Evaluation of forces in magnetic materials by means of energy and co-energy methods

The evaluation of the total force of magnetic origin acting upon a body in a stationary magnetic field is often carried out using the so-called magnetic energy (or co-energy) method, which is based on the derivation of the magnetic energy (or co-energy) with respect to a virtual rigid displacement of the considered body. The application of this method is usually justified by resorting to the energy conservation principle, written in terms both of electrical and of mechanical quantities. In this paper we shall re-examine the whole matter in the context of classical thermodynamics, in order to obtain a more comprehensive and general proof of the validity of the energy (or co-energy) approach and to point out its limitations. Two typical configurations will be discussed; in the first one, the field sources are represented by conducting bodies carrying free currents, whereas in the second one a permanent magnet creates the driving field. All magnetic materials are assumed to be non-hysteretic and permanent magnets are represented by means of the well-known linear model in the second quadrant of the (B,H) plane. Received 25 July 2001 and Received in final form 5 November 2001     

Diamagnetic interactions in disordered suspensions of metastable superconducting granules

The simulation of the transition sequence of superheated Type I superconducting granules (SSG) in disordered suspensions when an external magnetic field is slowly increased from zero has been studied. Simulation takes into account diamagnetic interactions and the presence of surface defects. Results have been obtained for the transition sequence and surface fields distribution covering a wide range of densities. These results are compared with previous analytical perturbative theory, which provides qualitative information on transitions and surface magnetic fields during transitions, but with a range of validity apparently limited to extremely dilute samples. Simulations taking into account the complete diamagnetic interactions between spheres appear to be a promising tool in interpreting SSG experiments, in applications such as particle detectors, and in some fundamental calculations of Solid State Physics. Received 6 April 2001 and Received in final form 15 October 2001     

Stern Gerlach interferometry with metastable argon atoms: an immaterial mask modulating the profile of a supersonic beam

A new Stern Gerlach interferometer operating with a nozzle beam of metastable argon atoms Ar^* (3p⁵ 4s, ³ P ₂) is described. The selection of incoming (polarisation) and outgoing (analysis) Zeeman sublevels is achieved by use of laser induced transitions at two wavelengths, 811.5 nm (closed J = 2 → J = 3 transition) and 801.5 nm (open J = 2 → J = 2 transition). Linear superpositions of Zeeman sublevels, just beyond the polariser and just before the analyser, are prepared by means of two zones where Majorana transitions take place. In between, a controlled magnetic field configuration (the phase object) is produced within a triple μ-metal shielding. Standard interference patterns are obtained by scanning the field and detecting the atoms by secondary electron emission from a Faraday cup. When a static radial magnetic gradient is used, the beam profile is modulated by interference. The transverse pattern, which can be translated at will by adding a homogeneous field, is observed for the first time using a multi-channel electron multiplier followed by a phosphor screen and a CCD camera. The results satisfactorily agree with all theoretical predictions. Received 27 June 2002 / Received in final form 20 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: perales@lpl.univ-paris13.fr RID="b" ID="b"UMR 7538 du CNRS     

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets. Received 13 June 2000 and Received in final form 15 December 2000     

Atom diffraction from magnetic gratings in the thin phase-grating approximation

The problem of atom diffraction from a reflecting magnetic diffraction grating is solved in the thin phase-grating approximation. The general problem for scalar diffraction is modelled using a semi-classical method in which the grating potential is separated into a reflecting term and a diffracting term. The trajectory of the atom in the reflecting potential is solved classically and the atom wave function in the diffracting potential found by integrating the phase change along the classical trajectory. The diffraction orders are obtained after Fourier transforming the result. This can be done independently of the grating potential resulting in a general formula for the diffraction efficiencies. The general result is applied to the problem of atom diffraction from a magnetic grating. Several approximations are required to reduce the problem to a form amenable to analytic solution. The results are compared with an accurate numerical method. Received 1st February 2001 and Received in final form 8 March 2001     

