Table of contents

The spin kinetics of ³He in contact with nanosized crystalline powders LaF₃ has been studied by NMR methods at the temperature 1.5 K. The ³He longitudinal relaxation time increases proportionally to the magnitude of the external magnetic field and the transverse relaxation time does not depend on the magnetic field. Relaxation of the gaseous and liquid ³He in contact with nanosized crystalline powder LaF3 takes place by the ³He adsorbed layer. The nuclear magnetic relaxation of adsorbed ³He layer on the surface of LaF₃ nanoparticles is due to the two-dimensional spin-diffusion motion.

A matter wave ghost imaging mechanism is proposed and demonstrated theoretically. This mechanism is based on the Talbot-Lau effect. Periodic gratings of matter wave density, which appear as a result of interference of atoms diffracted by pulses of an optical standing wave, are utilized to produce the reference wave and the signal wave simultaneously for the ghost imaging. An advantage of this mechanism is that during the imaging process, the beam-splitter is not needed, which highly simplifies the experimental setup and makes the ghost imaging possible in the field of matter wave.

The mechanical properties of crystals are strongly affected by dislocation mobility. Impurities can bind to dislocations and interfere with their motion, causing changes in the crystal's shear modulus and mechanical dissipation. In ⁴He crystals, the only impurities are ³He atoms, and they can move through the crystal at arbitrarily low temperatures by quantum tunneling. When dislocations in ⁴He vibrate at speeds v < 45 μm/sec, bound ³He impurities move with the dislocations and exert a damping force B_3v on them. In order to characterize ⁴He dislocation networks and determine the ³He binding energy, it is usually assumed that B₃ is proportional to the concentration of ³He bound to the dislocations. In this preliminary report, we determine B₃ in a crystal with 2.32 ppm ³He and compare with our previous measurements of B₃ in natural purity ⁴He crystals to verify the assumption of proportionality.

We investigate strong-coupling properties of a unitary Fermi gas consisting of two different species with different masses. Including pairing fluctuations within the self-consistent T-matrix approximation, we calculate the single-particle density of states in the normal state. We show that the pseudogap phenomenon, which is characterized by a dip structure in the density of states around ω = 0, appears more remarkably in the light mass component than in the heavy mass component. As a result, the pseudogap temperature, which is determined as the temperature at which the pseudogap disappears in the density of states, is higher in the former than in the latter. We also find that this different pseudogap temperatures lead to the existence of two kinds of pseudogap regions. That is, one is the ordinary pseudogap regime where the pseudogap appears in both the component, and the other case is that the light mass component only exhibits the pseudogap phenomenon. As the origin of these component- dependent pseudogap phenomena, we point out the importance of different Fermi temperatures between the two components. Since the formation of hetero-Cooper pairs and their condensation are expected in various systems, such as a ⁶Li-⁴⁰K Fermi gas mixture, an exciton (polariton) gas, as well as color superconductivity, our results would be useful for the understanding of strong-coupling properties of these novel Fermi condensates.

In order to elucidate the ultra-low temperature behavior of solid ⁴He, simultaneous measurements of longitudinal ultrasound (US) and torsional oscillation have been made. Changes in attenuation and velocity of US at 10 MHz have been measured in polycrystalline hcp ⁴He samples (0.3 or 20 ppm of ³He impurity) grown in a 1 kHz torsional oscillator (TO). In a 0.3 ppm ³He sample, the US attenuation and velocity were found to depend on the US drive voltage at temperatures below 70 mK where the anomalies in the TO frequency and dissipation were also observed. The US attenuation at low T (10 mK) decreased monotonically as the drive voltage was decreased but then remained small and constant as the drive voltage was increased again. The US velocity change at low T was negative with respect to the high-T (400 mK) value, contrary to the positive sign expected from the known variation in the shear modulus. In a 20 ppm ³He sample, both the US and TO anomalies shifted to 150 mK. The amplitude dependence and hysteresis of US attenuation were related to pinning of dislocations by ³He impurities, and nonlinear spatial variations of the amplitude of US pulses were derived.

