The viscosity of liquid helium 3

Fluctuation-response relation as a probe of long-range correlations in nonequilibrium quantum and classical fluids

The absence of a simple fluctuation-dissipation theorem is a major obstacle for studying systems that are not in thermodynamic equilibrium. We show that for a fluid in a nonequilibrium steady state characterized by a constant temperature gradient the commutator correlation functions are still related to response functions; however, the relation is to the bilinear response of products of two observables, rather than to a single linear response function as is the case in equilibrium. This modified fluctuation-response relation holds for both quantum and classical systems. It is both motivated and informed by the long-range correlations that exist in such a steady state and allows for probing them via response experiments. This is of particular interest in quantum fluids, where the direct observation of fluctuations by light scattering would be difficult. In classical fluids it is known that the coupling of the temperature gradient to the diffusive shear velocity leads to correlations of various observables, in particular temperature fluctuations, that do not decay as a function of distance, but rather extend over the entire system. We investigate the nature of these correlations in a fermionic quantum fluid and show that the crucial coupling between the temperature gradient and velocity fluctuations is the same as in the classical case. Accordingly, the nature of the long-ranged correlations in the hydrodynamic regime also is the same. However, as one enters the collisionless regime in the low-temperature limit the nature of the velocity fluctuations changes: they become ballistic rather than diffusive. As a result, correlations of the temperature and other observables are still singular in the long-wavelength limit, but the singularity is weaker than in the hydrodynamic regime.

Universal sound diffusion in a strongly interacting Fermi gas

Transport of strongly interacting fermions is crucial for the properties of modern materials, nuclear fission, the merging of neutron stars, and the expansion of the early Universe. Here, we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting atomic Fermi gas by studying sound propagation and its attenuation through the coupled transport of momentum and heat. In the normal state, the sound diffusivity D monotonically decreases upon lowering the temperature, in contrast to the diverging behavior of weakly interacting Fermi liquids. Below the superfluid transition temperature, D attains a universal value set by the ratio of Planck's constant and the particle mass. Our findings inform theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons, and quarks.

A switched vibrating-hot-wire method for measuring the viscosity and thermal conductivity of liquids

A method involving a vibrating hot wire is proposed for measuring the viscosity and thermal conductivity of liquids. A platinum wire is bent into a semicircular shape and immersed in the sample liquid in the presence of a static magnetic field. Alternating current is then applied to the wire, causing it to vibrate and generate heat. At low frequency, the frequency response of the vibration is used to calculate the viscosity. At high frequency, the vibration amplitude of the wire is less than the molecular free path, and the thermal conductivity of the sample is obtained from the temperature dependence of the resistance. The proposed method is validated using water, toluene, anhydrous ethanol, and ethanediol as the test samples. The measurement uncertainty is estimated to be 1.5% (k = 1) for thermal conductivity and 0.7% (k = 2) for viscosity.

Mass Flow through Solid ^{3}He in the bcc Phase

A number of experiments have shown that mass can be transported through solid ^{4}He at temperatures as low as 16 mK, with features that suggest superflow. But the nature of this flow remains unclear. The Fermi isotope ^{3}He provides the possibility of a direct comparison to a solid in which quantum effects are even more important but superfluidity is not expected. We have made flow measurements on high purity bcc ^{3}He, using the same cell in which we observed a superfluidlike response in hcp ^{4}He when pressure differences were applied. We observed flow but, in marked contrast to ^{4}He, it decreased monotonically with temperature. Near melting, the flow was thermally activated with an energy of 0.85 K, but some flow remained even at 30 mK. The flow rates in the solid were essentially constant below 100 mK, even in low density samples that remelted at low temperatures. The very different behaviors of solid ^{3}He and ^{4}He support the interpretation of superflow in ^{4}He. Although such superflow is not possible in ^{3}He, the temperature-independent flow below 100 mK indicates that the flow in this regime also has a quantum origin. The flow must involve defects and, based on the magnitude of the flow and comparisons to other experiments, we conclude that in both the thermal and the quantum regimes the flow involves motion of dislocations via thermally activated or tunneling motion of kinks.

Second sound tracking system

It is common that a physical system resonates at a particular frequency, whose frequency depends on physical parameters which may change in time. Often, one would like to automatically track this signal as the frequency changes, measuring, for example, its amplitude. In scientific research, one would also like to utilize the standard methods, such as lock-in amplifiers, to improve the signal to noise ratio. We present a complete He ii second sound system that uses positive feedback to generate a sinusoidal signal of constant amplitude via automatic gain control. This signal is used to produce temperature/entropy waves (second sound) in superfluid helium-4 (He ii). A lock-in amplifier limits the oscillation to a desirable frequency and demodulates the received sound signal. Using this tracking system, a second sound signal probed turbulent decay in He ii. We present results showing that the tracking system is more reliable than those of a conventional fixed frequency method; there is less correlation with temperature (frequency) fluctuation when the tracking system is used.

Operating Nanobeams in a Quantum Fluid

Microelectromechanical (MEMS) and nanoelectromechanical systems (NEMS) are ideal candidates for exploring quantum fluids, since they can be manufactured reproducibly, cover the frequency range from hundreds of kilohertz up to gigahertz and usually have very low power dissipation. Their small size offers the possibility of probing the superfluid on scales comparable to, and below, the coherence length. That said, there have been hitherto no successful measurements of NEMS resonators in the liquid phases of helium. Here we report the operation of doubly-clamped aluminium nanobeams in superfluid 4He at temperatures spanning the superfluid transition. The devices are shown to be very sensitive detectors of the superfluid density and the normal fluid damping. However, a further and very important outcome of this work is the knowledge that now we have demonstrated that these devices can be successfully operated in superfluid 4He, it is straightforward to apply them in superfluid 3He which can be routinely cooled to below 100 μK. This brings us into the regime where nanomechanical devices operating at a few MHz frequencies may enter their mechanical quantum ground state.

Anomalous vacuum energy and stability of a quantum liquid

We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives a negative contribution to a system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.