Observation of the scissors mode and evidence for superfluidity of a trapped bose-einstein condensed Gas

We report the observation of the scissors mode of a Bose-Einstein condensed gas of 87Rb atoms in a magnetic trap, which gives direct evidence of superfluidity in this system. The scissors mode of oscillation is excited by a sudden rotation of the anisotropic trapping potential. For a gas above T(c) (normal fluid) we detect the occurrence of oscillations at two frequencies, with the lower frequency corresponding to the rigid body value of the moment of inertia. Well below T(c) the condensate oscillates at a single frequency, without damping, as expected for a superfluid.     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

Triplet cooper pairing in nuclear matter and rotational states of superdeformed nuclei

One hundred and sixty-one rotational bands of superdeformed states in nuclei are considered on the basis of a model that admits triplet Cooper pairing in superfluid nuclear matter. The behavior of the dynamical moment of inertia for such states is investigated within this model, which is shown to comply well with available experimental data and to describe successfully the rotational spectra of superdeformed states.     

Moments of inertia of neutron stars in relativistic mean field theory: The role of the isovector scalar channel

With the inclusion of the isovector scalar channel in the meson-nucleon couplings, taking DD-MEδ as an effective interaction, the moments of inertia of neutron stars possessing various stellar masses are studied within the density dependent relativistic mean field(RMF) theory. The isovector scalar channel contributes to the softening of the neutron-star matter equation of state(EOS)and therefore the reduction of the maximum mass and radius of neutron stars. Smaller values of the total moment of inertia I and the crustal moment of inertia ?I are then obtained in DD-MEδ via numerical procedure in comparison with those in other selected RMF functionals. In addition, the involvement of the isovector scalar channel lowers the thickness of the neutron star crust and its mass fraction as well. The sensitivity to both the crustal mass and stellar radius causes the crustal moment of inertia to be more obviously reduced than the total one, eventually leading to a suppression on the fraction of crustal moment of inertia?I/I in DD-MEδ. The results indicate the crustal moment of inertia as a more sensitive probe of the neutron-star matter EOS than the total one, and demonstrate that the isovector scalar meson-nucleon couplings in the RMF theory could exert influence over the physics of pulsar glitches.     

Ring exchanges and the supersolid phase of 4He

Using path integral Monte Carlo simulations we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is, have a nonclassical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be observed in a perfect 4He crystal.     

On the moment of inertia of a quantum harmonic oscillator

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.     

Experimental moments of inertia in Pd and Cd isotopes and their interpretation within the extended Nilsson-Strutinsky model

High-spin properties of even Pd and Cd isotopes have been studied by means of a 118 MeV ¹²C beam impinging onto a ¹⁰⁰Mo target. The γ-rays following the reaction were recorded using six NaI(Tl) detectors in a two-dimensional coincidence arrangement. Energy-correlation spectra were extracted from the coincidence matrix and used to obtain information on the collective moment of inertia $\text{I}$. The gross properties of the behaviour of this moment of inertia are discussed within an extended Nilsson-Strutinsky model. The experimentally observed variation of the moment of inertia at high rotational frequencies is tentatively explained as being due to an increase of $\text{I}$ as the band approaches its termination.     

Temperature dependence of damping and frequency shifts of the scissors mode of a trapped Bose-Einstein condensate

We have studied the properties of the scissors mode of a trapped Bose-Einstein condensate of 87Rb atoms at finite temperature. We measured a significant shift in the frequency of the mode below the hydrodynamic limit and a strong dependence of the damping rate as the temperature increased. We compared our damping rate results to recent theoretical calculations for other observed collective modes, finding a fair agreement. From the frequency measurements we deduce the moment of inertia of the gas and show that it is quenched below the transition point, because of the superfluid nature of the condensed gas.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Phase diagram of superfluid 3He in 99.3% porosity aerogel

We report on continuous-wave NMR measurements of the energy gaps of the A-like and B-like superfluid phases of 3He at 28.4 mT confined to a 99.3% porosity silica aerogel. The gaps are suppressed by the presence of the aerogel in a temperature-independent manner, but the suppression is considerably stronger than expected from the suppression of T(c). We then use our measurements to calculate the free energy ratio between the A-like and B-like phases. The equilibrium AB transition temperature, derived from where this ratio reaches unity, is consistent with previous measurements of the initial displacement of the pinned AB interface on warming. On this basis, we present for the first time the equilibrium phase diagram of the A-like and B-like phases of superfluid 3He in aerogel.     

Kosterlitz-Thouless transition of the quasi-two-dimensional trapped Bose gas

We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to N ~ 5 x 10(5) atoms and parameters closely related to recent experiments. We locate the Kosterlitz-Thouless temperature T(KT) and discuss intrinsic signatures of the onset of superfluidity in the density profile. Below T(KT), the condensate fraction is macroscopic even for our largest systems and decays only slowly with system size. We show that the thermal population of excited states in the transverse direction changes the two-dimensional density profile noticeably in both the normal and the superfluid phase.     

