Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.     

Nanoscale molecular superfluidity of hydrogen

We present a microscopic quantum theoretical analysis of the nanoscale superfluid properties of solvating clusters of para-H2 around the linear OCS molecule. Path-integral calculations with N=17 para-H2 molecules, constituting a full solvation shell, show the appearance of a significant superfluid response to rotation around the molecular axis at T=0.15 K. This low-temperature superfluid response is highly anisotropic and drops sharply as the temperature increases to T approximately 0.3 K. These calculations provide definitive theoretical evidence that an anisotropic superfluid state exists for molecular hydrogen in this microscopic solvation layer.     

Superfluid helium interferometry: an introduction

This article describes, at an introductory level, how superfluids can be used to measure absolute rotations. To make it self-contained to some degree, I first introduce briefly the two-fluid model for superfluid helium and the concept of superfluid order parameter. These ideas, which were put forward for the superfluid heliums, are now widely used, in particular for the BEC gases which are the main topic of this volume. They are presented in the somewhat different perspective of helium physics. The second part will deal with the Josephson effects, the real engine behind superfluid interferometry. These effects were predicted in the early sixties for superconductors and were promptly observed in the laboratory. It was quickly realised that they would also exist in superfluids but the search took longer and conclusive experiments were performed in the eighties only in the B-phase of superfluid ³He. How these experiments are done, and how they can be used to measure the rotation of the Earth by superfluid interferometry is surveyed in the last two sections.     

Introduction to the vortex sheet of superfluid He-A

It is well known that superfluids respond to rotation by forming vortex lines. It has been recently discovered that a different type of state consisting of a vortex sheet, instead of lines, can be created in the A phase of superfluid ³He. This paper presents an introduction to the vortex sheet. We first discuss ⁴He, where a vortex sheet is unstable. The way to realize a stable sheet in ³He-A is called a vortex soliton. It consists of a topologically stable domain wall to which nonsingular vorticity is bound. The vortex soliton has been observed by nuclear magnetic resonance, and its most prominent experimental properties are explained. The macroscopic shape of the sheet and the superfluid flow in a rotating container are discussed.     

Observation of a superfluid component within solid helium

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.     

Geometric approach to stationary shapes in rotating Hele-Shaw flows

We consider the geometry of a special family of curves associated with the motion of a two-fluid interface in a rotating Hele-Shaw cell. This family of stationary exact solutions with surface tension consists of interface shapes which balance exactly the competing capillary and centrifugal forces. The result is the formation of patterned structures presenting fingers that eventually assume a teardrop-like shape, and tend to be detached from the main body of the rotating fluid (occurrence of a pinch-off event). By using the vortex-sheet formalism, we approach the problem analytically, and show that the curvature of these particular curves can be very simply expressed as a function of the radial distance to the rotation axis. Motivated by this fact, and through a simple geometric interpretation, we show that the exact solutions for the rotating Hele-Shaw problem satisfy a first-order ordinary differential equation which is readily solved, so that the shape solutions are determined up to quadratures. The ability to probe a number of key morphological features of such solutions analytically is demonstrated, and a gallery of plots is provided to highlight these findings. The possibility of accessing a criterion to predict the occurrence of pinch-off is also discussed. Finally, we prove that the general solutions are dense, and use this fact to guarantee the very existence of the neat, highly symmetric physical patterns.     

Gravitational Effects on the Vortex Distribution in Relativistic Superfluid Stars

Neutron stars are supposed to be mainly formed by a neutron superfluid. The angular momentum is given by the vortex array within the fluid, and a good account of the observable effects is determined by its coupling with the crust. In this article we show that the gravitational field introduces important modifications in the vortex distribution and shape. The inertial frame dragging on the quantum fluid produces a decrease in the vortex density, which for realistic models is in the order of 15%. This effect is relevant for neutron star rotation models and can provide a good framework for checking the quantum effect of the frame dragging.     

Mode-coupling control in resonant devices: Application to solid-state ring lasers

We report the theoretical and experimental investigation of the effects of mode coupling in a resonant macroscopic quantum device, in the case of a solid-state ring laser. This is achieved by introducing an additional coupling source whose interplay with the already-existing nonlinear effects ensures the coexistence of two counterpropagating cavity modes yielding a rotation-sensitive beat note. The determination of the condition for rotation sensing, both theoretically and experimentally, allows a quantitative study of the role of various mode-coupling mechanisms, in particular, the gain-induced mode coupling. We point out the connection between our work and the theoretical work on mode coupling in superfluid devices. This work opens up the possibility of new types of active rotation sensors.     

Shear flow and Kelvin-Helmholtz instability in superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.     

