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AIP conference proceedings

Third Sound Amplification and Detailed Balance

J. D. Eddinger, Fred M. Ellis

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Condensation of atoms from the vapor into a third sound resonance is expected to be capable of acoustic amplification. This results from normal to superfluid conversion that coherently accommodates atoms into the third sound velocity field. Consideration of third sound in light of the equilibrium detailed balance between vapor particles and the superfluid film provides further evidence that acoustic amplification is attainable.

DOI
10.1063/1.2354693

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Condensation of atoms from the vapor into a third sound resonance is expected to be capable of acoustic amplification. This results from normal to superfluid conversion that coherently accommodates atoms into the third sound velocity field. Consideration of third sound in light of the equilibrium detailed balance between vapor particles and the superfluid film provides further evidence that acoustic amplification is attainable.
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.
In order to minimize the possibility of spin flips due to interactions with and on the walls of a sample cell, spin-polarized hydrogen (H\ensuremath{\downarrow}) is studied in a 4He^{4}\mathrm{He}4He sample cell, i.e., a sample cell which has been coated with a film of superfluid 4He^{4}\mathrm{He}4He. At low temperatures it is expected that the most dense H\ensuremath{\downarrow} sample will first form in the physisorbed state on the 4He^{4}\mathrm{He}4He film. In this paper we examine in detail the hydrodynamic consequences of this layered film configuration. We derive the expression for third sound in the general case that the films are compressible and both films have undergone superfluid transitions. In this case two propagating modes will be seen which will provide an uneqivocal demonstration of a superfluid transition in the H\ensuremath{\downarrow} film. We specialize to various limiting cases: incompressible films, saturated and unsaturated films, and the normal fluid H\ensuremath{\downarrow} blanket. In our discussion we stress the point that even if the H\ensuremath{\downarrow} has not gone superfluid it will still shift the 4He^{4}\mathrm{He}4He third-sound speed, that this shift is a direct measure of the H\ensuremath{\downarrow} film areal density, and that the magnitude of this shift is expected to be well within the precision of present-day third-sound experimental techniques. Thus third sound is expected to be a primary diagnostic tool in the study of H\ensuremath{\downarrow} films.
Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χ nn ( q , ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S ( q , ω) in superfluid 4 He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below T c . In contrast to superfluid 4 He, LP is much larger in strongly interacting Fermi gases, being already of order unity for T ∼0.8 T c , thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S ( q , ω) (measured in pulse propagation studies) as compared with Imχ nn ( q , ω) (measured in two-photon Bragg scattering). We show that first and second sound in S ( q , ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S ( q , ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.
The wave propagation might be appropriately called quasi-particle sound, since in the long wave-length limit the only density fluctuations of importance are those produced by exciting a single quasi-particle from the condensate. Quasi-particle sound has essentially the same physical origin as zero sound in a Fermi liquid. The quasi-particle sound velocity will be temperature dependent, since the energy of a given quasi-particle depends on the thermal excitation of other quasi-particles. Superfluid hydrodynamics is richer than its Fermi liquid counterpart because one can have relative motion of the thermal quasi-particles and the condensate. This chapter describes the propagation of first and second sound in the hydrodynamic limit and then go on to a consideration of quasi-particle sound in the collisionless regime. A wide variety of irreversible phenomena which have as their physical origin collisions between the thermally-excited quasi-particles.