R. E. Packard

Observation of ‘third sound’ in superfluid 3He

Waves on the surface of a fluid provide a powerful tool for studying the fluid itself and the surrounding physical environment. For example, the wave speed is determined by the force per unit mass at the surface, and by the depth of the fluid: the decreasing speed of ocean waves as they approach the shore reveals the changing depth of the sea and the strength of gravity. Other examples include propagating waves in neutron-star oceans and on the surface of levitating liquid drops. Although gravity is a common restoring force, others exist, including the electrostatic force which causes a thin liquid film to adhere to a solid. Usually surface waves cannot occur on such thin films because viscosity inhibits their motion. However, in the special case of thin films of superfluid 4He, surface waves do exist and are called ‘third sound’. Here we report the detection of similar surface waves in thin films of superfluid 3He. We describe studies of the speed of these waves, the properties of the surface force, and the films superfluid density.

Quantum oscillations between two weakly coupled reservoirs of superfluid 3He

Arguments first proposed over thirty years ago, based on fundamental quantum-mechanical principles, led to the prediction that if macroscopic quantum systems are weakly coupled together, particle currents should oscillate between the two systems. The conditions for these quantum oscillations to occur are that the two systems must both have a well defined quantum phase, φ, and a different average energy per particle, μ: the term ‘weakly coupled’ means that the wavefunctions describing the systems must overlap slightly. The frequency of the resulting oscillations is then given by f = (μ2− μ1)/h, where h is Plancks constant. To date, the only observed example of this phenomenon is the oscillation of electric current between two superconductors coupled by a Josephson tunnelling weak link. Here we report the observation of oscillating mass currents between two reservoirs of superfluid 3He, the weak link being provided by an array of submicrometre apertures in a membrane separating the reservoirs. An applied pressure difference creates mass-current oscillations, which are detected as sound in a nearby microphone. The sound frequency (typically 6,000–200 Hz) is precisely proportional to the applied pressure difference, in accordance with the above equation. Thesesuperfluid quantum oscillations were first detected while monitoring an amplified microphone signal with the human ear.

Photographic studies of quantized vortex lines

A study of the behavior of systems of quantized vortex lines in rotating superfluid4He is described. Using a photographic technique, the positions of the vortex cores at the free surface of the liquid are recorded in the form of time-lapse motion pictures. The observation of stationary arrays of vortices are discussed and a comparison with the predictions of rectilinear vortex theory is made. Discrepancies between the observations and this theoretical model are noted, and the limitations of the experimental method are described. Several distinct types of periodic array motion have been observed. A description of their analysis as well as possible theoretical and experimental interpretations are given. The final part of this study involves phenomena associated with acceleration of the vessel. The analysis of film records and light signal amplitude measurements for repeated spinups of the vessel reveals statistical trends in the rate of appearance of vortices.

Superfluid helium quantum interference devices: physics and applications

We present an overview of recent developments related to superfluid helium quantum interference devices (SHeQUIDs). We discuss the physics of two reservoirs of superfluid helium coupled together and describe the quantum oscillations that result from varying the coupling strength. We explain the principles behind SHeQUIDs that can be built based on these oscillations and review some techniques and applications.

Discovery of a metastable π-state in a superfluid 3He weak link

Under certain circumstances,, a superconducting Josephson junction can maintain a quantum phase difference of π between the two samples that are weakly connected to form the junction. Such systems are called ‘π-junctions’ and have formed the basis of several experiments designed to investigate the much-debated symmetry of the order parameter of high-temperature superconductors. More recently, the possibility that similar phenomena might occur in another macroscopic quantum system — a pair of weakly coupled Bose–Einstein condensates — has also been suggested. Here we report the discovery of a metastable superfluid state, in which a quantum phase difference of π is maintained across a weak link separating two reservoirs of superfluid 3He. The existence of this state, which is the superfluid analogue ofa superconducting π-junction, is likely to reflect the underlying ‘p-wave’ symmetry of the order parameter of superfluid 3He, but a precise microscopic explanation is at present unknown.

Suppression of the critical current and the superfluid transition temperature of3He in a single submicron cylindrical channel

We report on an investigation into confined geometry effects and critical currents of superfluid3He in a single circular cylindrical channel. The diameter of the channel, 0.7 µm, is of the order of the (temperature-dependent) coherence length and its aspect ratio is ∼10. The reduction of the critical temperature demonstrates diffuse scattering on the solid walls of the microchannel. Using the Ginzburg-Landau formulation, we derive a model for the critical current and the critical temperature in a small, infinitely long, cylindrical channel with a circular cross section. The measured reductions of these quantities are in reasonable agreement with the predictions of the model.

A Technique for Photographing Vortex Positions in Rotating Superfluid Helium

A technique is described for photographing the positions of quantized vortex lines in rotating superfluid helium. Electron bubbles are trapped on the lines, and then extracted through the free surface and accelerated into a phosphor screen. Details of the apparatus are presented, along with examples of the data and the data collection techniques.

Quantum interference of superfluid 3He

Celebrated interference experiments have demonstrated the wave nature of light and electrons, quantum interference being the manifestation of wave–particle duality. More recently, double-path interference experiments have also demonstrated the quantum-wave nature of beams of neutrons, atoms and Bose–Einstein condensates. In condensed matter systems, double-path quantum interference is observed in the d.c. superconducting quantum interference device (d.c. SQUID). Here we report a double-path quantum interference experiment involving a liquid: superfluid 3He. Using a geometry analogous to the superconducting d.c. SQUID, we control a quantum phase shift by using the rotation of the Earth, and find the classic interference pattern with periodicity determined by the 3He quantum of circulation.

Fabrication of submicron apertures in thin membranes of silicon nitride

A technique for manufacturing submicron apertures used for investigating hydrodynamic quantum phenomena in the superfluids 4He and 3He is described. The apertures are fabricated in ∼100 nm thick suspended membranes of silicon nitride by using e‐beam lithography and reactive ion etching.

Observation of quantized circulation in superfluid 3He-B

We report the first observation of quantized circulation in superfluid {sup 3}He-{ital B}. The apparatus consists of a straight vibrating wire immersed in liquid {sup 3}He, which is cooled by a rotating nuclear demagnetization cryostat. The experiment is carried out at about 250 {mu}K. The superfluid at this temperature is in the ballistic quasiparticle regime. Circulation around the wire is found to be stable only when it takes on the values {minus}{ital h}/2{ital m}{sub 3}, 0, and +{ital h}/2{ital m}{sub 3}, where {ital h} is Plancks constant and {ital m}{sub 3} is the mass of the {sup 3}He atom. This experiment confirms that superfluid {sup 3}He-{ital B} is a Cooper-paired superfluid with a macroscopic quantum wave function.