Quantum-limited mass flow of liquid He3

Abstract

We consider theoretically the possibility of observing unusual quantum fluid behavior in liquid 3 He and solutions of 3 He in 4 He systems confined to nano-channels. In the case of pure ballistic flow at very low temperature conductance will be quantized in units of 2m 2 /h. We show that these steps should be sensitive to increases in temperature. We also use a random scattering matrix simulation to study flow with diffusive wall scattering. Universal conductance fluctuations analogous to those seen in electron systems should then be observable. Finally, we consider the possibility of the cross-over to a one-dimensional system at sufficiently low temperature where the system could form a Luttinger liquid.

Two-terminal transport measurements with cold atoms

“…For very dilute mixtures at the lowest temperatures, 3 He behaves like an ideal Fermi gas with a very long mean free path of several tens of micrometers. An array of nanopores was then proposed as a connection between two tanks of helium, with holes on the order of 10 nm, which is compatible with the Fermi wavelength of 3 He [135,136].…”

Flow Conductance of a Single Nanohole

“…Future experiments will focus on reducing the size of the nanofluidic channel even further, towards the one-dimensional limit [19,20], where quantum ballistic transport should give rise at low temperatures to a conductance quantized in the unit of G m ¼ 2m 2 =h, the quantum of conductance for mass flow.…”

“…In conclusion, we have made a direct observation of the smooth crossover between the collective transport of particles emanating from a continuum to a single-particle statistical flow occurring in a single nanohole. Future experiments will focus on reducing the size of the nanofluidic channel even further, towards the one-dimensional limit [19,20], where quantum ballistic transport should give rise at low temperatures to a conductance quantized in unit of G m = 2m 2 /h, the quantum of conductance for mass flow.…”

Noise and fluctuations in nanoscale gas flow

“…Both will be referred to as f in their respective contexts, with chemical potentials μ L and μ R , referring to the left and right side of the channel, where (μ L − μ R ) = mΔP/ (ρ). Transport from the left to right is defined as positive in quantized units of G where [22]:…”

“…The noise, δQ, will be calculated as a mean squared fluctuation, 〈δQ 2 〉, where 〈...〉 refers to an average with respect to time. Recent work found that G is quantized in units of 2m 2 /h, where m is the mass of a fluid particle and h is Planck's constant [22,23]. The resemblance with the quantum of electrical conductance (2e 2 /h where e is the electrical charge) highlights the close analogy between mass flow and charge flow.…”