Resolving the puzzle of sound propagation in liquid helium at low temperatures (original) (raw)
Related papers
Nonlinear acoustics of superfluid helium
Soviet Physics Uspekhi, 1990
The results of theoretical investigation of first and second sound in mathrmHmathrmemathrmImathrmI\mathrm{H}\mathrm{e}\mathrm{I}\mathrm{I}mathrmHmathrmemathrmImathrmI are reviewed. The variety of "standard" nonlinear phenomena are described such as nonlinear transformation of wave modes into one another, formation of shock fronts, nonlinear renormaJization of sound velocity, stability and parametric transformation of nonlinear waves etc. The effects of mathrmdmathrmamathrmmmathrmI)mathrmgmathrmimathrmn\mathrm{d}\mathrm{a}\mathrm{m}_{\mathrm{I}^{)}\mathrm{g}}\mathrm{i}\mathrm{n}mathrmdmathrmamathrmmmathrmI)mathrmgmathrmimathrmn and dispersion are studied. The possibility of self-focusing of the second sound in cubically nonlinear case as well as in the quadratically one is discussed. We also presented the investigation of stochastic wave fields and acoustic turbulence. In conclusion some of the open problems and the paths for further development touched upon are discussed.
2011
We review current understanding of the non-equilibrium dynamics of collective quantum systems. We describe an approach based on the Hamiltonian formulation of superfluid hydrodynamics. It is shown that, in the presence of constant energy pumping, the nonlinear coupling of fluctuations in the density and entropy strongly affects the nonequilibrium dynamics of the system. We use the results obtained to analyze the properties of out-of-equilibrium superfluid 4He and of exciton polariton Bose-Einstein condensates, both in semiconductor quantum wells and in graphene layers in presence of high magnetic field.
arXiv (Cornell University), 2001
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/nll1n_0/n\ll 1n0/nll1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0ll1(n-n_0)/n_0\ll 1(n−n_0)/n_0ll1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.
This book introduces the theoretical description and properties of quantum fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a minor extent, superfluid helium, but the underlying concepts are relevant to other forms of quantum fluids such as polariton and photonic condensates. The book is pitched at the level of advanced undergraduates and early postgraduate students, aiming to provide the reader with the knowledge and skills to develop their own research project on quantum fluids. Indeed, the content for this book grew from introductory notes provided to our own research students. It is assumed that the reader has prior knowledge of undergraduate mathematics and/or physics; otherwise, the concepts are introduced from scratch, often with references for directed further reading.
Sound propagation in a Bose-Einstein condensate at finite temperatures
Physical Review A, 2009
We study the propagation of a density wave in a magnetically trapped Bose-Einstein condensate at finite temperatures. The thermal cloud is in the hydrodynamic regime and the system is therefore described by the two-fluid model. A phase-contrast imaging technique is used to image the cloud of atoms and allows us to observe small density excitations. The propagation of the density wave in the condensate is used to determine the speed of sound as a function of the temperature. We find the speed of sound to be in good agreement with calculations based on the Landau two-fluid model.
Parametric generation of second sound in superfluid helium: Linear stability and nonlinear dynamics
Physical Review B, 2001
We report the experimental studies of a parametric excitation of a second sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties of the instability, namely, the threshold, its temperature and geometrical dependencies, and the spectra of SS just above the onset were measured. They were found to be in a good quantitative agreement with the theory. (ii) It was shown that the mechanism of SS amplitude saturation is due to the nonlinear attenuation of SS via three wave interactions between the SS waves. Strong low frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with exponentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are discussed with respect to the nonlinear SS behavior. The first evidence of Gaussian statistics of the wave amplitudes for the parametrically generated wave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed new effects. Below the instability threshold, the SS phase conjugation as a result of three-wave
Mixtures of Euler’s fluids and second sound propagation in superfluid helium
Zeitschrift für angewandte Mathematik und Physik, 2006
We study the second sound propagation in superfluid helium using the theoretical background developed in a recent paper [1], through which this phenomenon, both in crystals and in Helium II, can be inserted in a unique framework. In particular, considering an initial rectangular heat pulse and exploiting the selection rules of the physical shocks, a wide phenomenology of travelling shock waves, including the very special case of double shocks, is explained. . 76A25, 35L60, 35L67.
We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau's two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii-Kosterlitz-Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. Our predictions can be readily examined in current experimental setups for 2D dilute Bose gases. PACS numbers: 67.85.De, 03.75.Kk, 05.30.Jp
Second sound and the superfluid fraction in a resonantly interacting Fermi gas
Bulletin of the American Physical Society, 2013
Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and neutron stars. More recently, ultracold atomic gases have emerged as new superfluid systems with unprecedented possibilities to control interactions and external confinement. Here we report the first observation of `second sound' in an ultracold Fermi gas with resonant interactions. Second sound is a striking manifestation of the two-component nature of a superfluid and corresponds to an entropy wave, where the superfluid and the non-superfluid components oscillate in opposite phase, different from ordinary sound (`first sound'), where they oscillate in phase. The speed of second sound depends explicitly on the value of the superfluid fraction, a quantity sensitive to the spectrum of elementary excitations. Our measurements allow us to extract the temperature dependence of the superfluid fraction, which in strongly interacting quantum gases has been an inaccessible quantity so far.