (0D) crossover. Liquid helium is introduced into this structure via a filling line which is interfaced with the bonded wafers. Scaling theories predict that if one performs a measurement on the same geometry, but different confinement sizes, the data will collapse onto a universal curve that is a function of the ratio between the spatial size and the correlation length. Data of the specific heat of helium confined in one spatial dimension show remarkable agreement with scaling except in a temperature region near the specific heat maximum and below [1-3]. Likewise data available for helium confined in two spatial dimensions also agree with scaling [4]. However, the limited data available for helium confined in all three spatial dimensions are substantially different, showing a lack of scaling throughout the critical region [5]. We believe that this lack of scaling may be attributed to a coupling between the boxes of confined helium through the small channels used to fill the millions of boxes in an experimental cell [6]. Our current work is investigating this possible coupling. We are systematically changing Figure 1: A cartoon of our current confinement cell design.
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