Phonon-roton modes in liquid ⁴He coincide with Bose-Einstein condensation

¹ Institut Néel, CNRS-UJF - BP 166, F-38042 Grenoble Cedex 9, France, EU
² Institut Laue-Langevin - BP 156, F-38042 Grenoble, France, EU
³ Université Joseph Fourier, UFR de Physique - F-38041 Grenoble Cedex 9, France, EU
⁴ Department of Physics and Astronomy, University of Delaware - Newark, DE 19716-2593, USA

Received: 11 February 2012
Accepted: 15 May 2012

Abstract

We present neutron scattering measurements of the phonon-roton (P-R) and layer modes of liquid ⁴He confined in MCM-41 under pressure up to 38 bar. The data shows unambiguously that the P-R mode exists at low temperature only. As temperature is increased, there is a gradual transfer of intensity from the P-R mode to the normal liquid response, which lies at a lower energy at higher pressure. The transfer takes place with no observable mode broadening. The loss of P-R modes is identified with the loss of Bose-Einstein condensation (BEC). The mode giving rise to the specific heat, c_V, of liquid ⁴He in porous media (e.g., gelsil) at higher temperature is the layer mode since the energy of the mode extracted from c_V and the layer mode energy are the same.