In superfluid ³He-A, it was theoretically predicted that the half-quantum vortex (HQV) is stable where the order parameters and are perpendicular to each other in the order parameter configuration. However, the existence of the HQV has not been reported experimentally. Now we are trying to detect the HQV in superfluid ³He-A confined in the parallel-plates sample cell with 12 μm gap, where and are perpendicular to each other, by using a NMR technique under a rotation at ISSP. In order to detect the HQV, we improved the magnet system for NMR so far, but we have not observed the HQV yet. We report here the experimental details and some results for investigating the HQV.

We show by numerical renormalization group calculations that a quantum defect with a two-dimensional rotational degree of freedom, immersed in a bath of fermionic particles with angular momentum scattering, exhibits an extended 2CK phase without fine-tuning of parameters. It is stabilized by a correlation effect which causes the states with angular momentum m=±1 to be the lowest energy states of the defect. This level crossing with the noninteracting m = 0 ground state is signaled by a plateau in the temperature-dependent impurity entropy at S(T) = k_B ln 2, before the 2CK ground state value S(0) = k_B In is reached.

We have used a Source-Gate-Drain configuration with electrons on liquid helium (the Helium Field Effect Transistor "He-FET") to study the transport of "classical" electrons through narrow channels. The channels, formed by the split gate of the device, were between ten and a hundred μm long and several μm wide, and could be blocked completely by a negative bias voltage applied to the gate. In contrast to previous experiments, where the electron densities in source and drain were nearly the same and the system therefore was close to equilibrium, in the present measurement the drain was empty. The transport of the electrons through the channel was initiated by opening the gate with a short positive pulse with a duration down to nanoseconds, and the amount of electrons which passed during this time was registered. In this way, we could determine for the first time the transport properties of such a system on a nanosecond time scale and far off equilibrium. Measurements with varying gate voltage provide clear evidence for the formation of lanes of electrons in the channels.

In this paper we study the thermodynamics of a crystalline solid by applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q₁ and q₂. We find a (q₁, q₂)-deformed Hamiltonian and consequently the q-deformed thermodynamic quantities. The results led us to interpret the deformation parameters acting as disturbance or impurities factors modifying the characteristics of a crystal structure. More specifically, we found the possibility of adjusting the Fibonacci oscillators to describe the change of thermal conductivity of a given element as one inserts impurites.

We have performed calculations of the properties of bubbles in liquid helium containing small numbers of electrons. We use an iterative approach to estimate the energy of the electrons inside a bubble of given shape, and then vary the shape of the bubble to find the minimum energy. For helium-3 we show that at zero applied pressure bubbles containing 4 electrons are unstable against breakup into single electron bubbles, but are stable at pressures between -0.23 and -0.15 bars. Bubbles with 6 electrons are stable between -0.17 and -0.05 bars and bubbles with 12 electrons are stable over the pressure range -0.1 to 0.08 bars.

We have extended our measurements of the properties of exotic negatively-charged ions in superfluid helium-4. We measured the ion mobility using the time-of-of-flight method at temperatures in the range between 1.03 and 1.16 K. Ions were generated by an electrical discharge produced by applying a voltage to sharp tips in the helium vapor above the liquid surface. Previous studies by Ihas and Sanders, Eden and McClintock, and by our group used tungsten tips and were able to detect at least twelve exotic ions in addition to the normal electron bubble. In the present work we have experimented with tips each consisting of a stainless steel wire coated with carbon nanotubes. We have found that with these tips the strength of the exotic ion signal is substantially increased making it possible to detect several ions which previously could not be seen. The present data combined with the results of the previous studies indicate that there are at least eighteen exotic ions with different mobility.