Gravitational decoherence of atomic interferometers

We study the decoherence of atomic interferometers due to the scattering of stochastic gravitational waves. We evaluate the “direct” gravitational effect registered by the phase of the matter waves as well as the “indirect” effect registered by the light waves used as beam-splitters and mirrors for the matter waves. Considering as an example the space project HYPER, we show that both effects are negligible for the presently studied interferometers. Received 15 February 2002 / Received in final form 12 April 2002 Published online 19 July 2002     

Loading of a cold atomic beam into a magnetic guide

We demonstrate experimentally the continuous and pulsed loading of a slow and cold atomic beam into a magnetic guide. The slow beam is produced using a vapor loaded laser trap, which ensures two-dimensional magneto-optical trapping, as well as cooling by a moving molasses along the third direction. It provides a continuous flux larger than 10⁹ atoms/s with an adjustable mean velocity ranging from 0.3 to 3 m/s, and with longitudinal and transverse temperatures smaller than 100 μK. Up to 3×10⁸ atoms/s are injected into the magnetic guide and subsequently guided over a distance of 40 cm. Received 19 February 2002 Published online 28 June 2002     

Temperatures in 3D optical lattices influenced by neighbouring transitions

A detailed experimental study of the steady-state temperature in a 3D optical lattice for cesium has been performed for a wide range of detunings. Specifically, we have investigated the situation with the cooling and trapping light detuned far red of a ( J _g↦J _e = J _g + 1)-transition, where the blue detuned interaction with a ( J _g↦J _e = J _g)-transition can not be neglected. We find that the temperature scales with the optical potential due to the interaction with just the ( J _g↦J _e = J _g + 1)-transition. This indicates that blue Sisyphus cooling has essentially no effect on the dynamics of the system, when there exists a neighbouring red detuned transition. Received 6 June 2000 and Received in final form 26 September 2000     

Implementation of a sapphire cell with external electrodes for laser excitation of a forbidden atomic transition in a pulsed E-field

We demonstrate the production of an electric field inside a high temperature cesium vapor cell with external electrodes. This external control of the electric field, which is not possible with a glass cell in presence of a cesium vapor, is achieved using a cell made of sapphire, and is of particular interest for our ongoing Parity Violation experiment. We describe the main components and the implementation on the set-up, including the pulsed high voltage generator. With pulse duration not exceeding 200 ns the system provides a reversible longitudinal E-field of up to 2 kV/cm in the vapor at a density of ∼ 2×10¹⁴ at/cm³ without discharge. Atomic signals attest the application of the electric field in the cell, with the predicted value. Further improvements obtained with sapphire cells are also presented. Received 15 September 2000     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Quantum wires and quantum dots for neutral atoms

By placing changeable nanofabricated structures (wires, dots, etc.) on an atom mirror one can design guiding and trapping potentials for atoms. These potentials are similar to the electrostatic potentials which trap and guide electrons in semiconductor quantum devices like quantum wires and quantum dots. This technique will allow the fabrication of nanoscale atom optical devices. Received: 28 October 1997 / Revised: 17 February 1998 / Accepted: 17 July 1998     

Fibrillation of solar magnetic fields

Solar magnetic structures are often observed in the form of flux tubes composed of a number of smaller elements called fibres or threads, although theoretically such concentrations should not appear but should be flattened by magnetic diffusivity into a uniform, low intensity field. In this paper we describe a mechanism which may be responsible for the fibrillation and also for the very large diffusivity which dissipates magnetic flux tubes in hours instead of years. Firstly, the electric current associated with magnetic field gradients usually increases the local electron temperature and reduces the resistivity, so that the current becomes concentrated into sheets or streamers. Secondly, the magnetic field gradients continue to increase until the current magnitude reaches its limit, which is determined by the electron-ion streaming instability. Then with appropriate temperature and number densities, the Larmor radius of the ions overlaps the near discontinuity in B_z and generates a sharply peaked fluid motion at the edge that is close to the thermal speed. Finally, the resulting vorticity generates an axial magnetic field opposing B_z in the term , and if this is sufficient to change the sign of this term, the very unstable backward heat equation results. This instability repeatedly switches on and off and maintains the magnetic structure in the fibrillated form. Such structures are eventually eliminated by magnetic diffusivity in the usual way, but because of the fluctuations in B_z, this occurs at a vastly increased rate. We show that this phenomenon increases the magnetic diffusivity, D, by a factor ~ 10⁸ in agreement with some observations of plasma loops and supergranules.     

Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

Basis-dependent dynamics of trapped Bose-Einstein condensates and analogies with semi-classical laser theory

We present a consistent second order perturbation theory for the lowest-lying condensed modes of very small, weakly-interacting Bose-Einstein condensates in terms of bare particle eigenstates in a harmonic trap. After presenting our general approach, we focus on explicit expressions for a simple three-level system, mainly in order to discuss the analogy of a single condensate occupying two modes of a trap with the semi-classical theory for two-mode photon lasers. A subsequent renormalization of the single-particle energies to include the dressing imposed by mean fields demonstrates clearly the consistency of our treatment with other kinetic approaches. Received 14 December 2001     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

A lattice of magneto-optical and magnetic traps for cold atoms

We describe basic periodic trapping configurations for ultracold atoms above surfaces. The approach is based on a simple wire grid and can be scaled to provide large arrays of periodically arranged magnetic or magneto-optical traps. The unit cells of the trap lattices are based on crossed wire segments. By alternating the current directions in the wires of the grid it can be distinguished between 3 basic lattice configurations. As a first demonstration, we used macroscopic wires in a 2 layer configuration to realize the unit cells of the lattices. With this experimental setup, we observe two of the basic unit cells and an array of 2×2 magneto optical traps. Received 29 August 2002 / Received in final form 12 December 2002 Published online 18 February 2003     

Multiple atomic wave interferometry with standing-waves of light

Fringe shapes in a multiple-beam de Broglie-wave interferometer based on the atomic Kapitza-Dirac effect are studied. An all-optical implementation of such a device is proposed. A realization in the time-domain, using Bose-Einstein condensates released from a trap, seems viable within the present state of the art. Received 5 April 2000 and Received in final form 14 July 2000     

Microfabricated magnetic waveguides for neutral atoms

We describe how tightly confining magnetic waveguides for atoms can be created with microfabricated or nanofabricated wires. Rubidium atoms guided in the devices we have fabricated would have a transverse mode energy spacing of K. We discuss the creation of a single-mode waveguide for atom interferometry whose depth is comparable to magneto-optical trap (MOT) temperatures. We also discuss the application of microfabricated waveguides to low-dimensional systems of quantum degenerate gases, and show that confinement can be strong enough to observe fermionization in a strongly interacting bosonic ensemble. Received 1st December 1998 and Received in final form 23 February 1999     

Metastable rare gas atoms scattered by nano- and micro-slit transmission gratings

The transmission of metastable argon atoms through nano-slit or micro-slit gratings is studied by use of time of flight and angular analysis. This transmission departs from the simple geometric one essentially by two ways: (i) the elastic or diagonal part of the van der Waals (vW) interaction with the solid causes an angular narrowing of the emerging beam; (ii) the off-diagonal vW interaction induces the exothermal fine structure transition ³ P ₀↦³ P ₂ (ΔE = 175 meV) leading to large scattering angles; the resulting angular distribution is very sensitive to the roughness of the surface in the direction of the depth. An extension of these experiments to transversally coherent beams is proposed. It should be considered as a first step towards a new type of interferometer in which the inelastic diffraction makes the gratings work as beam splitters or mirrors. Received 6 July 2001 and Received in final form 17 September 2001