Flow Conductance of a Single Nanohole

Savard, M.; Tremblay-Darveau, Charles; Gervais, G.

doi:10.1103/physrevlett.103.104502

Cited by 32 publications

(52 citation statements)

References 19 publications

(22 reference statements)

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“…Recently, exciting possibilities for experimental realizations of Luttinger liquids have appeared, involving ultracold atoms in cigar-shaped traps, 2 screw dislocations in solid 4 He ͑Ref. 3͒, and helium-4 confined to flow in nanopores.…”

mentioning

confidence: 99%

Interacting bosons in one dimension and the applicability of Luttinger-liquid theory as revealed by path-integral quantum Monte Carlo calculations

Maestro

Affleck

2010

Phys. Rev. B

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Harmonically trapped ultracold atoms and 4 He in nanopores provide different experimental realizations of bosons in one dimension, motivating the search for a more complete theoretical understanding of their lowenergy properties. Worm algorithm path-integral quantum Monte Carlo results for interacting bosons restricted to the one dimensional continuum are compared to the finite temperature and system size predictions of Luttinger-liquid theory. For large system sizes at low temperature, excellent agreement is obtained after including the leading irrelevant interactions in the Hamiltonian which are determined explicitly.Luttinger-liquid ͑LL͒ theory 1 provides a universal description of interacting fermions or bosons at sufficiently low energies in one dimension ͑1D͒. Recently, exciting possibilities for experimental realizations of Luttinger liquids have appeared, involving ultracold atoms in cigar-shaped traps, 2 screw dislocations in solid 4 He ͑Ref. 3͒, and helium-4 confined to flow in nanopores. 4 While the latter experiment examines a system that is highly out of equilibrium, future iterations 5 could be well described by a translationally invariant model of interacting bosons. There have been numerous numerical studies of 1D fermion models on lattices using exact diagonalization, Monte Carlo, and density matrix renormalization-group methods, but numerical results on free space interacting bosons at nonzero temperature, T, are much rarer. Exact studies in the continuum may provide insights, specifically on issues of dimensional crossover in nanopores. 6 Zero-temperature variational Monte Carlo calculations for the 1D case were reported in Ref. 7 and finite T worm algorithm path-integral Monte Carlo ͑WA-PIMC͒ simulations for a screw dislocation 3 have claimed the observation of LL behavior. In order to systematically explore the regime of energies and pore lengths, where LL behavior may occur we have performed WA-PIMC simulations on the N-particle Hamiltonianin 1D with periodic boundary conditions on an interval of length L in angstroms and we will work in units where ប = k B = 1. The WA-PIMC method, recently introduced by Boninsegni et al. 8 extends the original PIMC algorithm of Ceperley 9 to include configurations of the single-particle Matsubara Green's function, allowing for intermediate particle trajectories which are not periodic in imaginary time.The inclusion of such trajectories yield an efficient and robust grand canonical quantum Monte Carlo ͑QMC͒ technique that accurately incorporate complete quantum statistics and provides exact and unbiased estimations of many physical observables at finite temperature. In the WA-PIMC simulations performed here, the short-range repulsive interaction V͑r͒ = ͑g / ͱ a͒e −r 2 /4a 2 is chosen for convenience to be Gaussian with integrated strength 2g and spatial extent a. The numerical values of all microscopic parameters were optimized to ensure an experimentally relevant and efficient simulation at low energies, where the temperature is much smaller than both the k...

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mentioning

confidence: 99%

Interacting bosons in one dimension and the applicability of Luttinger-liquid theory as revealed by path-integral quantum Monte Carlo calculations

Maestro

Affleck

2010

Phys. Rev. B

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“…The dynamic resonance described below, therefore, only appears in the superfluid phase (T < T λ ) when ρ s /ρ = 0. In the case of dc flow, however, it is possible to measure a contribution from the normal density component even for nanoscale channels 34,35 . We drive an ac Helmholtz resonance 23,24 with the same voltage V d that is used to measure the capacitance of the nanofluidic capacitor.…”

Section: Resultsmentioning

confidence: 99%

Superfluid nanomechanical resonator for quantum nanofluidics

Rojas

Davis

2015

Phys. Rev. B

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We have developed a nanomechanical resonator, for which the motional degree of freedom is a superfluid 4 He oscillating flow confined to precisely defined nanofluidic channels. It is composed of an in-cavity capacitor measuring the dielectric constant, which is coupled to a superfluid Helmholtz resonance within nanoscale channels, and it enables sensitive detection of nanofluidic quantum flow. We present a model to interpret the dynamics of our superfluid nanomechanical resonator, and we show how it can be used for probing confined geometry effects on thermodynamic functions. We report isobaric measurements of the superfluid fraction in liquid 4 He at various pressures, and the onset of quantum turbulence in restricted geometry.

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“…The membranes are custom made on chips with size of 5 mm Â 5 mm, window size 100 lm Â 100 lm, thickness 200 nm and are able to resist 100 kPa of pressure differential. Considering the geometric characteristics (length and diameter) of the nano-holes used in this work, the FIB machining overcomes the speed limitation of others techniques used to drill nano-holes, and in addition does not need chemically assisted etching by gas injection, such as in the case of others techniques used for this purpose [4][5][6].…”

Section: Leak Elements Fabrication and Their Geometrical Characterizamentioning

confidence: 98%

“…1) by a focused ion beam (FIB) [3,4]. The membranes are custom made on chips with size of 5 mm Â 5 mm, window size 100 lm Â 100 lm, thickness 200 nm and are able to resist 100 kPa of pressure differential.…”

Section: Leak Elements Fabrication and Their Geometrical Characterizamentioning

confidence: 99%

Nano-holes as standard leak elements

et al. 2014

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Keywords:Focused ion beam Nanotechnology Si 3 N 4 SEM STEM AFM Standard leak Gas flow meter Leak rate measurement Vacuum metrology DSMC a b s t r a c t Short tubes with diameters of the order of 200 nm were drilled into silicon nitride (Si 3 N 4 ) membranes of 200 nm thickness by focused ion beam technology and examined as leak elements for vacuum technology applications. These nano-holes exhibit molecular flow in the pressure range from high vacuum up to 10 kPa and can therefore be used as predictable leak elements for any non-condensable gas species. The geometrical dimensions were determined by SEM, STEM and AFM techniques. By Direct Simulation Monte Carlo method the conductances of these short tubes were calculated from the measured dimensions. The calculated conductance agreed with the value measured by comparison with a primary gas flowmeter within their respective uncertainties.

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Flow Conductance of a Single Nanohole

Cited by 32 publications

References 19 publications

Interacting bosons in one dimension and the applicability of Luttinger-liquid theory as revealed by path-integral quantum Monte Carlo calculations

Interacting bosons in one dimension and the applicability of Luttinger-liquid theory as revealed by path-integral quantum Monte Carlo calculations

Superfluid nanomechanical resonator for quantum nanofluidics

Nano-holes as standard leak elements

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