Superfluid interfaces in quantum solids

One scenario for the nonclassical moment of inertia of solid 4He discovered by Kim and Chan [Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal--the checkerboard lattice solid--we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U(1) universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.     

Molecular superfluid: nonclassical rotations in doped para-hydrogen clusters

Clusters of para-hydrogen (pH?) have been predicted to exhibit superfluid behavior, but direct observation of this phenomenon has been elusive. Combining experiments and theoretical simulations, we have determined the size evolution of the superfluid response of pH? clusters doped with carbon dioxide (CO?). Reduction of the effective inertia is observed when the dopant is surrounded by the pH? solvent. This marks the onset of molecular superfluidity in pH?. The fractional occupation of solvation rings around CO? correlates with enhanced superfluid response for certain cluster sizes.     

Interfacial pinning in the superfluid 3He A-B transition in aerogel

Continuous-wave NMR studies of 3He in the presence of 99.3% porosity silica aerogel at 34.0 bars and in a magnetic field of 28.4 mT reveal a first-order phase transition between A-like and B-like superfluid phases on both warming and cooling. NMR spectra show that the phases on warming are the same as the phases on cooling, and the interface between them is found to be strongly pinned, even close to T(c,aero). The observed behavior is consistent with spatial variation of pinning strengths within the aerogel.     

Static fluid spheres admitting Karmarkar condition

We explore a new relativistic anisotropic solution of the Einstein field equations for compact stars based on embedding class one condition.For this purpose,we use the embedding class one methodology by employing the Karmarkar condition.Employing this methodology,we obtain a particular differential equation that connects both the gravitational potentials e^λ and e^ν.We solve this particular differential equation choosing a simple form of generalized gravitational potential grr to describe a complete structure of the space-time within the stellar configuration.After determining this space-time geometry for the stellar models,we discuss thermodynamical observables including radial and tangential pressures,matter density,red-shift,velocity of sound,etc.,in the stellar models.We also perform a complete graphical analysis,which shows that our models satisfy all the physical and mathematical requirements of ultra-high dense collapsed structures.Further,we discuss the moment of inertia and M-R curve for rotating and non-rotating stars.     

Anomalous intensity of pinned speckles at high adaptive correction

Ground-based optical searches for faint stellar or planetary companions about other stars may be limited by speckle noise, which is the rapid intensity fluctuations that are due to motions of remnant atmospheric speckles. Adaptive optics (AO) can reduce residual wave-front phase errors to low values, substantially reducing the unwanted power in the speckle halo. At high correction, however, the noise in the halo will be dominated by anomalously bright "pinned" speckles that have a number of unusual properties. They can have negative intensities and will appear in spatially antisymmetric patterns; they are spatially pinned to Airy rings and have zero mean in a sufficiently long integration. Some of these properties may be used to reduce the unanticipated effect of pinned speckles on companion searches, depending on details of the AO system. But, in short exposures, pinned speckles dominate speckle noise over much of the inner halo for Strehl ratios S as low as 0.6 and over much of the outer halo too as Strehl and deformable-mirror actuator densities increase. I show that these anomalously bright pinned speckles are not included in the traditional expression for speckle power in an image, (1 - S), on which sensitivity estimates of future high-performance AO systems have been based.     

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners with nanometer resolution are studied by using an electro-mechanical coupling Timoshenko beam model.Meanwhile,the effects of friction,the first moment,and moment of inertia induced by mass loads are considered.The predicted resonance frequencies of the ceramic tubes are sensitive to not only the mechanical parameters of the scanners,but also the friction acting on the attached shaking ball and corresponding bending moment on the tubes.The theoretical results are in excellent agreement with the related experimental measurements.This model and corresponding results are applicable for optimizing the structures and performances of the scanners.     

Study on fast linear scanning for a new laser scanner

In the field of lidar system design, there is a need for laser scanners that offer fast linear scanning, are small size and have small a rotational inertia moment. Currently, laser scanners do not meet the above needs. A new laser scanner based on two amplified piezoelectric actuators is designed in this paper. The laser scanner has small size, high mechanical resonance frequencies and a small rotational inertia moment. The size of the mirror is 20 mm×15 mm. To achieve fast linear scanning performance, an open-loop controller is designed to compensate the hysteresis behavior and to restrain oscillations that are caused by the mechanical resonances of the scanner's mechanical structure. By comparing measured scanning waveforms, nonlinearities and scan line images between the uncontrolled and controlled scanner, it was found that the scanning linearity of linear scanning was improved The open-loop controlled laser scanner realizes linear scanning at 250 Hz with optical scan angle of ±12 mrad.     

Memory effect in dielectric relaxation I

Dielectric relaxation theory is formulated taking into account the effect of inertia and the memory effect. With the use of the damping theoretical expansion formula, a rigorous equation for the probability density is derived and solved exactly in terms of the Jacobi theta function. Dielectric absorption, dispersion and fluctuation of the dipole moment are determined. For higher frequencies (i.e. short time behavior), deviation from the Debye result is found and the relevance to experiments is discussed.