Of the three superfluid phases of He3, the one labeled He3-B has often been considered the “dull” superfluid because it lacked the interesting anisotropies of the A and A1 phases. The B phase has now become more intriguing: Over the past few years, ultrasonic spectroscopy has uncovered ever more details of the excited states of He3-B, and has revealed that the collective excitations of this many-body system have a form reminiscent of simple atomic spectra. As Peter Wolfle from the Technical University of Munich told us, the superfluid He3-B acts like “a giant molecule in momentum space.” The excited states, observed through strong absorption peaks in the transmission of ultrasound, have essentially the structure one would expect from a triplet p-wave pairing of the helium atoms. Measurements have uncovered effects that are the equivalent of Zeeman splitting and the Paschen-Back effect. Some of these measurements were described at the International Symposium on Quantum Fluids and Solids held at Sanibel Island, Florida, in April. (The story on page 23 describes other work on He3-B presented at the same meeting.)
Of the three superfluid phases of He3, the one labeled He3-B has often been considered the “dull” superfluid because it lacked the interesting anisotropies of the A and A1 phases. The B phase has now become more intriguing: Over the past few years, ultrasonic spectroscopy has uncovered ever more details of the excited states of He3-B, and has revealed that the collective excitations of this many-body system have a form reminiscent of simple atomic spectra. As Peter Wolfle from the Technical University of Munich told us, the superfluid He3-B acts like “a giant molecule in momentum space.” The excited states, observed through strong absorption peaks in the transmission of ultrasound, have essentially the structure one would expect from a triplet p-wave pairing of the helium atoms. Measurements have uncovered effects that are the equivalent of Zeeman splitting and the Paschen-Back effect. Some of these measurements were described at the International Symposium on Quantum Fluids and Solids held at Sanibel Island, Florida, in April. (The story on page 23 describes other work on He3-B presented at the same meeting.)
The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.
The past two decades have seen great progress in our understanding of the properties of condensed helium 3. Research on He3 in our lab (see figure 1 for its modern form) began in 1958. At that time the properties of the more abundant isotope, helium 4, were rather well known: A phase transition at about 2 K transforms it from a normal liquid to a superfluid, a liquid that under some conditions will flow without viscous drag. The explanation for this behavior is rooted in concepts from the condensation of an ideal Bose–Einstein gas. But He3 obeys Fermi–Dirac statistics; would it show any likeness to a Fermi gas or liquid? Would it also exhibit a transition to superfluidity?
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.
The field of Bose-Einstein condensation (BEC) in dilute atomic gases provides a fruitful playground to test well-developed theories of quantum fluids. Research using BECs can address open questions relating to the many-body aspects of two-component quantum liquids, namely the interaction between the hydrodynamic normal and the superfluid component at finite temperatures. After the first realization of BEC some pilot experiments have been carried out, but detailed experiments are missing. This has to be compared to the case of liquid helium II, where many experiments since the 1950s have added to our understanding of novel phenomena in quantum liquids, like collective excitations, first and second sound, and others. One of the drawbacks of liquid helium is that the interactions are so strong that a clear distinction between the two components is difficult and the interpretation of the phenomena remains ambiguous. Most experimental studies of dilute Bose-Einstein condensed gases use clouds, which are in the collisionless regime. The reason for the lack of detailed experiments in BECs to study quantum liquids and in particular the hydrodynamical aspects of it, is the limited number of atoms (typically 1--10 million) in the experiments leaving the thermal atoms virtually collisionless. Efforts to decrease the mean free path by increasing the confinement limits the lifetime of the sample, since the density is limited by three-body decay. Experiments on dilute clouds of cold atoms are generally conducted in highly asymmetric traps. In these elongated, cigar-shaped geometries the mean free path of the atoms can become much shorter than the size of the cloud in the long, axial direction, but at the same time exceeds the size in the other, radial directions. In this so-called hydrodynamic-collisionless regime the system can be considered radially collisionless and axially hydrodynamic. In our setup we have created BECs containing up to 300 million sodium atoms by evaporation of atoms in an axially strongly decompressed trap with an aspect ratio of 1:65. Hot atoms created in three-body collisions are able to leave the sample in this highly asymmetric trap, before they can heat other atoms in an avalanche. The sample is axially hydrodynamic, but due to the large aspect ratio collisionless in the radial direction. Such samples are ideal for the observation of the interaction between the superfluid and normal fluid component of the cloud. In this thesis we describe the setup which is used to reach the hydrodynamic regime and we describe a novel implementation of the well-known phase contrast imaging technique. Next, we study collective excitations in the crossover from the collisionless toward the hydrodynamic regime, we determine the heat conduction in a cold, hydrodynamic thermal cloud and observe the propagation of a thermal wave in the two-fluid regime. Furthermore, we study the friction between the superfluid and normal fluid component of the cloud. In the final chapters of this thesis we study the propagation of second sound, as well as the formation and propagation of shock waves.
We have used the acoustic Faraday effect in superfluid 3He to perform high resolution spectroscopy of an excited state of the superfluid condensate, called the imaginary squashing mode. With acoustic cavity interferometry we measure the rotation of the plane of polarization of a transverse sound wave propagating in the direction of the magnetic field from which we determine the Zeeman energy of the mode. We interpret the Landé g factor, combined with the zero-field energies of this excited state, using the theory of Sauls and Serene, to calculate the strength of f-wave interactions in 3He.