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A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.
Bose-Einstein gas model to investigate transition temperature of liquid helium in narrow channels
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
Investigations are proposed involving an experimental and theoretical program designed to investigate various properties of the structure of helium both in its atomic form and in the aggregates of the liquid and solid states. The key to the possibilities of performing the experiments lies in the relatively weak electric fields existing in liquid and solid helium and the possibility of producing external fields almost comparable with the internal fields. It is proposed to examine a) the melting pressure curve for helium as a function of electric field b) the dielectric constant of helium as a function of pressure and electric field c) in future, the effect of electric fields on the lambda transition. From the results of these experiments one would expect to be able to gather at least corroborative evidence on a) the crystal structure of solid helium on b) the effect of the Van der Waal interaction of the electric polarizability of helium, c) the possibility of producing helium molecules d) the effective volume available to helium atoms in the liquid and possibly e) the effect of particle interactions on the Bose-Einstein condensation.
The exact Mayer series is derived for the pressure, density, and equation of state of a hard-sphere fluid in the limit of infinite space dimensions D. The Mayer series can be analytically continued into the full (cut) activity plane, and there is no sign of a phase transition. The quantum-mechanical system is also treated. For D = infinity, the fluid behaves like an ideal Bose gas and undergoes a Bose-Einstein condensation.
The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.
The general status of a grant to investigate the applications of quantum theory in atomic and molecular scattering problems in hypersonic flow is summarized. Abstracts of five articles and eleven full-length articles published or submitted for publication are included as attachments. The following topics are addressed in these articles: fragmentation of heavy ions (HZE particles); parameterization of absorption cross sections; light ion transport; emission of light fragments as an indicator of equilibrated populations; quantum mechanical, optical model methods for calculating cross sections for particle fragmentation by hydrogen; evaluation of NUCFRG2, the semi-empirical nuclear fragmentation database; investigation of the single- and double-ionization of He by proton and anti-proton collisions; Bose-Einstein condensation of nuclei; and a liquid drop model in HZE particle fragmentation by hydrogen.
Collisions between ultracold neutral atoms have for some time been the subject of investigation, initially with hydrogen and more recently with laser cooled alkali atoms. Advances in laser cooling and trapping of neutral atoms in a Magneto-Optic Trap (MOT) have made cold atoms available as the starting point for many laser cooled atomic physics investigations. The most spectacularly successful of these, the observation of Bose-Einstein Condensation (BEC) in a dilute ultra-cold spin polarized atomic vapor, has accelerated the study of cold collisions. Experimental and theoretical studies of BEC and the long range interaction between cold alkali atoms is at the boundary of atomic and low temperature physics. Such studies have been difficult and would not have been possible without the development and advancement of laser cooling and trapping of neutral atoms. By contrast, ion-atom interactions at low temperature, also very difficult to study prior to modern day laser cooling, have remained largely unexplored. But now, many laboratories worldwide have almost routine access to cold neutral atoms. The combined technologies of ion trapping, together with laser cooling of neutrals has made these studies experimentally feasible and several very important, novel applications might come out of such investigations . This paper is an investigation of ion-atom interactions in the cold and ultra-cold temperature regime. Some of the collisional ion-atom interactions present at room temperature are very much reduced in the low temperature regime. Reaction rates for charge transfer between unlike atoms, A + B(+) approaches A(+) + B, are expected to fall rapidly with temperature, approximately as T(sup 5/2). Thus, cold mixtures of atoms and ions are expected to coexist for very long times, unlike room temperature mixtures of the same ion-atom combination. Thus, it seems feasible to cool ions via collisions with laser cooled atoms. Many of the conventional collisional interactions, exploited as a useful tool at room temperature and higher, are greatly enhanced at low energy. For example, collisional spin transfer from one species of polarized atoms to another has long been a useful method for polarizing a sample of atoms where no other means was available. Because optical pumping cannot be used to polarize the nuclear spin of Xe-129 or He-3 (for use in nmr imaging of the lungs), the nuclear spins are polarized via collisions with an optically pumped Rb vapor in a cell containing both gases. In another case, a spin polarized thermal Cs beam was used to polarize the hyperfine states of trapped He(+)-3 ions in order to measure their hyperfine clock transition frequency. The absence of an x-ray light source to optically pump the ground state of the He(+)-3 ion necessitated this alternative state preparation. Similarly, Cd(+) and Sr(+) ions were spin-oriented via collisions in a cell with optically pumped Rb vapor. Resonant RF spin changing transitions in the ground state of the ions were detected by changes in the Rb resonance light absorption. Because cold collision spin exchange rates scale with temperature as T(sup -1/2) this technique is expected to be a far more powerful tool than the room temperature counterpart. This factor of 100 or more enhancement in spin exchange reaction rates at low temperatures is the basis for a novel trapped ion clock where laser cooled neutrals will cool, state select and monitor the ion clock transition. The advantage over conventional direct laser cooling of trapped ions is that the very expensive and cumbersome UV laser light sources, required to excite the ionic cooling transition, are effectively replaced by simple diode lasers.
