Phonon-roton modes of liquid4He beyond the roton in the porous medium MCM-41

Abstract

We present neutron scattering measurements of the phonon-roton (P-R) mode of superfluid ${}^{4}$He confined in 47 \AA{} MCM-41 at $T=0.5$ K at wave vectors, $Q$, beyond the roton wave vector (${Q}_{R}=1.92$ \AA{}${}^{\ensuremath{-}1}$). Measurements beyond the roton require access to high wave vectors (up to $Q=4$ \AA{}${}^{\ensuremath{-}1}$) with excellent energy resolution and high statistical precision. Only one previous measurement in porous media (in aerogel) with low statistical precision has been reported. At $T=0.5$ K, we find that the P-R mode in MCM-41 extends out to wave vector $Q\ensuremath{\simeq}3.6$ \AA{}${}^{\ensuremath{-}1}$, with the same energy and zero width (within precision) as observed in bulk superfluid ${}^{4}$He. Layer modes in the roton region are also observed. Specifically, the P-R mode energy, ${\ensuremath{\omega}}_{Q}$, increases with $Q$ for $Q>{Q}_{R}$ and reaches a plateau at a maximum energy ${\ensuremath{\omega}}_{Q}=2\ensuremath{\Delta}$ where $\ensuremath{\Delta}$ is the roton energy, $\ensuremath{\Delta}=0.74$ $\ifmmode\pm\else\textpm\fi{}$ 0.01 meV in MCM-41. This upper limit means the P-R mode decays to two rotons if its energy exceeds 2$\ensuremath{\Delta}$. It also means that the P-R mode does not decay to two-layers modes. If the P-R could decay to two-layer modes, ${\ensuremath{\omega}}_{Q}$ would plateau at a lower energy, ${\ensuremath{\omega}}_{Q}=2{\ensuremath{\Delta}}_{L}$, where ${\ensuremath{\Delta}}_{L}=0.60$ meV is the energy of the roton-like minimum of the layer mode. Rather the P-R mode and the layer modes observed in porous media appear to be quite different modes with little interaction between them.