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Physical Review Letters

Creation and identification of R− rotons in liquid He4 and an estimate of their probability for quantum evaporation

G. M. Wyborn, A. F. G. Wyatt

Published Jul 16, 1990• 14 citations
Publisher

Abstract

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 $^{4}\mathrm{He}$. ${\mathit{R}}^{\mathrm{\ensuremath{-}}}$ 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.

DOI
10.1103/physrevlett.65.345

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A beam of R\ensuremath−{\mathit{R}}^{\mathrm{\ensuremath{-}}}R\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. R\ensuremath−{\mathit{R}}^{\mathrm{\ensuremath{-}}}R\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. R\ensuremath−{\mathit{R}}^{\mathrm{\ensuremath{-}}}R\ensuremath− rotons can specularly reflect from a solid-liquid He interface with high probability, if the interface is particularly good.
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.
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.
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 ${R}^{\ensuremath{-}}$ rotons do quantum evaporate atoms in the presence of phonons. We also compare our quantum evaporation results with those of experimental simulations.
We studied the low-energy limit of atomsurface scattering and the phenomenon of quantum reflection by using hydrogen atoms and the surface of liquid helium. Measuring the specular reflectivity of a liquid-helium-covered hemispheric mirror for a beam of hydrogen atoms we obtained information on elastic and inelastic scattering phenomena. At 100 mK, reflectivities larger than 90% were achieved; this can be used to demonstrate atomic beam focusing. Approximately three-fourths of the atoms escaping from a small orifice in a cell were reflected back into the cell. The dominant inelastic processes at work here are surface absorption and direct inelastic scattering over small angles under excitation of surface ripplons (quantized capillary waves). Helium-covered surfaces maybe useful for atomic-beam manipulation of atomic hydrogen.
We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors QQQ, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with 3He^{3}\mathrm{He}3He concentrations xxx between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction n0{n}_{0}n0​ and the momentum distributions of 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He atoms. We find that n0{n}_{0}n0​ increases somewhat above the pure 4He^{4}\mathrm{He}4He value when 3He^{3}\mathrm{He}3He is added; e.g., from ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at x=0x=0x=0 to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at x=15−−20x=15--20\phantom{\rule{0.2em}{0ex}}%x=15−−20. This agrees with predictions but is less than the only previous measurement. We find a 4He^{4}\mathrm{He}4He kinetic energy K4{K}_{4}K4​ for pure 4He^{4}\mathrm{He}4He that agrees with previous determinations. K4{K}_{4}K4​ decreases somewhat with increasing 3He^{3}\mathrm{He}3He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The 3He^{3}\mathrm{He}3He response is not well reproduced by a Fermi-gas momentum distribution, n(k)n(\mathbf{k})n(k). Rather an n(k)n(\mathbf{k})n(k) having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This n(k)n(\mathbf{k})n(k) is consistent with calculated n(k)n(\mathbf{k})n(k). Thus agreement between theory and experiment is obtained comparing n(k)n(\mathbf{k})n(k) in contrast to earlier findings based on comparing calculated and observed 3He^{3}\mathrm{He}3He kinetic energies.