Techniques to generate cold atom beams are of great interest in a variety of applications, from atomic frequency standards and atom optics to experimental studies of Bose-Einstein condensation. Cold atom beams have been produced by slowing thermal atomic beams using the Zeeman-slowing technique or chirped lasers, or using laser-cooling techniques to extract a slow atomic beam from the background gas in a low-pressure vapor cell. These laser-cooling techniques include "atomic funnels" or two-dimensional magneto-optical traps, as well as a variation of the conventional vapor cell magneto-optical trap called the "low-velocity intense source" (LVIS). Variations of the LVIS have been realized with unique trap geometries such as conical or pyramidal mirror traps. The present work implements a simple and robust design based on the pyramidal trap geometry and allows use of a single large diameter (<less than or = 20 cm) laser beam to obtain large capture rates of atoms from the background vapor. The four 45 deg mirrors are truncated just before the apex of the pyramid, and the 1 sq cm region at the center of the incident laser beam is retro-reflected by lambda /4 plate with a high-reflectance gold coating on the second surface. A small (1 mm diameter) hole in this retro-optic forms an extraction column for the atoms while maintaining a low conductance between the source region and an adjacent UHV chamber.
Experimental methods of laser and evaporative cooling, used in the production of atomic Bose-Einstein condensates have recently been extended to realize quantum degeneracy in trapped Fermi gases. Fermi gases are a new rich system to explore the implications of Pauli exclusion on scattering properties of the system, and ultimately fermionic superfluidity. We have produced a new macroscopic quantum system, in which a degenerate Li-6 Fermi gas coexists with a large and stable Na-23 BEC. This was accomplished using inter-species sympathetic cooling of fermionic 6Li in a thermal bath of bosonic Na-23. We have achieved high numbers of both fermions (less than 10(exp 5) and bosons (less than 10(exp 6), and Li-6 quantum degeneracy corresponding to one half of the Fermi temperature. This is the first time that a Fermi sea was produced with a condensate as a "refrigerator".
Atom skimmers are devices that act as low-pass velocity filters for atoms in thermal atomic beams. An atom skimmer operating in conjunction with a suitable thermal atomic-beam source (e.g., an oven in which cesium is heated) can serve as a source of slow atoms for a magneto-optical trap or other apparatus in an atomic-physics experiment. Phenomena that are studied in such apparatuses include Bose-Einstein condensation of atomic gases, spectra of trapped atoms, and collisions of slowly moving atoms. An atom skimmer includes a curved, low-thermal-conduction tube that leads from the outlet of a thermal atomic-beam source to the inlet of a magneto-optical trap or other device in which the selected low-velocity atoms are to be used. Permanent rare-earth magnets are placed around the tube in a yoke of high-magnetic-permeability material to establish a quadrupole or octupole magnetic field leading from the source to the trap. The atoms are attracted to the locus of minimum magnetic-field intensity in the middle of the tube, and the gradient of the magnetic field provides centripetal force that guides the atoms around the curve along the axis of the tube. The threshold velocity for guiding is dictated by the gradient of the magnetic field and the radius of curvature of the tube. Atoms moving at lesser velocities are successfully guided; faster atoms strike the tube wall and are lost from the beam.
Topics covered include: Apparatus Characterizes Transient Voltages in Real Time; Measuring Humidity in Sealed Glass Encasements; Adaptable System for Vehicle Health and Usage Monitoring; Miniature Focusing Time-of-Flight Mass Spectrometer; Cryogenic High-Sensitivity Magnetometer; Wheel Electrometer System; Carbon-Nanotube Conductive Layers for Thin-Film Solar Cells; Patch Antenna Fed via Unequal-Crossed-Arm Aperture; LC Circuits for Diagnosing Embedded Piezoelectric Devices; Nanowire Thermoelectric Devices; Code for Analyzing and Designing Spacecraft Power System Radiators; Decision Support for Emergency Operations Centers; NASA Records Database; Real-Time Principal- Component Analysis; Fuzzy/Neural Software Estimates Costs of Rocket- Engine Tests; Multicomponent, Rare-Earth-Doped Thermal-Barrier Coatings; Reactive Additives for Phenylethynyl-Containing Resins; Improved Gear Shapes for Face Worm Gear Drives; Alternative Way of Shifting Mass to Move a Spherical Robot; Parylene C as a Sacrificial Material for Microfabrication; In Situ Electrochemical Deposition of Microscopic Wires; Improved Method of Manufacturing SiC Devices; Microwave Treatment of Prostate Cancer and Hyperplasia; Ferroelectric Devices Emit Charged Particles and Radiation; Dusty-Plasma Particle Accelerator; Frozen-Plug Technique for Liquid-Oxygen Plumbing; Shock Waves in a Bose-Einstein Condensate; Progress on a Multichannel, Dual-Mixer Stability Analyzer; Development of Carbon- Nanotube/Polymer Composites; Thermal Imaging of Earth for Accurate Pointing of Deep-Space Antennas; Modifications of a Composite-Material Combustion Chamber; Modeling and Diagnostic Software for Liquefying- Fuel Rockets; and Spacecraft Antenna Clusters for High EIRP.
