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Physical Review Letters

R− Rotons and Quantum Evaporation

M. B. Sobnack, John C. Inkson

Published May 3, 1999• 8 citations
Publisher

Abstract

We apply Beliaev's theory to superfluid ${}^{4}\mathrm{He}$ with a free surface at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0\phantom{\rule{0ex}{0ex}}\mathrm{K}$ to derive equations of motion valid in bulk helium, through the surface, and in the vacuum. We solve the equations and calculate probabilities for the one-to-one surface scattering processes as a function of energy, both for fixed parallel momenta and fixed angles of incidence. In particular, in contrast with the recent calculations of Stringari and co-workers, we show that ${R}^{\ensuremath{-}}$ rotons do quantum evaporate atoms in the presence of phonons. We also compare our quantum evaporation results with those of experimental simulations.

DOI
10.1103/physrevlett.82.3657

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We apply Beliaev's theory to superfluid 4He{}^{4}\mathrm{He}4He with a free surface at T=0KT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0\phantom{\rule{0ex}{0ex}}\mathrm{K}T=0K to derive equations of motion valid in bulk helium, through the surface, and in the vacuum. We solve the equations and calculate probabilities for the one-to-one surface scattering processes as a function of energy, both for fixed parallel momenta and fixed angles of incidence. In particular, in contrast with the recent calculations of Stringari and co-workers, we show that R\ensuremath−{R}^{\ensuremath{-}}R\ensuremath− rotons do quantum evaporate atoms in the presence of phonons. We also compare our quantum evaporation results with those of experimental simulations.
We have shown that rotons as well as phonons can evaporate 4He^{4}\mathrm{He}4He atoms in a single-quantum process. Measurements of the time of flight and the angular distribution of the evaporated atoms clearly distinguish between evaporation by phonons and rotons. The results indicate that energy and the parallel component of momentum are conserved at the free liquid surface.
A beam of ${\mathit{R}}^{\mathrm{\ensuremath{-}}}$ rotons, i.e., rotons which have oppositely directed group velocity and momentum, is reated by condensing an atom beam onto the surface of liquid 4He^{4}\mathrm{He}4He. ${\mathit{R}}^{\mathrm{\ensuremath{-}}}$ rotons are identified by quantum evaporation and their time of flight. Measured signal shapes agree well with those modeled. Signal sizes are compared with those from atoms specularly reflected from the He surface, from which it is estimated that the quantum efficiency for the condensation or evaporation process is high and of the order of 0.5 for angles of incidence where mainly rotons are created. ${\mathit{R}}^{\mathrm{\ensuremath{-}}}$ rotons can specularly reflect from a solid-liquid He interface with high probability, if the interface is particularly good.
Theory of superfluid ^{4}He shows that, due to strong correlations and backflow effects, the density profile of a vortex line has the character of a density modulation and it is not a simple rarefaction region as found in clouds of cold bosonic atoms. We find that the basic features of this density modulation are represented by a wave packet of cylindrical symmetry in which rotons with a positive group velocity have a dominant role: The vortex density modulation can be viewed as a cloud of virtual excitations, mainly rotons, sustained by the phase of the vortex wave function. This suggests that in a vortex reconnection some of these rotons become real so that a vortex tangle is predicted to be a source of nonthermal rotons. The presence of such vorticity induced rotons can be verified by measurements at low temperature of quantum evaporation of ^{4}He atoms. We estimate the rate of evaporation and this turns out to be detectable by current instrumentation. Additional information on the microscopic processes in the decay of quantum turbulence will be obtained if quantum evaporation by high energy phonons should be detected.
Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.