A novel approach to the observation of the condensate fraction in superfluid helium four

Halleý, J. W.

doi:10.1016/0921-4526(94)90211-9

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…We argued [4,5] that the transmission time associated with a condensate mediated transmission process should be both shorter than the time required for transmission of a sound wave through the slab and, more strikingly, independent of the thickness of the slab (in a calculation neglecting retardation effects in the atomic interactions):…”

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confidence: 99%

Variational Monte Carlo Studies of the Rate of Transmission of an Atomic Helium Beam through a Slab of Superfluid Helium by a Condensate Mediated Process

1997

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We report variational Monte Carlo calculations which give amplitudes and phases of the reflected and transmitted components of states representing scattering of helium atoms normally incident on a superfluid 4 He slab. The wave function describes a previously postulated condensate mediated process [J. W. Halley et al., Phys. Rev. Lett. 71, 2429(1993] and the results are consistent with uncertainty principle arguments suggesting that the transmission time for thin (but macroscopic) samples will be independent of slab thickness. [S0031-9007 (97)04554-7] PACS numbers: 67.40.DbWhile Bose condensation has been believed to be the fundamental reason for superfluidity in liquid helium four since London proposed it [1], direct experimental information concerning the nature of the condensate has remained sparse. Interpretation of deep inelastic scattering experiments [2,3] requires the impulse approximation, which in turn requires correction to account for final state interactions. Recently we proposed [4] an alternative experimental approach in which pulses of very low energy (ഠ1 K) helium atoms are to be fired at a suspended droplet or slab of superfluid helium. A model calculation suggested that transmission of a component of the incident beam through the slab would occur and that by measuring the dependence of the transmission on the area of the incident beam, one could experimentally confirm the existence of the condensate and extract information about it. The process by which this transmission would occur was envisioned to be the virtual excitation of the entire system into the ground state of the superfluid containing one extra particle, followed by reemission of the incident particle to form the final state. Crude estimates gave large rates for this process. However, a rigorous many-body calculation was required in order to study this possibility more fully. Here we report results of such a study which confirm several aspects of the previous work and provide estimates of transmission times and amplitudes.We consider the problem of transmission and reflection of an atomic beam incident normally on a slab of superfluid helium. Let the number of particles in the slab be N and consider the case of a single incident helium atom propagating along the z axis. We consider only elastic processes, normal incidence, and zero temperature here. Then the scattering states c must satisfy boundary conditions c ! ͑e ikz s 1 R e 2ikz s ͒ 3 c N ͑ r 1 2 r N cm , r 2 2 r N cm , . . . , r N 2 r N cm ͒ (1) as z s ! 2`for any s, and c ! Te ikz s c N ͑ r 1 2 r N cm , r 2 2 r N cm , . . . , r N 2 r N cm ͒ (2) as z s !`for any s. T jT je if and R jRje if 0 are transmission and reflection amplitudes. The condition jT j 2 1 jRj 2 1 is imposed by global current conservation. c N ͑ r 1 , . . . , r s21 , r s11 , . . . , r N11 ͒ is the N particle ground state wave function. We carry out a variational calculation of a steady state scattering wave function satisfying Eqs. (1) and (2) in which the amplitude jTj and phase f of T are obtained as a func...

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Variational Monte Carlo Studies of the Rate of Transmission of an Atomic Helium Beam through a Slab of Superfluid Helium by a Condensate Mediated Process

1997

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“…The most direct of such experiments are deep inelastic neutron-scattering measurements. 1,2 Several years ago [4][5][6][7] we proposed that observation of anomalous elastic helium atom transmission would also be an experimental signature of the existence of a condensate. We argued that the quantum mechanical amplitudes for absorption and reemission of bosons (say from state λ) from a system in which there are already n λ bosons present are respectively enhanced by factors √ n λ + 1 and √ n λ .…”

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Diffusion Monte Carlo calculation of rate of elastic transmission of a helium vapor beam through a slab of superfluid helium

Lutsyshyn

Halleý

2011

Phys. Rev. B

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We present the results of diffusion Monte Carlo calculations of the elastic transmission of a low-energy beam of helium atoms through a suspended slab of superfluid helium. These calculations represent a significant improvement on variational Monte Carlo methods which were previously used to study this problem. The results are consistent with the existence of a condensate-mediated transmission mechanism, which would result in very fast transmission of pulses through a slab.

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Phonon Mediated Helium Atom Transmission through Superfluid Helium Four

et al. 2005

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A novel approach to the observation of the condensate fraction in superfluid helium four

Cited by 4 publications

References 13 publications

Variational Monte Carlo Studies of the Rate of Transmission of an Atomic Helium Beam through a Slab of Superfluid Helium by a Condensate Mediated Process

Variational Monte Carlo Studies of the Rate of Transmission of an Atomic Helium Beam through a Slab of Superfluid Helium by a Condensate Mediated Process

Diffusion Monte Carlo calculation of rate of elastic transmission of a helium vapor beam through a slab of superfluid helium

Phonon Mediated Helium Atom Transmission through Superfluid Helium Four

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