Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.
Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.
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, 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.
Experimental results on the achievement of high degrees of quantum degeneration in two-dimensional atomic hydrogen (2D H↓) by the magnetic-compression method are analyzed by taking into account current data on the binding energy E a = 1.14(1) K of hydrogen atoms with the 4He surface and the constant K ab of the two-particle exchange recombination of adsorbed H atoms. The behavior of pair and three-particle correlation functions, as well as the transverse delocalization of the wavefunction of adsorbed atoms due to their interaction with each other, is taken into account self-consistently. A new mechanism of cooling of the compression region by means of the flow of H atoms on the helium surface with the subsequent evaporation and emission from a magnetic trap is proposed. This mechanism prevails at high densities, whereas the heat transfer at low densities occurs owing mainly to the interaction of ripplons with the phonons of the helium film. Existing data corroborate the achievement of the phase density σλ2 ≳ 10, which is certainly higher than the density necessary for both the arrangement of local coherence in 2D H↓ and its transition to the superfluid state. The results agree with the representations on quasi-condensation; however, direct evidence of this phenomenon is not revealed. The probability of three-particle dipole recombination that is corrected for the quantum correlation and delocalization is equal to 7(2) × 10−26 cm4 s−1 (T = 0.15, …, 0.21 K, B = 6.6 T, and σλ2 = 1, …, 9). The results are compared with other theoretical and experimental data.
The binding energy of a hydrogen atom to the surface of liquid 4He has been calculated to be at least 0.6K by Mantz and Edwards. This means that the properties of adsorbed spin-polarized hydrogen (H↑), a 2D Bose fluid, may soon be observed experimentally. Since 4He is used as a neutral coating for vessels to contain H↑ gas, adsorption onto the 4He surface may enhance the rate of recombination into H2 molecules. For given temperature and density in the gas, the amount of H↑ adsorbed depends strongly on the H↑-H↑ interaction on the 4He surface. We estimate the interaction in a simple approximation, and find that it limits the surface density to not more than 1014 cm-2. Nevertheless this density should be sufficient for a 2D superfluid transition to be observed, under conditions close to those achieved experimentally.
In superfluid systems several sound modes can be excited, such as, for example, first and second sound in liquid helium. Here, we excite running and standing waves in a uniform two-dimensional Bose gas and we characterize the propagation of sound in both the superfluid and normal regimes. In the superfluid phase, the measured speed of sound is in good agreement with the prediction of a two-fluid hydrodynamic model, and the weak damping is well explained by the scattering with thermal excitations. In the normal phase we observe a stronger damping, which we attribute to a departure from hydrodynamic behavior.
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.
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.