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Physical Review Letters

Coupling of zero sound to the real squashing mode in rotating B3

Riitta H. Salmelin, Jukka P Pekola, Antti J. Manninen, Kenji Torizuka, M. Berglund, Jukka M. Kyynarainen, Olli V. Lounasmaa, George Tvalashvili, O. V. Magradze, Eric Varoquaux, Olivier Avenel, V. P. Mineev

Published Aug 7, 1989• 10 citations
Publisher

Abstract

Rotation of superfluid $^{3}\mathit{B}$ in an magnetic field enhances the coupling of the nonzero ${\mathrm{m}}_{\mathrm{J}}$ substrates of the real squashing collective mode to the zero sound, and the fivefold line splitting becomes observable even when H is parallel to \ensuremath{\Omega} and to the direction of sound propagation. Equilibrium vortex lattices and vortex-free states can be distinguished by their characteristic absorption spectra. The dependence of the sound attenuation on the angular velocity in magnetic fields up to 32 mT is reported; the data are qualitatively compared with theory.

DOI
10.1103/physrevlett.63.620

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AIP conference proceedings•Jan 1, 1989•0 citations
Rotation of superfluid 3B^{3}\mathit{B}3B in an magnetic field enhances the coupling of the nonzero mJ{\mathrm{m}}_{\mathrm{J}}mJ​ substrates of the real squashing collective mode to the zero sound, and the fivefold line splitting becomes observable even when H is parallel to \ensuremath{\Omega} and to the direction of sound propagation. Equilibrium vortex lattices and vortex-free states can be distinguished by their characteristic absorption spectra. The dependence of the sound attenuation on the angular velocity in magnetic fields up to 32 mT is reported; the data are qualitatively compared with theory.
We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid 3B^{3}\mathit{B}3B in a magnetic field. All five of the expected Zeeman sublevels for this J=${2}^{\mathrm{\ensuremath{-}}}$ mode were observed. The investigation was done at a very low temperature (T/${\mathit{T}}_{\mathit{c}}$0.35) to reduce the quasiparticle broadening that tends to smear the collective modes and makes resolution of the individual sublevels impossible. Variation of the pressure was used to sweep the collective-mode frequencies through the operating frequency, 137.6 MHz of the resonant-sound transducers. Both group-velocity spectroscopy and pulse-shape analysis were used for identification of different sublevels. Performing experiments at different orientations of the sound propagation with respect to magnetic-field direction (parallel, perpendicular, 55\ifmmode^\circ\else\textdegree\fi{}, and 13\ifmmode^\circ\else\textdegree\fi{}) was the key to observation of all five modes and their identification. The Land\'e g factor was obtained from the linear dependence of the Jz{\mathit{J}}_{\mathit{z}}Jz​=+2 sublevel on magnetic field and compared with theory.
Parametric excitation yields new results, which cannot be obtained by conventional linear spectroscopy, on the collective modes in superfluid 3B^{3}\mathit{B}3B. In our ultrasonic experiments, performed in a chamber with four quartz crystals, we have excited the real squashing (J=2+{2}^{+}2+) modes by two simultaneous sound waves which are mutually either parallel, orthogonal, or antiparallel. Qualitatively these results are in agreement with the theoretical dispersion relation of the J=2+{2}^{+}2+ modes, and quantitatively we have been able to extract the collective-mode velocities from the line splittings in zero magnetic field.
Measurements of the attenuation of zero sound in superfluid 3B^{3}\mathit{B}3B show coupling to a collective mode in applied magnetic fields at frequencies \ensuremath{\nu}\ensuremath{\sim}2\ensuremath{\Delta}(T), which is identified as the J${=1}^{\mathrm{\ensuremath{-}}}$ mode. The attenuation as a function of reduced temperature in zero magnetic field is subtracted from that measured in magnetic fields up to 80 mT to reveal both the Jz{J}_{z}Jz​=+1 and Jz{J}_{z}Jz​=-1 components. The measured G factor is in good agreement with theory. The Jz{J}_{z}Jz​=+1 resonance occurs in the pair excitation continuum and subtracts from the total attenuation, resulting in an antipeak.
We have observed in superfluid 3B^{3}\mathit{B}3B two-phonon absorption, which is one of the nonlinear effects recently predicted by McKenzie and Sauls. The J=2+{2}^{+}2+ real squashing mode was excited with two coincident sound pulses at the temperature T+{\mathit{T}}^{+}T+, fsignal{\mathrm{f}}_{\mathrm{signal}}fsignal​+fpump{\mathit{f}}_{\mathrm{pump}}fpump​=frsq{\mathit{f}}_{\mathrm{rsq}}frsq​(T+{\mathit{T}}^{+}T+), under 0, 2.7, and 3.5 bars pressure. The heights of the attenuation peaks scale almost linearly with the energy of the higher-intensity wave, in qualitative agreement with the theory. Furthermore, a satellite peak appears even in zero magnetic field, which originates from the reflected wave.
A wave-acoustics theory has been developed to describe the propagation of zero sound parallel to vortex lines in rotating 3A^{3}\mathit{A}3A. We show that a diffraction ``shadow'' is formed in which the wave amplitude is suppressed by interference around vortices. This phenomenon contributes to the experimentally observed effect of rotation on the sound amplitude and exceeds the attenuation at large core radii. The dependence of the diffraction contribution on the angular velocity changes drastically at the transition from vortices with a finite core to coreless vortices when the magnetic field is decreased to zero. We derive conditions for the applicability of the effective-medium theory and the classical geometrical acoustic method in describing sound propagation along vortices.
We have conducted an ultrasonic pulse‐time‐of‐flight investigation of the squashing mode of the superfluid 3He‐B in a magnetic field. All five of the expected Zeeman sublevels for this J=2− mode were observed. The investigation was done at very low temperature (T/Tc<0.35) to reduce the quasi‐particle broadening that tends to smear the collective modes and makes resolution of the individual sublevels impossible. Variation of the pressure was used to sweep the collective modes’ frequencies through the operating frequency, 137.6 MHz of the resonant sound transducers. Both group velocity spectroscopy and pulse‐shape analysis were used for identification of different sublevels. Performing experiment at different orientations of the sound propagation with respect to magnetic field direction (parallel, perpendicular, 55 and 13 degrees) was the key to observation of all 5 modes and their identification. The Landé g factor was obtained from the linear dependence of the Jz=+2 mode on magnetic field and compared to theory.