Part I. Collective Excitation of a Fermi Gas. Part II. Superfluidity of Nuclear Matter and Liquid Helium -3.

V. N. Minasyan

First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute Bose gas, where presence atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition is defined by a condition for the Bose-Einstein transition, which transforms reflected neutron pair modes to single neutron modes.

Victor Nikolaevich Popov

Bao-Xi Sun

The collective excitation of the nuclear matter is analyzed in a bosonizated formula of Landau Fermi liquid theory. When the nonlinear self-interacting terms of the scalar meson are taken into account in the Walecka model, the collective excitation energies of the nuclear matter can be obtained self-consistently. It shows that the calculation results are consistent with the corresponding experimental data of the nucleus ${}^{208}Pb$ when the quantum number of the orientation of the orbital angular momentum $m$ is zero. Moreover, the cases with the nonzero $m$ values are also studied, it manifests that the collective excitation energy with the fixed nonzero $m$ value are almost invariant when the quantum number of the orbital angular momentum $l$ changes. However, the collective excitation energy of the nuclear matter decreases with the absolute value of $m$ increasing. The direct interaction between two nucleons near the Fermi surface only changes the Fermi velocity, while the exchange interaction causes the collective excitation of the nuclear matter. At this point, it is different from the traditional views in nuclear physics, which announce that the random phase approximation is essential to generate the nuclear collective excitation states.

Dieter Zawischa

Sascha Hoinka, Carlos Kuhn, James P. Denier +5 more

Li You

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.