Theory of Cooling by Flow through Narrow Pores

Abstract

We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by "filtering out" hot atoms. Three methods are considered: (1) effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; (2) particle waveguidelike motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel; (3) wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimensions are smaller than the mean-free path for atom-atom interactions. The particle waveguide and the wall-limited diffusion methods using channels on order of the de Broglie wavelength give cooling. Recent advances in nanofilters give this method some hope of being practical.

Quantum-limited mass flow of liquid He3

“…The crossover around ∼ 1 mK is within the regime of the cooling technique by filtering discussed by Ref. [1]. The use of isotopic helium solutions may allow one to adjust the parameters into the needed ranges.…”

“…At very low temperatures, the thermal motion of the 3 He atoms in the liquid becomes very small as the de Broglie wavelength becomes comparable with the distance between the atoms and so quantum effects become significant enough to dictate the macroscopic properties of the liquid. In a recent paper [1], one of us noted that degenerate dilute solutions of 3 He in liquid 4 He might be cooled by flow through an array of nano-channels whose diameters are comparable to the de Broglie wave length of the channel. Aligning the Fermi energy of a container of fermions with the lowest allowed band in the channel would allow only the hot gases through the channel, thereby cooling the remaining gas in the container.…”

“…In a recent paper [1], one of us noted that degenerate dilute solutions of 3 He in liquid 4 He might be cooled by flow through an array of nano-channels whose diameters are comparable to the de Broglie wave length of the channel. Aligning the Fermi energy of a container of fermions with the lowest allowed band in the channel would allow only the hot gases through the channel, thereby cooling the remaining gas in the container.…”