Physical Review Letters

Observation of dispersion in theJ= 2+ collective modes of B3 by nonlinear acoustic spectroscopy

Antti J. Manninen, Harry Alles, А. В. Бабкин, Jukka P Pekola, Ross H. McKenzie

Published Jun 22, 1992• 44 citations

Abstract

Parametric excitation yields new results, which cannot be obtained by conventional linear spectroscopy, on the collective modes in superfluid $^{3}\mathit{B}$. In our ultrasonic experiments, performed in a chamber with four quartz crystals, we have excited the real squashing (J=${2}^{+}$) 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=${2}^{+}$ modes, and quantitatively we have been able to extract the collective-mode velocities from the line splittings in zero magnetic field.

DOI: 10.1103/physrevlett.68.3725

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Physical Review Letters

Observation of dispersion in theJ= 2+ collective modes of B3 by nonlinear acoustic spectroscopy

Antti J. Manninen, Harry Alles, А. В. Бабкин, Jukka P Pekola, Ross H. McKenzie

Published Jun 22, 1992• 44 citations

Publisher

Abstract

Parametric excitation yields new results, which cannot be obtained by conventional linear spectroscopy, on the collective modes in superfluid

^{3}\mathit{B}

. In our ultrasonic experiments, performed in a chamber with four quartz crystals, we have excited the real squashing (J=

{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}^{+}

modes, and quantitatively we have been able to extract the collective-mode velocities from the line splittings in zero magnetic field.

DOI: 10.1103/physrevlett.68.3725

Related papers

Fivefold splitting of the squashing collective mode of superfluid B3 by a magnetic field

Roman Movshovich, Eric Varoquaux, N. Kim +1 more

We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid $^{3}\mathit{B}$ 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 ${\mathit{J}}_{\mathit{z}}$ =+2 sublevel on magnetic field and compared with theory.We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid $^{3}\mathit{B}$ 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 ${\mathit{J}}_{\mathit{z}}$=+2 sublevel on magnetic field and compared with theory.

Physical review. B, Condensed matterJul 1, 199145 citations

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

Riitta H. Salmelin, Jukka P Pekola, Antti J. Manninen +9 more

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.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.

Physical Review LettersAug 7, 198910 citations

Ultrasonic spectroscopy of the J =1− collective mode in superfluid B3

Renzhi Ling, J. Saunders, E. Roland Dobbs

Measurements of the attenuation of zero sound in superfluid $^{3}\mathit{B}$ 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 ${J}_{z}$ =+1 and ${J}_{z}$ =-1 components. The measured G factor is in good agreement with theory. The ${J}_{z}$ =+1 resonance occurs in the pair excitation continuum and subtracts from the total attenuation, resulting in an antipeak.Measurements of the attenuation of zero sound in superfluid $^{3}\mathit{B}$ 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 ${J}_{z}$=+1 and ${J}_{z}$=-1 components. The measured G factor is in good agreement with theory. The ${J}_{z}$=+1 resonance occurs in the pair excitation continuum and subtracts from the total attenuation, resulting in an antipeak.

Physical Review LettersJul 27, 198762 citations

Two-phonon absorption by the real squashing mode in superfluid B3

Kenji Torizuka, Jukka P Pekola, Antti J. Manninen +2 more

We have observed in superfluid $^{3}\mathit{B}$ two-phonon absorption, which is one of the nonlinear effects recently predicted by McKenzie and Sauls. The J= ${2}^{+}$ real squashing mode was excited with two coincident sound pulses at the temperature ${\mathit{T}}^{+}$ , ${\mathrm{f}}_{\mathrm{signal}}$ + ${\mathit{f}}_{\mathrm{pump}}$ = ${\mathit{f}}_{\mathrm{rsq}}$ ( ${\mathit{T}}^{+}$ ), 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.We have observed in superfluid $^{3}\mathit{B}$ two-phonon absorption, which is one of the nonlinear effects recently predicted by McKenzie and Sauls. The J=${2}^{+}$ real squashing mode was excited with two coincident sound pulses at the temperature ${\mathit{T}}^{+}$, ${\mathrm{f}}_{\mathrm{signal}}$+${\mathit{f}}_{\mathrm{pump}}$=${\mathit{f}}_{\mathrm{rsq}}$(${\mathit{T}}^{+}$), 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.

Physical Review LettersJun 17, 199154 citations

Five-fold splitting of the squashing mode of superfluid 3He-B in a magnetic field

Roman Movshovich, Nam Kim, David M. Lee +1 more

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.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.

AIP conference proceedingsJan 1, 19890 citations

Response functions and collective modes of superfluid B3 in strong magnetic fields

R. S. Fishman, James A. Sauls

The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid $^{3}\mathit{B}$ are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim} ${q}^{2}$ ${v}_{f}^{2}$ /\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of $^{3}\mathit{B}$ depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid $^{3}\mathit{B}$ are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim}${q}^{2}$${v}_{f}^{2}$/\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of $^{3}\mathit{B}$ depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.

Physical review. B, Condensed matterMay 1, 198680 citations

Parametric excitation yields new results, which cannot be obtained by conventional linear spectroscopy, on the collective modes in superfluid

^{3}\mathit{B}

. In our ultrasonic experiments, performed in a chamber with four quartz crystals, we have excited the real squashing (J=

{2}^{+}

{2}^{+}

modes, and quantitatively we have been able to extract the collective-mode velocities from the line splittings in zero magnetic field.

We have conducted an ultrasonic pulse-time-of-flight investigation of the squashing mode of superfluid

^{3}\mathit{B}

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

{\mathit{J}}_{\mathit{z}}

=+2 sublevel on magnetic field and compared with theory.

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.

Measurements of the attenuation of zero sound in superfluid

^{3}\mathit{B}

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

{J}_{z}

=+1 and

{J}_{z}

=-1 components. The measured G factor is in good agreement with theory. The

{J}_{z}

=+1 resonance occurs in the pair excitation continuum and subtracts from the total attenuation, resulting in an antipeak.

We have observed in superfluid

^{3}\mathit{B}

two-phonon absorption, which is one of the nonlinear effects recently predicted by McKenzie and Sauls. The J=

{2}^{+}

real squashing mode was excited with two coincident sound pulses at the temperature

{\mathit{T}}^{+}

{\mathrm{f}}_{\mathrm{signal}}

{\mathit{f}}_{\mathrm{pump}}

{\mathit{f}}_{\mathrm{rsq}}

(

{\mathit{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.

The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid

^{3}\mathit{B}

are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim}

{q}^{2}

{v}_{f}^{2}

/\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of

^{3}\mathit{B}

depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.