Physical Review Letters

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

Kenji Torizuka, Jukka P Pekola, Antti J. Manninen, Jukka M. Kyynarainen, Ross H. McKenzie

Published Jun 17, 1991• 54 citations

Abstract

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.

DOI: 10.1103/physrevlett.66.3152

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Pair Breaking by Two Phonons in 3 He-B

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

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

Physical Review LettersAug 7, 198910 citations

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

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

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

Renzhi Ling, J. Saunders, E. Roland Dobbs

Physical Review LettersJul 27, 198762 citations

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

R. S. Fishman, James A. Sauls

Physical review. B, Condensed matterMay 1, 198680 citations

Physical Review Letters

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

Kenji Torizuka, Jukka P Pekola, Antti J. Manninen, Jukka M. Kyynarainen, Ross H. McKenzie

Published Jun 17, 1991• 54 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevlett.66.3152

Related papers

Pair Breaking by Two Phonons in 3 He-B

J. Peters, Georg Eska

We report on pulsed zero-sound experiments in the B-phase of superfluid 3 He down to 0.6 mK. The investigated pressure and frequency range was 5 to 16 bar and 10 to 70 MHz, respectively. The dissipated energy within the 1 to 5 μs long sound pulses was 0.4 to 90 nJ, yielding up to 2.5 kW/m 2 sound intensities. We did not observe two-phonon absorption due to nonlinear coupling of zero sound to the J = 2 + mode within a resolution in attenuation of about Δα ∼ 0.1 cm −1 . However, a new structure was found in the attenuation spectrum. With increasing pulse power the absorption of this structure increased up to values of Δα ∼ 5 cm −1 . This structure depends on pulse setting, but always occurred at temperatures where pair breaking was induced by a two-phonon absorption process.We report on pulsed zero-sound experiments in the B-phase of superfluid 3 He down to 0.6 mK. The investigated pressure and frequency range was 5 to 16 bar and 10 to 70 MHz, respectively. The dissipated energy within the 1 to 5 μs long sound pulses was 0.4 to 90 nJ, yielding up to 2.5 kW/m 2 sound intensities. We did not observe two-phonon absorption due to nonlinear coupling of zero sound to the J = 2 + mode within a resolution in attenuation of about Δα ∼ 0.1 cm −1 . However, a new structure was found in the attenuation spectrum. With increasing pulse power the absorption of this structure increased up to values of Δα ∼ 5 cm −1 . This structure depends on pulse setting, but always occurred at temperatures where pair breaking was induced by a two-phonon absorption process.

Europhysics Letters (EPL)Sep 15, 19927 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

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

Antti J. Manninen, Harry Alles, А. В. Бабкин +2 more

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.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.

Physical Review LettersJun 22, 199244 citations

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

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

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

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}}^{+}

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.

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.

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.

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.

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.