Viscosity of Liquid Helium below the λ-Point

Kapitza, P. L.

doi:10.1038/141074a0

Cited by 730 publications

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“…DOI: 10.1103/PhysRevLett.103.265301 PACS numbers: 67.85.De, 03.75.Kk, 47.37.+q, 67.90.+z In 1938, Kapitza, and independently Allen and Misener, discovered that liquid 4 He below the -point can flow almost frictionless. Kapitza named this behavior superfluidity [1,2]. Many of the properties of superfluid helium also appear in dilute Bose-Einstein condensation (BEC).…”

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Damping of Superfluid Flow by a Thermal Cloud

et al. 2009

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One of the principal signatures of superfluidity is the frictionless flow of a superfluid through another substance. Here, we study the flow of a Bose-Einstein condensate through a thermal cloud and study its damping for different harmonic confinements and temperatures. The damping rates close to the collisionless regime are found to be in good agreement with Landau damping and become smaller for more homogeneous systems. In the hydrodynamic regime, we observe additional damping due to collisions, and we discuss the implications of these findings for superfluidity in this system. DOI: 10.1103/PhysRevLett.103.265301 PACS numbers: 67.85.De, 03.75.Kk, 47.37.+q, 67.90.+z In 1938, Kapitza, and independently Allen and Misener, discovered that liquid 4 He below the -point can flow almost frictionless. Kapitza named this behavior superfluidity [1,2]. Many of the properties of superfluid helium also appear in dilute Bose-Einstein condensation (BEC). The most striking signatures of superfluidity in BEC are quantized vortices [3,4], second sound [5], Josephson oscillations [6], and persistent flow [7]. In contrast to liquid helium, where the interatomic interaction is too strong to investigate the microscopic properties of superfluidity, the interactions in BEC are much weaker. The study of superfluid flow in dilute BECs can therefore deepen our understanding of superfluidity.In this Letter, the flow of a BEC (the superfluid) through a thermal cloud is studied in a harmonic potential by exciting a dipole oscillation of the BEC, whereas the thermal cloud initially remains at rest. In the hydrodynamic regime, this out-of-phase mode of the trapped Bose gas is the analog of the usual second sound mode in bulk superfluid helium [8]. For this second sound dipole mode, we study for the first time its frequency and damping rate from the collisionless to the hydrodynamic regime. In contrast to liquid helium, our analysis allows for a direct measurement of the position of the superfluid component (condensed atoms) with respect to the normal fluid (thermal atoms), which allows for an unequivocal determination of the second sound dipole mode.The thermal cloud can be tuned from the hydrodynamic regime into the collisionless regime, in which the meanfree path of the thermal atoms is larger than the axial size of the cloud. As we will show, the damping of the second sound dipole mode in a collisionless, partly condensed BEC is primarily caused by Landau damping; i.e., meanfield interactions mediate the transfer of energy from the condensate to the thermal cloud, leading to the damping of collective modes. Landau damping was first discussed by Landau in the context of the damping of plasma oscillations and plays a key role in a broad variety of fields, for instance the damping of phonons in metals, the damping of quarks and gluons in quark-gluon plasmas, and the anomalous skin effect in metals.Previously, some experiments have been performed in which the BEC and the thermal cloud move with respect to each other [9,10]. In the latter e...

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Damping of Superfluid Flow by a Thermal Cloud

et al. 2009

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“…Hh, 05.30.Jp, 67.85.Bc Nearly a century after the first observation of the lambda transition in liquid helium [1], a quantitative, first-principles description of strongly-correlated bosons remains a challenge. After the transition was recognized as the onset of superfluidity [2], the connection with Bose-Einstein condensation (BEC) was proposed[3], but it was Bogoliubov's work [4] pointing out that the dispersion of the elementary BEC excitations satisfy the Landau criterion for superfluidity [5] that motivated weaklyinteracting BEC studies to investigate superfluid properties. In weakly-interacting systems, the many-body properties do not depend on the shape of the interaction potential, but only on the s-wave scattering length, a 0 , and the boson fluid acts as point-like interacting particles [6].…”

