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Europhysics Letters (EPL)

Pair Breaking by Two Phonons in 3 He-B

J. Peters, Georg Eska

Published Sep 15, 1992• 7 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/20/2/008

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Water flowing down a pipe experiences viscous drag that causes it to lose energy and slow down. A superfluid, such as liquid helium (3He and 4He) or electrons in a superconductor, can flow without friction when in contact with a wall. This fascinating phenomenon, or superfluidity, was discovered by Kapitza [1], Allen and Misener [2] in 1937. The formation of a superfluid is related to the formation of a Bose--Einstein condensate (BEC). 4He is a boson as its total spin is zero, an integer. Condensation in fermionic 3He liquid occurs through composite bosons of paired atoms in a process similar to electron pairing in a superconductor. To explain the peculiar properties of superfluid helium, Landau considered a superfluid to be comprised of two parts: a ‘pure’ superfluid component with zero entropy and viscosity, and a normal component that behaves like ordinary fluid. 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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 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.
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.
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid 4He^{4}\mathrm{He}4He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
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.
Water flowing down a pipe experiences viscous drag that causes it to lose energy and slow down. A superfluid, such as liquid helium (3He and 4He) or electrons in a superconductor, can flow without friction when in contact with a wall. This fascinating phenomenon, or superfluidity, was discovered by Kapitza [1], Allen and Misener [2] in 1937. The formation of a superfluid is related to the formation of a Bose--Einstein condensate (BEC). 4He is a boson as its total spin is zero, an integer. Condensation in fermionic 3He liquid occurs through composite bosons of paired atoms in a process similar to electron pairing in a superconductor. To explain the peculiar properties of superfluid helium, Landau considered a superfluid to be comprised of two parts: a ‘pure’ superfluid component with zero entropy and viscosity, and a normal component that behaves like ordinary fluid. An interesting manifestation of this two-fluid model is the existence of two types of oscillations, the ‘first and second sounds’ as named by Landau. The ‘first sound’ is a wave that propagates at constant entropy per particle, just like sounds in ordinary fluids. It propagates with pressure and density oscillations. ‘Second sound’, unlike what its name suggests, is not audible as it propagates at nearly constant pressure (isobaric oscillation). Here, entropy density takes the role of pressure/density in normal sound waves. Historically, the observation of the second sound in superfluid helium, and the measurement of its speed, played a crucial role in understanding the nature of superfluid helium. The speed of the second sound can be used to determine the superfluid fraction, i.e. the ratio of the superfluid density to the total fluid density [3,4]. In the past decades, the field of ultracold atomic gases has developed into a fertile ground for studying superfluid physics, as the inter-particle interactions between two atoms can be tuned using the so-called Fano–Feshbach resonances. Systematic studies on Fermi gases can be preformed in the limit of strong interactions, whose properties are difficult to predict but important to the understanding of strongly correlated quantum systems of many particles, such as high-temperature superconductors, quark–gluon plasmas and neutron stars. Quantitative determination of the superfluid fraction in strongly interacting Fermi gases has been an elusive goal of scientists for many years, as the methods that allow the determination of the superfluid fraction in liquid helium cannot be directly applied to ultracold gases. For example, to excite the second sound in liquid helium, a local heat pulse can be created by passing a current through a heating wire submersed in the liquid. The heat pulse can then be detected at the other end of the liquid using a temperature sensitive sensor as illustrated in Fig. 1(a). Such methods cannot be implemented with ultracold atomic gas ensembles that typically contain only about hundreds of thousand atoms at μK (1 millionth of a kelvin) temperatures. Further adding to the difficulties, the propagation of the second sound in liquid helium usually involves no density variation/oscillation. This means that the second sound could not be detected easily with the absorption imaging technique typically used for probing cold atoms, assuming that the strongly interacting Fermi gases behave very much like strongly interacting bosonic liquid helium (4He). (a) Excitation and detection of the second sound in superfluid helium; (b) local heating through the power modulation of an excitation laser beam; (c) the detection of the second sound in a strongly interacting Fermi gas with direct absorption imaging. Recently, the group of Professor Rudolf Grimm from the University of Innsbruck (Austria), in collaboration with a theoretical team from the Trento University (Italy) led by Professors Sandro Stringari and Lev Pitaevskii, successfully measured the speed of second sound in a resonantly interacting Fermi gas using a simple and elegant method. Their results were published in [5]. To observe the second sound, the authors created a local heat pulse at the center of an elongated trapped gas by creating a short burst of modulation to the power of a light beam intercepting this gas (see Fig. 1b). They then measured the speed of the second sound by observing the movement of a thermal-induced density dip along the elongated gas (Fig. 1c). Taking advantage of the inhomogeneous density distributions of the superfluid atoms in the trap, they ingeniously determined the temperature dependence of the superfluid fraction without needing to vary the temperature of the samples. The observation of the second sound in the strongly interacting Fermi gases opens up a new horizon for studying the superfluid properties with tunable interactions. Knowing the speed of second sound can provide a lot of valuable information, allowing physicists working on many-body theories to falsify their models and theories. It demonstrates the importance of using experimentally measured quantities, such as the equation of state employed here, to calibrate and to supplement theoretical investigations. Significant new advances will follow in the understanding of superfluidity of many strongly interacting particles, where faithful theoretical modeling and calculations are impossible at the microscopic level.
Second sound attenuation, a distinctive dissipative hydrodynamic phenomenon in a superfluid, is crucial for understanding superfluidity and elucidating critical phenomena. Here, we report the observation of second sound attenuation in a homogeneous Fermi gas of lithium-6 atoms at unitarity by performing Bragg spectroscopy with high energy resolution in the long-wavelength limit. We successfully obtained the temperature dependence of second sound diffusivity [Formula: see text] and thermal conductivity κ. Furthermore, we observed a sudden rise-a precursor of critical divergence-in both [Formula: see text] and κ at a temperature of about 0.95 superfluid transition temperature [Formula: see text]. This suggests that the unitary Fermi gas has a much larger critical region than does liquid helium. Our results pave the way for determining the universal critical scaling functions near quantum criticality.