Optical measurement of the equation of state of bulk liquid helium-4 around 1 K

Abstract

Using a stimulated Brillouin gain spectroscopy technique, we have measured the equation of state of bulk liquid helium-4 at ∼ 1 K between 0 and 10 bars. Our results are in very good agreement with previous measurements and with theoretical equations of states. However our specific method allows for the first time to determine it on space / time scales as narrow as 35 µm / 190 ns. This technique is of particular interest for solving a remaining debate about the value of the homogeneous cavitation pressure of liquid 4 He at T ∼ 1 K.

Brillouin Spectroscopy of Metastable Superfluid Helium-4

“…Slightly higher temperature and higher frequency measurements suggest the absence of dispersion at our temperature (∼ 1 K) and frequency (∼ 300 MHz) [16,17,18,19]. We used this SB gain spectrometer to measure the EoS of stable liquid helium-4 (P > 0) at T ∼ 1 K [13] and the experimental EoS obtained is in very good agreement with the theoretical one at T = 0 K [20,21,22].…”

“…For that purpose, we have developed a Stimulated Brillouin (SB) gain spectrometer capable of measuring the Brillouin frequencies of superfluid 4 He on such a narrow spatio-temporal domain [11,12,13]. Brillouin scattering refers to the scattering of light by a transparent medium due to the coupling of incoming photons with phonons of the material [14].…”

“…We sample these data in time by interval of δt = 100 ns. One then gets the Brillouin gain spectrum g(f, t) from which we can extract the corresponding value of the Brillouin frequency f B (t) as detailed in refs [12,13]. Finally by varying t we are able to record a "movie" of the local variations of the Brillouin frequencies as the wave propagates through the acoustic focus.…”

Measurement of the Equation of State of Superfluid Helium-4 at Negative Pressure

“…Brillouin frequencies are measured on a space scale of (2w) 3 = 40 3 µm 3 . We used this SB gain spectrometer to measure the equation of state (EOS) of stable liquid helium-4 between 0 and 10 bar at T ∼ 1 K by measuring the Brillouin frequency dependence on the static pressure [17]. The experimental EOS obtained is in very good agreement with the theoretical one at T = 0 K [20,21,22].…”

“…1 right). In order to measure the compressibility of the metastable states of superfluid 4 He, we have recently developed a Stimulated Brillouin (SB) gain spectrometer capable of measuring the Brillouin frequencies on such a narrow spatio-temporal domain [15,16,17].…”