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Nonperturbative Predictions for Cold Atom Bose Gases with Tunable Interactions

et al. 2010

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We derive a theoretical description for dilute Bose gases as a loop expansion in terms of compositefield propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this non-perturbative approach describes a large interval of coupling-constant values, satisfies Goldstone's theorem, yields a BoseEinstein transition that is second-order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading order large-N expansion.PACS numbers: 03.75. Hh, 05.30.Jp, 67.85.Bc Nearly a century after the first observation of the lambda transition in liquid helium [1], a quantitative, first-principles description of strongly-correlated bosons remains a challenge. After the transition was recognized as the onset of superfluidity [2], the connection with Bose-Einstein condensation (BEC) was proposed[3], but it was Bogoliubov's work [4] pointing out that the dispersion of the elementary BEC excitations satisfy the Landau criterion for superfluidity [5] that motivated weaklyinteracting BEC studies to investigate superfluid properties. In weakly-interacting systems, the many-body properties do not depend on the shape of the interaction potential, but only on the s-wave scattering length, a 0 , and the boson fluid acts as point-like interacting particles [6].Unlike liquid helium, cold atoms remain point-like even when the scattering length is tuned near a Feshbach resonance. Then, strongly-correlated cold atom bosons offer the exciting prospect of studying point-like strongly interacting bosons, possibly in the universal regime where the scattering length greatly exceeds the inter-particle distance and the latter becomes the only relevant length scale [7]. This hope appeared thwarted when it was shown that the three-body loss rate in cold atom traps scales as a 4 0 near a Feshbach resonance [8]. In accordance, the universal regime was reached only in ultra-cold fermionic gases [9], where the three-body loss is reduced by virtue of the Pauli exclusion principle. However, the recent observation that three-body losses are strongly suppressed in optical lattices when the average number of bosons per site is two or less [10], rekindles the prospect of studying medium and strongly-correlated cold atom bosons. Novel cold-atom trap technologies that produce stable, flat potentials bound by a sharp edge [11], suggest the study of finite-temperature properties such as the BEC transition temperature T c and the superfluid to normal fluid ratio and depletion, at fixed density, ρ.At finite temperature, the description of BEC's remains a challenge even in the weakly-interacting regime. Standard approximations such as the Hartree-FockBogoliubov and the Popov schemes, generally fall within the Hohenberg and Martin classification [12] of conserving and gapless approximations, which implies that they either violate Goldstone's theorem or general conservation laws [13]. These approximations generally pred...

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“…[1] The low viscosity of a superfluid was successfully explained by Landau. The lack of dissipation between the liquid and its surroundings is rooted in the dispersion relation for elementary excitation of bosons.…”

Section: Introductionmentioning

confidence: 99%

Potential generation and path‐integral Monte Carlo in study of microscopic superfluidity

Zeng

Roy

2014

Int J of Quantum Chemistry

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The idea of a macroscopic Andronikashvili experiment used to measure superfluid fraction of bulk liquid 4 He can be ported into the realm of spectroscopic studies to measure the superfluid fraction of microscopic systems at the nanoscale. Theoretical studies are needed to fully unravel the superfluid information contained in such a microscopic Andronikashvili experiment. Two aspects of the theoretical studies, the generation of accurate and efficient potential energy surfaces, and the methodology of path-integral Monte Carlo simulations are briefly introduced in this article.

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Viscosity of Liquid Helium below the λ-Point

Cited by 730 publications

References 2 publications

Damping of Superfluid Flow by a Thermal Cloud

Damping of Superfluid Flow by a Thermal Cloud

Nonperturbative Predictions for Cold Atom Bose Gases with Tunable Interactions

Potential generation and path‐integral Monte Carlo in study of microscopic superfluidity

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