Surface tension in unitary fermi gases with population imbalance

We study the effects of surface tension between normal and superfluid regions of a trapped Fermi gas at unitarity. We find that surface tension causes notable distortions in the shape of large aspect ratio clouds. Including these distortions in our theories resolves many of the apparent discrepancies among different experiments and between theory and experiments.     

Critical behavior of the meniscus in helium crystals

The equilibrium shape of the interface between superfluid and crystalline ⁴He near the (0001) orientation is analyzed. A feature is observed in the edge angle as a function of the wall inclination with respect to the gravitational field. The step energy on the basal plane of the crystal is measured.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Spatially varying interactions induced in ultra-cold atoms by optical Feshbach resonance

Optical Feshbach resonance can induce spatially varying interactions in ultra-cold atoms. Its applications to pancake-shaped clouds of bosons and fermions enable one to study several fresh phenomena. We examine possibilities of unexplored structures such as a bosonic superfluid enclave inside a Mott insulator and a normal-gas core enclosed by a fermionic superfluid shell. We discuss feasible experimental setups and signatures of those interesting structures. While a superfluid enclave in a Mott insulator may be useful for atomic devices in atomtronics, the superconducting islands observed in scanning-tunneling microscopy of heavily underdoped high-temperature superconductors may be simulated by ultra-cold fermions.     

Giant vortex phase transition in rapidly rotating trapped Bose-Einstein condensates

A Bose-Einstein condensate of cold atoms is a superfluid and thus responds to rotation of its container by the nucleation of quantized vortices. If the trapping potential is sufficiently strong, there is no theoretical limit to the rotation frequency one can impose to the fluid, and several phase transitions characterized by the number and distribution of vortices occur when it is increased from 0 to ∞. In this note we focus on a regime of very large rotation velocity where vortices disappear from the bulk of the fluid, gathering in a central hole of low matter density induced by the centrifugal force.     

Effects of contact shape on ballistic phonon transport in semiconductor nanowires

We study the effects of contact shape on ballistic phonon transport in semiconductor nanowires at low temperatures using an approximative scalar model of continuum elasticity. Five different contacts connected to two semiconductor nanowires with different transverse widths are discussed. Numerical results show that the contact shape acts as an ‘acoustic impedance adaptor’, playing a crucial role on the ballistic phonon transmission and thermal conductance. The phonon coupling in the contacts with certain length facilitates ballistic phonon transmission compared to the abrupt interface, in which the phonon scattering is the strongest. It is found that the more the contact is abrupt, the smaller the thermal conductance is. The catenoidal contact rather than the abrupt interface is also the competitive candidate to obtain bigger thermal conductance. These results indicate that choosing an appropriate contact shape is one of the most critical factors to accurately measure the thermal conductance with a very high precision and reliability in different temperature ranges at low temperatures.     

Cumulative mechanical moments and microstructure deformation induced by growth shape in columnar solidification

The dynamical interaction between columnar interface microstructure and self-stress, resulting in unforeseen mechanical deformation phenomena, is brought to light by means of in situ and real-time synchrotron x-ray topography during directional solidification of dilute aluminum alloys. Beyond long-known local mechanical stresses, global mechanical constraints are found to be active. In particular, column rotation results from deformation caused by the mechanical moments associated with the very growth shape, namely, the cumulative torque acting together with the cumulative bending moment under gravity. A basic model allowing for a qualitative explanation of the observed distinctive features of the self-stress effects on microstructure dynamics is proposed.     

Quantum capillary waves at the superfluid-Mott-insulator interface

We discuss quantum fluctuations of the interface between a superfluid and a Mott-insulating state of ultracold atoms in a trap. The fluctuations of the boundary are due to a new type of surface modes, whose spectrum is similar--but not identical--to classical capillary waves. The corresponding quantum capillary length sets the scale for the penetration of the superfluid into the Mott-insulating regime by the proximity effect and may be on the order of several lattice spacings. It determines the typical magnitude of the interface width due to quantum fluctuations, which may be inferred from single-site imaging of ultracold atoms in an optical lattice.     

Magnetoacoustic spectroscopy in superfluid 3He-B

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.     

Quantum stripe ordering in optical lattices

We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.     

Superfluidity versus disorder in the discrete nonlinear Schrödinger equation

We study the discrete nonlinear Schr?dinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective nonrigid pendulum Hamiltonian. The different regimes include the complete reflection and refocusing of the initial wave, solitonic structures, and a superfluid state. In the superfluid regime, which occurs above a critical value of nonlinearity, a plane wave travels coherently through the randomly distributed defects. This superfluidity criterion for the DNLS is analogous to (yet very different from) the Landau superfluidity criteria in translationally invariant systems. Experimental implications for the physics of Bose-Einstein condensate gases trapped in optical potentials and of arrays of optical fibers are discussed.