We investigate single-particle excitations and strong-coupling effects in a twodimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states ρ(ω) near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T_BKT. Near T_BKT, we show that superfluid fluctuations induce a pseudogap in ρ(ω). The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a twodimensional ⁴⁰K Fermi gas has recently been realized, our results would contribute to the understanding of single-particle properties near the BKT instability.

We present a rigorous framework to obtain evolution equations for the momentum distribution and higher order correlation functions in weakly interacting systems based on the Projection Operator Technique. These equations can be numerically solved in an efficient way. We compare the solution of the equations with known results for 1D models and find an excellent agreement.

We study the non-equilibrium properties of nonlinear QED-cavities coupled via photon tunneling in the presence of dissipation and coherent pumping. To illustrate the interplay between photon leakage, Rabi oscillations, and coherent photon hopping, we examine the dynamical evolution and the stationary states of finite cavity arrays in the highly nonlinear regime. Finally, we employ a cluster version of the self-consistent Mori projector method and show both its accuracy and efficiency for the determination of local quantities in the highly complex many-body situation at hand.

We describe recent progress in developing a superfluid helium analog of the superconducting dc-SQUID. The devices tested thus far are sensitive detectors of rotation as well as useful probes for studies of superfluidity. The key ingredients of the superfluid helium quantum interference device (SHeQUID) involve commercially available technology and modest cryogenic facilities.

Multielectron bubbles (MEBs) in liquid helium were first observed in the late 1970s, but their properties have never been explored experimentally due to their short lifetimes and the difficulty to localize them. We report the observation of long- lived MEBs in a novel cell filled with superfluid helium at static negative pressures. MEBs were extracted from the electron filled vapor sheath of a heated filament loop embedded in the superfluid helium and observed by high-speed photography. MEBs are 2D electron gases on the 3D surface of hollow helium bubbles. Diameters can range from nanometers to millimeters, depending on the number of enclosed electrons. Electrons move in angular momentum states; deformations of the surface are called spherical ripplons. The attractive electron-ripplon interaction leads to an unusual form of superconductivity. If they can be compressed, Wigner crystallization and quantum melting can be observed, as well as a new phase for localization called the ripplo- polaron lattice. MEBs are unstable to tunneling discharge when pressed against a surface. Just as Bose gases are captured in a trap for study, MEBs must also be localized away from walls. We shall discuss methods of capturing them in an electromagnetic trap embedded in the liquid helium.

Measurements of the ³He nuclear spin relaxation times of dilute ³He impurities in solid ⁴He have been used to explore the unusual dynamics of solid 4He at low temperatures. The ³He impurities move through the lattice by quantum mechanical exchange with neighboring ⁴He atoms. Because of the larger zero point motion of the ³He atoms, there is an appreciable lattice distortion that accompanies the tunneling ³ He atom and the tunneling motion depends on the elastic properties of the ⁴He lattice. This motion modulates the ³He-³He nuclear dipole- dipole interactions and thus determines the NMR relaxation rates. We compare the observed temperature dependence of the NMR relaxation rates with that expected from the measurements of the shear modulus by Syshchenko et al. [Phys. Rev. Lett. 104, 195301 (2009)].

We report the results of NMR studies of the dynamics of ³He adsorbed on hexagonal boron nitride. These studies can identify the phase transitions of the 2D films as a function of temperature. A thermally activated temperature dependence is observed for 2.6 < T < 8 K compared to a linear temperature dependence for 0.7 < T < 2.6 K. This linear dependence is consistent with that expected for thermal diffusion in a fluid for coverages of 0.4 - 0.6 of a monolayer.

We investigate magnetic properties of a strongly interacting ultracold Fermi gas. Within the framework of an extended T-matrix approximation, we calculate the spin susceptibility χ in the unitarity limit. We show that effects of pairing fluctuations on this magnetic quantity are quite different in between the normal state and the superfluid phase. In the normal state, pairing fluctuations cause spin-gap phenomenon near the superfluid phase transition temperature T_c, where χ is anomalously suppressed. In the superfluid phase, on the other hand, the ordinary suppression of χ by the BCS energy gap is weakened by pairing fluctuations, because they induce finite density of states inside the gap. Our results indicate that the spin susceptibility is a useful quantity for the study of pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas.

