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

We present neutron scattering measurements of the phonon-roton (P-R) and layer modes of liquid He 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, cV , of liquid He in porous media (e.g., gelsil) at higher temperature is the layer mode since the energy of the mode extracted from cV and the layer mode energy are the same. Copyright c © EPLA, 2012 There is a rich and long-standing debate on the nature of phonon-roton (P-R) modes in liquid He. The first picture is that they are collective density modes of a strongly interacting cold Bose liquid. This picture was initiated by Landau [1,2] and developed by Feynman [3] and others [4–7]. It forms the basis used today to calculate P-R mode energies with high accuracy [8–10]. In this picture gradual thermal broadening of modes with increasing temperature is expected [11–14]. The second is that they are density modes but Bose-Einstein condensation (BEC) plays a critical role in establishing them as sharply defined modes at low temperature, especially at higher wave vectors in the roton region Q≃ 2 Å and beyond. When there is BEC, the density and single-particle (SP) modes have the same energy [15–18]. There are therefore no independent, low-energy SP modes to which the P-R mode can decay. The P-R mode can decay only to itself, which becomes vanishingly small at low temperature. This picture originated with Bogoliubov [15] and was extended to Bose liquids by Gavoret and Nozières [16] and others [17,18]. The single-particle and density responses observed in the dynamic structure factor, S(Q,E), are coupled via the condensate. In this picture we expect a difference [19] in S(Q, E) below and above TBEC , the temperature at which BEC vanishes and above which independent SP modes can exist. We present new data on liquid He under pressure in MCM-41 which shows that the P-R mode at higher wave vectors exists at low temperature only. As the temperature is increased, there is a transfer of intensity from the P-R mode to new intensity at low energy. Above a specific temperature, denoted TBEC , there is no longer an observable P-R mode. TBEC is identified as the temperature at which BEC and as a result P-R modes no longer exist in the liquid. Above TBEC , all the intensity is at low energy, which is interpreted as the response of the normal liquid (NL) where there is no BEC. A simple transfer of intensity from the P-R mode to NL response with no mode broadening is observed at 34 bar because, under pressure, a) the P-R mode disappears at low temperature (TBEC ≃ 1.5K) before thermal broadening of the mode becomes significant and b) the “normal” liquid response lies at low energy (E ≃ 0) that can be readily distinguished from the P-R mode. The P-R mode is therefore not simply a sharp density mode in a cold Bose liquid which broadens with increasing temperature. Rather it depends for its existence as a sharp mode on BEC. The transfer of intensity is not so