Collective Modes and $f$-Wave Pairing Interactions in Superfluid ${}^3\mathrm{He}$

Precision measurements of collective mode frequencies in superfluid ${}^3\mathrm{He}\mathrm{\text{−}}B$ are sensitive to quasiparticle and $f$-wave pairing interactions. Measurements were performed at various pressures using interference of transverse sound in an acoustic cavity. We fit the measured collective mode frequencies, which depend on the strength of $f$-wave pairing and the Fermi liquid parameter $F_2^s$, to theoretical predictions and discuss what implications these values have for observing new order parameter collective modes.

Figure 1

Schematic of the collective mode spectrum for ${}^3\mathrm{He}\mathrm{\text{−}}B$ normalized to twice the value of the gap at zero temperature, $2{\Delta }^{+}(0)$. From low to high frequency we show the real squashing mode (dashed line), the imaginary squashing mode (solid line), and $2{\Delta }^{+}(T)$ (dotted line), the threshold for pair-breaking. The straight line is an example of a measurement frequency crossing the imaginary squashing mode and pair-breaking.

Figure 2

Interference of transverse sound near the imaginary squashing mode using 99.9484 MHz sound at various pressures near 9 bar. Note that as the pressure is changed the frequency of the ISQ mode changes accordingly since the gap amplitude, Eq. (2), is approximately proportional to $T_c$. The cessation of wiggles and the bend in the acoustic impedance marks the location of the imaginary squashing mode, delineated by the arrow for 9.31 bar (see Fig. 3).

Figure 3

Temperatures of maxima and minima in impedance for determining the ISQ mode crossing at 99.9484 MHz.

Figure 4

Imaginary squashing mode crossings as determined by the oscillation period shift analysis of Fig. 3 corrected to be at constant pressures. The fits are to Eq. (4).

Figure 5

Pressure dependence of (top) $a_{-}(0,P)/\sqrt{12/5}$ and (bottom) $x_3^{-1}$ from the fits of Eq. (4) to the ISQ mode frequencies. The straight lines through the data are guides to the eye. The open symbols use the Greywall temperature scale [5]. The dashed lines (top) correspond to a $\pm 1\%$ change to this scale. The values of $x_3^{-1}$ are obtained with $F_2^s$ from Ref. 2. The dashed line (bottom) shows the effect of adding 0.25 to $F_2^s$.