Units of superconducting circuitry that exploit the concept of the single- Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom. An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooper-pair charges via a Josephson junction. The logical quantum states of the device, .0. and .1., are implemented physically as a pair of charge-number states that differ by 2e (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit. A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1-qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation.
A laser cooling apparatus that generates a cold beam of rubidium and cesium atoms at low pressure has been constructed as one of several intermediate products of a continuing program of research on laser cooling and atomic physics. Laser-cooled atomic beams, which can have temperatures as low as a microkelvin, have been used in diverse applications that include measurements of fundamental constants, atomic clocks that realize the international standard unit of time, atom-wave interferometers, and experiments on Bose-Einstein condensation. The present apparatus is a prototype of one being evaluated for use in a proposed microgravitational experiment called the Quantum Interferometric Test of Equivalence (QuITE). In this experiment, interferometric measurements of cesium and rubidium atoms in free fall would be part of a test of Einstein s equivalence principle. The present apparatus and its anticipated successors may also be useful in other experiments, in both microgravity and normal Earth gravity, in which there are requirements for dual-species atomic beams, low temperatures, and low pressures. The apparatus includes a pyramidal magneto-optical trap in which the illumination is provided by multiple lasers tuned to frequencies characteristic of the two atomic species. The inlet to the apparatus is located in a vacuum chamber that contains rubidium and cesium atoms at a low pressure; the beam leaving through the outlet of the apparatus is used to transfer the atoms to a higher-vacuum (lower-pressure) chamber in which measurements are performed. The pyramidal magneto-optical trap is designed so that the laser cooling forces in one direction are unbalanced, resulting in a continuous cold beam of atoms that leak out of the trap (see figure). The radiant intensity (number of atoms per unit time per unit solid angle) of the apparatus is the greatest of any other source of the same type reported to date. In addition, this is the first such apparatus capable of producing a slow, collimated beam that contains two atomic species at the same time.
opics covered include: Integrated Electrode Arrays for Neuro-Prosthetic Implants; Eroding Potentiometers; Common/Dependent-Pressure-Vessel Nickel-Hydrogen Batteries; 120-GHz HEMT Oscillator With Surface-Wave-Assisted Antenna; 80-GHz MMIC HEMT Voltage-Controlled Oscillator; High-Energy-Density Capacitors; Microscale Thermal-Transpiration Gas Pump; Instrument for Measuring Temperature of Water; Improved Measurement of Coherence in Presence of Instrument Noise; Compact Instruments Measure Helium-Leak Rates; Irreversible Entropy Production in Two-Phase Mixing Layers; Subsonic and Supersonic Effects in Bose-Einstein Condensate; Nanolaminate Mirrors With "Piston" Figure-Control Actuators; Mixed Conducting Electrodes for Better AMTEC Cells; Process for Encapsulating Protein Crystals; Lightweight, Self-Deployable Wheels; Grease-Resistant O Rings for Joints in Solid Rocket Motors; LabVIEW Serial Driver Software for an Electronic Load; Software Computes Tape-Casting Parameters; Software for Tracking Costs of Mars Projects; Software for Replicating Data Between X.500 and LDAP Directories; The Technical Work Plan Tracking Tool; Improved Multiple-DOF SAW Piezoelectric Motors; Propulsion Flight-Test Fixture; Mechanical Amplifier for a Piezoelectric Transducer; Swell Sleeves for Testing Explosive Devices; Linear Back-Drive Differentials; Miniature Inchworm Actuators Fabricated by Use of LIGA; Using ERF Devices to Control Deployments of Space Structures; High-Temperature Switched-Reluctance Electric Motor; System for Centering a Turbofan in a Nacelle During Tests; Fabricating Composite-Material Structures Containing SMA Ribbons; Optimal Feedback Control of Thermal Networks; Artifacts for Calibration of Submicron Width Measurements; Navigating a Mobile Robot Across Terrain Using Fuzzy Logic; Designing Facilities for Collaborative Operations; and Quantitating Iron in Serum Ferritin by Use of ICP-MS.
A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.