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Cavitation in superfluid helium-4 at negative pressure

Context

Low-temperature liquid helium-4 is a model material for condensed matter physics for two reasons. First, atomic interactions are weak and quantum effects play an important role at the macroscopic scale. Second, liquid helium-4 can be obtained with remarkable purity. When preparing a sample of liquid helium-4 in an experimental cell, atomic or molecular impurities other than helium are frozen along the cell filling line or on the walls of the cell itself. It is then expected that the intrinsic properties of the liquid can be studied without being modified by the presence of impurities. In particular, liquid helium-4 is a system for probing in depth the metastable states of condensed matter and hoping to study homogeneous nucleation phenomena, i.e. not assisted by impurities in the liquid.

Our group creates metastable states of liquid helium by focusing an intense sound wave on it. In doing so, it is possible, during the decompression phases of the wave, to bring the liquid to pressures lower than the saturation vapor pressure; it is then in a metastable state where its pressure can be negative (see figure). The concept of negative pressure may be surprising but is easily understood by imagining a real fluid contained in a container. When the fluid particles push on the walls of the container, the fluid pressure is positive, when they pull on it thanks to van der Waals interactions, the pressure is negative!

For sufficient acoustic intensities, the liquid destabilizes and a bubble appears in the bulk of the liquid at the acoustic focus: this phenomenon is called cavitation. The aim of our experimental work is to provide measurements of thermodynamic properties of the liquid in the vicinity of the cavitation threshold in order to test predictions of nucleation theory in a quantum liquid.

Phase diagram of helium-4 and principle of acoustically driven negative pressure states of superfluid helium-4 (Liquid II)
 
 

Stimulated Brillouin gain spectroscopy of superfluid helium-4

Brillouin scattering refers to the scattering of light by a transparent medium due to the coupling of incoming photons with phonons of the material. The energy-momentum conservation in the photon-phonon collision imposes that the Brillouin scattered light is frequency shifted by the so called Brillouin frequency fB which is proportional to the value of the sound velocity in the material.  Stimulated Brillouin gain spectroscopy  is a pump/probe laser spectroscopy technique. When the frequency difference f=f1-f2 between the crossing probe (f2) and pump (f1) laser beams is approaching +/- fB, energy is transferred from the high frequency laser to the low frequency one. Monitoring the probe intensity as a function of f gives a resonance curve (the Brillouin gain spectrum) of central frequency +/- fB.We have developed a Stimulated Brillouin gain spectrometer allowing us to measure the speed of sound and hence the compressibility of a liquid on spatial scales of the order of 20 µm and temporal scales of the order of 200 ns(Djadaojee et al. 2020, Djadaojee et al. 2021). This allowed us to measure the compressibility of the metastable states of helium-4 produced by the acoustic methods previously described.

Artist view of our Brillouin spectrometer. The probe laser is CW and the pump is pulsed with a pulse duration of about 200 ns giving the time scale on which Brillouin frequencies are measured. Both lasers are focused and cross on a volume of about (20 µm)3  giving the spatial scale of the Brillouin frequency measurements.

Brillouin spectroscopy of metastable superfluid helium-4

By combining the method of acoustic production of the metastable states of the liquid (see context) and the use of our time-resolved spectrometer (previous section), it was possible for us to measure the speed of sound in the metastable states of the superfluid up to at the cavitation threshold (Djadaojee and Grucker 2022). This measurement associated with older measurements of the density of the liquid in the vicinity of destabilization (Qu An et al. 2015) allowed us to estimate the pressure of the fluid at the cavitation threshold. This estimate challenges previous estimates and suggests that, in this type of experiment, nucleation may in fact be heterogeneous. The quantized vortices of the superfluid would play the role of quantum defects on which the cavitation bubbles are created.

Detailed figure caption:

Top: principle; metastable states are produced on a time scale of about 500 ns (half period of the 1 MHz acoustic wave) and on a spatial scale of about 100 µm (size of the acoustic focus). Our Brillouin gain spectrometer allows sound velocity measurements on such a spatio-temporel domain.


Bottom: Brillouin frequency measurements at acoustic focus. Dash line: Brillouin frequency in the stable equilibrium state (no acoustic wave driving the metastable state).  Orange circles: Brillouin frequencies evolution for low acoustic drive; the Brillouin frequency oscillates around the equilibrium value at the acoustic driving frequency (1 MHz). Red circles:  Brillouin frequencies evolution for intense acoustic drive close to the cavitation threshold. The Brillouin frequency oscillation is not harmonic anymore due to non linear effects in the driving acoustic wave propagation.  Inset: Brillouin gain spectrum obtained at a given time.

Sound velocity measurements in the metastable states of superfluid helium-4. See detailed figure caption in the text.

Ongoing projects

We are currently investigating the possibility of making Stimulated Brillouin gain spectroscopy of condensed helium-4 using a single laser. Till now, the compressibility measurement is performed with two independent lasers. The idea is to take advantage of the particularly low value of the speed of sound in liquid or solid helium-4 (~ 250 m/s) corresponding to a Brillouin shift being quite small (~ 350 MHz). This allows, from a single laser, to produce both the pump beam and the probe beam by shifting a part of the laser using an acousto optic modulator. One advantage of this configuration is that, as the probe and the pump beams originated from the same laser, the beat note spectral width is considerably lowered with respect to one of a Brillouin spectrometer with two independent lasers.

On a longer term, our goal is to provide the first experimental measurement of the elastic constants of solid helium in a metastable (low density) state. Those constants are directly linked to the propagation speeds of the different acoustic modes and therefore accessible by Brillouin spectroscopy. Our group has discovered an unexpected instability in depressurized solid helium (for a review see Grucker 2019) and the behavior of the elastic constants when approaching it could certainly teach us more about the link or the absence of link between this instability and a potential supersolid state of helium-4 at low pressure.

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