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Physica B Condensed Matter

Theoretical analysis of an experiment to measure the condensate fraction in superfluid helium four

C. E. Campbell, J. W. Halleý

Published Feb 1, 1994• 3 citations
Publisher
DOI
10.1016/0921-4526(94)90596-7

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In previous work on the interaction of single helium atoms with a slab of superfluid helium the authors found a large amplitude, dependent on the condensate fraction, for transmission with re-emission of a helium atom at the other side of the slab. Here they report a variational formulation of the problem which permits a time dependent calculation and which does not require any perturbation expansion. The variational principle involves a minimization of the expectation value of the square of the difference H-E. They will present preliminary results of a variational Monte Carlo calculation using a simple variational form for the wave function.

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We present a phenomenological analysis of an experiment to observe the condensate fraction of helium-4 by firing low-energy pulses of helium atoms at suspended droplets of the superfluid and observing the resulting emission of helium atoms from the fluid. Emission occurs through a conventional process in which rotons are produced and propagate to the other side of the droplet, and through a second process depending on the existence of the condensate. If A is the area of the incoming beam, the cross section scales with A2{\mathit{A}}^{2}A2 (first process) and A4{\mathit{A}}^{4}A4 (second process), respectively, for small A. Aspects of a fully many body calculation and the performance of such an experiment are briefly discussed.
In previous work on the interaction of single helium atoms with a slab of superfluid helium the authors found a large amplitude, dependent on the condensate fraction, for transmission with re-emission of a helium atom at the other side of the slab. Here they report a variational formulation of the problem which permits a time dependent calculation and which does not require any perturbation expansion. The variational principle involves a minimization of the expectation value of the square of the difference H-E. They will present preliminary results of a variational Monte Carlo calculation using a simple variational form for the wave function.