Producing and imaging quantum turbulence via pair-breaking in superfluid ${}^3\mathrm{He}\text{−}B$

Destroying superfluidity is a fundamental process and in fermionic superfluid such as ${}^3\mathrm{He}\text{−}B$ it splits Cooper pairs into thermal excitations, quasiparticles. At the lowest temperatures, a gas of these quasiparticle excitations is tenuous enough for the propagation to be ballistic. We describe here an exploitation of the ballistic quasiparticles as the “photons” to observe the local destruction of superfluid ${}^3\mathrm{He}\text{−}B$ by a mechanical resonator. We use a 5 by 5 pixel quasiparticle camera to image an emergence of quasiparticle excitations and a tangle of quantized vortices accompanying the pair-breaking. The detected quantum tangle is asymmetric around the mechanical resonator and is governed by the stability of vortices on the resonator surface. The vortex distribution shows that a conventional production of a quantum tangle via repetitive emission of vortex rings starts on the top surface of the generator and spreads around whole surface at high velocity when escaping vortex rings get retrapped by the moving resonator.

Figure 1

(Left) A sketch of the experimental cell used to controllably destroy the superfluidity and image an accompanying quantum vortex tangle. The quasiparticle source (blackbody radiator, BBR) illuminates a turbulent tangle created by the generator wire in front of a quasiparticle camera. The BBR consists of a box, containing two vibrating wires to generate (heater ${\mathrm{Q}}_{\mathrm{BBR}}$) and detect (thermometer ${\mathrm{T}}_{\mathrm{BBR}}$) excitations [10]. Excitations produced within the box quickly thermalise and emerge from a small hole (the radiator orifice), forming a wide beam of ballistic excitations. The beam propagates towards the quasiparticle camera [30], which is placed 2 mm away from the radiator's orifice and has a $5\times 5$ array of pixels. Each pixel in the camera consists of a 1-mm-diameter cylindrical cavity in a copper matrix with a miniature quartz tuning fork resonator inside that detects incident quasiparticles. The turbulent tangle reduces number the quasiparticles reaching the camera and forms a shadowgram. (Right) The force-velocity dependence of the generator wire. The onset velocity for excitation production is highlighted by an arrow. The inset depicts emission of a quasiparticle beam by the generator wire above the onset velocity.

Figure 2

Measurements of quasiparticle beam produced by the generator wire. (Left) Hinton-based diagrams of the detected quasiparticle flux for four generator wire velocities that are marked on the right panel as the dashed vertical lines. At $9\mathrm{mm}{\mathrm{s}}^{-1}$ the measured beam is narrowest and broadens as the velocity of the generator wire increases. Each diagram is normalized by the largest flux measured at the given velocity. The radius of a circle corresponds to the value of the flux measured by the pixel. The green circle shows the scaled size and location of the BBR orifice. (Right) The dependence of the detected power carried by incoming quasiparticles for the diagonal pixels of the camera as a function of the generator wire's velocity. The nondiagonal pixels were measured but omitted from the figure for clarity. They are, however, included in the left panel images. The central pixels of the camera detect a quasiparticle beam when the generator velocity reaches approximately $7.5\mathrm{mm}{\mathrm{s}}^{-1}$, while the peripheral pixels detect the change at higher velocities. The solid black line shows the power $P=Fv$ emitted by the generator wire, which we can measure directly. The power detected by each pixel can only be inferred, which is why the data points are presented in arbitrary units. However, if we sum this quantity over each pixel we get the dashed cyan curve, which is directly proportional within the noise to the total emitted power.

Figure 3

The blackbody radiator's beam as the ratio of detected and emitted quasiparticle flux. The solid lines correspond to an analytical model of the quasiparticle emission. The dashed lines and mesh shows a numerical simulation of quasiparticle beam behavior (see text).

Figure 4

The principle behind the measurement of turbulent shadow on camera pixel C3. The blue-open circles show the power measured by pixel C3 as a function of the generator wire velocity. The orange-dashed line equals the power detected by the pixel below the onset of pair-breaking and turbulence production on the generating wire and corresponds to the power emitted by the BBR. The blue-solid circles is the sum of the BBR and generator beam powers expected to reach pixel C3 in the absence of vortices. The observed flux reduction is the signature of Andreev reflection and presence of turbulence (see text). The inset illustrates the Andreev reflection of quasiparticles (red solid circles) and holes (blue open circles) approaching the velocity flow field surrounding a quantum vortex (see text).

Figure 5

“Shadowgram” of a turbulent tangle produced by the generator wire and illuminated by the blackbody radiator quasiparticle source. (Left) Hinton-based diagrams of the detected turbulence for four generator wire velocities that are marked on the left panel of this figure as the dashed vertical lines. The orange and blue colors correspond to positive and negative values, respectively. All the diagrams are normalized by the same value of fractional screening. The measured turbulent shadow differs drastically from the quasiparticle beams and indicates that vortex production is highly nonuniform around the wire. The green circle shows the scaled size and location of the BBR orifice. (Right) The dependence of fractional screening (amount of turbulence) for the diagonal pixels of the camera as a function of the generator wire's velocity. The camera detects vortices when the generator wire reaches the onset velocities for pair-breaking. The turbulent screening increases until a velocity of $12\mathrm{mm}{\mathrm{s}}^{-1}$ and then remains nearly constant.

Figure 6

A side-on sketch of the experiment with the most probable tangle configuration (not to scale). We illuminate the turbulence created by the wire with a quasiparticle flux emitted from the orifice of the blackbody radiator. A fraction of quasiparticles experience Andreev retroreflection, and retrace their path leaving a shadow behind the vortex tangle. The quasiparticle camera detects the reduction of flux and ‘images’ distribution of quantum turbulence formed by the wire. The insets A and B show tangle distribution resulting in symmetrical shadow: In (A) turbulence forms behind the wire's direction of motion, while in (B) turbulence develops above and below the wire.