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arXiv:cond-mat/0605072 · Physical Review Letters

Theory of Cooling by Flow through Narrow Pores

William J. Mullin, Neal Kalechofsky

Published Jul 7, 2006• 1 citation
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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.

DOI
10.1103/physrevlett.97.010801

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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.
We consider the possibility of cooling 3He atoms in dilute solutions with liquid 4He by “filtering out” the hot atoms through a screen of small holes or channels. The proposed method is somewhat analogous to that employed to evaporatively cool trapped gases, and the specific heat of the 3He‐4He mixture makes it feasible to use in a device to refrigerate other samples. Three methods are considered: 1) Effusion through holes having diameters larger than a mean free path allowing atoms to pass through easily; 2) Particle waveguide‐like motion (also effusive) using very narrow channels that greatly restrict the quantum states of the atoms in them; and 3) Wall‐limited diffusion through channels of various widths, in which the wall scattering is disordered so that local density equilibrium is established within a channel. The methods studied all require sufficiently low temperatures and holes or channels with sufficiently small dimensions that temperature equilibrium between the escaping gas and the original gas is avoided; that is, we assume that channel dimensions are smaller than the mean free path for atom‐atom interactions. We find that the particle waveguide and the wall‐limited diffusion methods using channels on the order of the de Broglie wavelength give cooling. Recent advances in nano‐filters give these methods some hope of being practical.
An extension to a previous model [ J. Opt. Soc. Am. B8, 1594 ( 1991)], which described the collision between two atoms in a cooling laser field, is made, which allows diffusive effects to be analyzed. A method similar to that used in Monte Carlo studies is developed, except that the diffusion is now determined exactly at all times. This approach relies directly on making a local classical path approximation for the atoms’ trajectories. For the simple case of a single two-level atom in the cooling field, the energy of the atom reaches equilibrium at the Doppler limit, as one would expect. In the full collisional situation we make the assumption that each atom undergoes a series of binary collisions. For sufficiently high atomic densities these collisions provide a limit on the lowest temperature that may be achieved by the cooling process.
Clouds of cold atoms, collected and refrigerated by laser light, can be cooled to nanoKelvin temperatures. This has created the new field of atom optics where cold atoms are manipulated, much as photons are controlled in traditional optics using mirrors, lenses, and gratings. It is also becoming possible to confine and manipulate atoms in extremely small traps and waveguides, which give access to de Broglie wave physical optics. Atoms flowing in such structures could provide a new technology based on the flow and quantum interactions of neutral atoms. Atom 'chips' could lead to integrated atom interferometers and even possibly to a quantum information processor.
In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4 He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature T C of the heat capacity at each coverage n . The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of T C is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to ( n - n c ) 2/3 , where n c is the onset coverage. In the case of the 1D pores (channels), T C is proportional to ( n - n c ) at 0.1 < T C < 1K. This T C is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T , with decreasing temperature. At T C , the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below T C , which indicates the 1D phonon state.