We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchange- correlation component was found to provide a large contribution to the total energy for a large range of interaction strengths and particle numbers. In addition, the density profiles of the dipoles are shown to display important features around the origin that is not possible to capture by earlier, simpler treatments of such systems.

We consider two parallel layers of two-dimensional spin-polarized dipolar Fermi gas without any tunneling between the layers. The effective interactions describing screening and correlation effects between the dipoles in a single layer (intra-layer) and across the layers (interlayer) are modeled within the Hubbard approximation. We calculate the rate of momentum transfer between the layers when the gas in one layer has a steady flow. The momentum transfer induces a steady flow in the second layer which is assumed initially at rest. This is the drag effect familiar from double-layer semiconductor and graphene structures. Our calculations show that the momentum relaxation time has temperature dependence similar to that in layers with charged particles which we think is related to the contributions from the collective modes of the system.

We have performed continuous-wave (cw) nuclear magnetic resonance measurements for ³He confined in 2.8-nm channel of FSM16. The magnetization shows a reduction from the Curie law at low temperature for the high areal density where ³ He in the channel consists of three portions; a solid first-layer, an amorphous-solid overlayer, and a fluid inside. By an analysis for the magnetization and the available heat capacity data, the reduction can be attributed to an interaction of spins in amorphous solid and a degenerate of fluid.

Pure superfluid ⁴He at very low temperatures is thought to be free of mechanisms producing dissipation for slowly moving objects, and the superfluid merely contributes an effective mass to the motion without any anticipated dependence on temperature below 0.1 K. To our great surprise, we found that the smallest commercially available quartz tuning fork oscillators with tines shorter than 2 mm and resonance frequency 32 kHz experienced attenuation by as much as 100 times more than the internal dissipation of the oscillator at certain values of pressure at millikelvin temperatures in superfluid ⁴He. These features smeared out at temperatures above 20 mK, although practically no thermal excitations in ⁴He are yet present. Another fork somewhat larger showed indication of similar anomalies as well, but at greatly lesser scale.

The BCS-BEC crossover phenomenon in a 3D attractive Fermi gas is revisited by using finite temperature Green functions formalism derived from the quantum path integral technique and Mean Field Approximation (MFA). Collective modes for weak and strong coupling particle-particle interaction g are obtained after recovering the dynamical coefficients in the nonlinear Time Dependent Ginzburg Landau (TDGL) equation, and numerically simulated under those particular states for the filling energy g ~ 0 and order parameter Δ(x,τ) ~ Δ₀. Explicit formulas for the first order average fluctuations ⟨η²_q,ω⟩ and the scaling law for the thermal energy associated to the non-linear collective modes are also reported.

Measurements of Casimir effects in ⁴He films in the vicinity of the bulk superfluid transition temperature T_λ have been carried out, where changes in the film thickness and the superfluid density are both monitored as a function of temperature. The Kosterlitz-Thouless superfluid onset temperature in the film is found to occur just as the Casimir dip in the film thickness from critical fluctuations becomes evident. Additionally, a new film-thickening effect is observed precisely at T_λ when the temperature is swept extremely slowly. We propose that this is a non-universal Casimir effect arising from the viscous suppression of second sound modes in the film.

Third sound is studied for superfluid films of 4He adsorbed on multiwall carbon nanotubes packed into an annular resonator. The third sound is generated with mechanical oscillation of the cell, and detected with carbon bolometers. A filling curve at temperatures near 250 mK shows oscillations in the third sound velocity, with maxima at the completion of the 4th and 5th atomic layers. Sharp changes in the Q factor of the third sound are found at partial layer fillings. Temperature sweeps at a number of fill points show strong broadening effects on the Kosterlitz-Thouless (KT) transition, and rapidly increasing dissipation, in qualitative agreement with the predictions of Machta and Guyer. At the 4th layer completion there is a sudden reduction of the transition temperature T_KT, and then a recovery back to linear variation with temperature, although the slope is considerably smaller than the KT prediction.

An oscillating object immersed in superfluid helium generates quantum turbulence, emitting quantized vortices to its surroundings. We report vortex emissions in directions parallel and perpendicular to the oscillating motion of a thin wire used as a turbulence generator. Two vibrating wires are used to detect the vortex emissions. We use superfluid ⁴He as a medium, with the temperature set to 1.25 K, at which a small amount of normal fluid component is present. In this setup, only vortex loops with sizes larger than a certain loop diameter D = 42 μm can be detected. In the perpendicular direction, vortex loops are detected when the oscillation amplitude is comparable with D. In the parallel direction, however, no vortex loops are detected at the same amplitude, suggesting an anisotropic emission of vortex loops.

We perform a numerical analysis of superfluid turbulence produced by thermal counterflow in He II by using the vortex filament model. Counterflow in a low aspect ratio channel is known to show the transition from laminar flow to the two turbulent states TI and TII. The present understanding is that the TI has the turbulent superfluid and the laminar normal fluid but both fluids are turbulent in the TII state. This work studies the vortex tangle in the TI state. Solid boundary condition is applied to walls of a square channel, and the velocity field of the normal fluid is prescribed to be a laminar Poiseuille profile. An inhomogeneous vortex tangle, which concentrates near the solid boundaries, is obtained as the statistically steady state. It is sustained by its characteristic space-time oscillation. The inhomogeneity of the vortex tangle shows the characteristic dependence on temperature, which is caused by two effects, namely the profile of the counterflow velocity and the mutual friction.

We have developed a relatively simple cryostat which allows us to image turbulent flows in superfluid helium at temperatures below 2 K, using frozen H2 particles. We analyze the statistics of the velocities of these solid tracers, which follow the turbulent flow generated by oscillating bodies. We have also studied one of the oscillators working in air at room temperature, and traced the flow with solid talcum particles for comparison. Images were recorded by a digital camera at 240 frames per second, while frequencies of the oscillators are between 20 to 45 Hz. The flow is characterized by a modified Reynolds number Re_δ based on the viscous penetration depth δ. Software in a dedicated particle tracking velocimetry code allows us to compute the trajectories and velocities of tens of thousands of particles. We have obtained the number of particles for equally spaced intervals of the velocity modulus. For the oscillators in the superfluid, the probability of finding particles at higher velocities has an exponential decay. Within our resolution the statistics in the superfluid for oscillating objects with sharp borders is largely independent of Re_δ, while the logarithmic decay at low velocities seems faster than for high velocities for rounded objects. On the other hand, for data taken in air the result is closer to a classical Gaussian distribution of velocities.

A micro-electro-mechanical system (MEMS) device with a 1.25 μm gap between a movable plate and the substrate was immersed in superfluid ³He and cooled below 500 μK at 21.2 bar. Mechanical resonances of its shear motion were monitored on warming from the base temperature. Our preliminary results demonstrate increasing damping and decreasing resonance frequencies with temperature, consistent with a thermal damping model caused by thermal quasiparticles. The quality factor (Q) of the oscillator remains surprisingly low (Q ≈ 30) down to 0.2 T/T_c, about 4 orders of magnitude smaller than the value in vacuum at 4K. The average superfluid gap was determined to be significantly suppressed from the value in bulk at the corresponding pressure.

The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial seperation (the stirring code) at a constant rate. They move to smaller scales with constant current under the action of frictional forces, finally reaching the core size separation, where they annihilate and the energy is removed by a thermal bath. On switching off the injection, the pair distribution first decays starting from the initial stirring scale, with the total vortex density decreasing linearly in time at a rate equal to the initial injection rate. As pairs at smaller scales decay, the vortex density then falls off as a power law, the same power law found in recent exact solutions of quenched 2D superfluids.