Quantum motion of three trapped ions in one dimension

The hyperspherical-coordinate approach is employed to a one-dimensional model of three ions in a Paul trap. It is shown that the eigen wave functions have well-defined nodal structure indicating a near separability in the hyperspherical coordinates, then two approximate good quantum numbers are introduced to classify the eigenstates. Three important classical periodic motions, including the breathing motion and the (distorted-)symmetric or anti-symmetric stretching motion, are found to dominate the wave function distribution. Received: 10 February 1999 / Received in final form: 25 March 1999     

Generation of exact analytic bound state solutions from solvable non-powerlaw potentials by a transformation method

A transformation method has been applied to the exactly solvable Hulthen problem to generate a hierarchy of exactly solved quantum systems in any chosen dimension. The generated quantum systems are, in general, energy-dependent with a single normalized eigenfunction, as the Hulthen potential is a non-powerlaw potential. A method has been devised to convert a subset of the generated quantum systems with energy-dependent potentials to a single normal system with an energy-independent potential that behaves like a potential qualitatively similar to the Poschl-Teller potential. A second-order application of the transformation method on the Hulthen system produces another Sturmian quantum system and a different method is given to regroup them into a normal quantum system which resembles the Morse potential. Existence of normalizable eigenfunctions for these systems are found to be dependent on the local and asymptotic behaviour of the transformation function. Received 30 August 2000 and Received in final form 16 March 2001     

Improvement of numerical integration algorithms by means of coordinate transformations

We study the effect of coordinate transformations on numerical integration algorithms and the Richardson extrapolation. Present method is based on Hermitian transformed eigenvalue equations and symmetrical tridiagonal matrices. Received 18 March 2002 / Received in final form 23 May 2002 Published online 24 September 2002     

Transmission resonances in magnetic-barrier structures

Quantum transport properties of electrons in simple magnetic-barrier (MB) structures and in finite MB superlattices are investigated in detail. It is shown that there exists a transition of transmission resonances, i.e., from incomplete transmission resonances in simple MB structures consisting of unidentical blocks, to complete transmission resonances in comparatively complex MB structures (, n is the number of barriers). In simple unidentical block arrangements in double- and triple-MB structures we can also obtain complete transmission by properly adjusting parameters of the building blocks according to k_y-value (k_y is the wave vector in y direction). Strong suppression of the transmission and of the conductance is found in MB superlattices which are periodic arrangements of two different blocks. The resonance splitting effect in finite MB superlattices is examined. It is confirmed that the rule (i.e., for n-barrier tunneling the splitting would be (n-1)-fold) obtained in periodic electric superlattices can be extended to periodically arranged MB superlattices of identical blocks through which electrons with tunnel, and it is no longer proper for electrons with k _y <0 to tunnel. Received: 18 August 1997 / Revised: 20 September 1997 / Accepted: 13 October 1997     

Semi-classical theory of laser cooling in two dimensions

We present a semi-classical theory of the light pressure force for atoms interacting with a two-dimensional laser field. Unlike previous 2D theory, ours is valid for general atomic level and laser field configurations. We show that striking new features appear in the velocity-dependent force arising from the multi-dimensionality. Finally, we describe in detail the novel numerical technique used in the calculation. Received 4 December 1998 and Received in final form 13 February 1999     

Trapping and cooling cesium atoms in a speckle field

We present the results of two experiments where cold cesium atoms are trapped in a speckle field. In the first experiment, a YAG laser creates the speckle pattern and induces a far-detuned dipole potential which is a nearly-conservative potential. Localization of atoms near the intensity maxima of the speckle field is observed. In a second experiment we use two counterpropagating laser beams tuned close to a resonance line of cesium and in the linlin configuration, one of them being modulated by a holographic diffuser that creates the speckle field. Three-dimensional cooling is observed. Variations of the temperature and of the spatial diffusion coefficient with the size of a speckle grain are presented. Received 16 December 1998 and Received in final form 16 April 1999     

Blue-Sisyphus cooling in cesium gray molasses and antidot lattices

We present an experimental study of the kinetic temperature of cesium atoms interacting with laser beams tuned on the blue side of the transition. In the case of a three-dimensional four-beam molasses, temperatures as low as 800 nK were found. These low temperatures are compatible with a good capture efficiency. The influence of other hyperfine transitions on the temperature is significant. In the presence of a static magnetic field (antidot lattices), the temperatures are slightly higher but show a much weaker dependence on the other hyperfine transitions. Received: 14 May 1998 / Received in final form: 16 October 1998 / Accepted: 2 November 1998     

Anisotropic velocity distributions in 3D dissipative optical lattices

We present a direct measurement of velocity distributions in two dimensions by using an absorption imaging technique in a 3D near resonant optical lattice. The results show a clear difference in the velocity distributions for the different directions. The experimental results are compared with a numerical 3D semi-classical Monte-Carlo simulation. The numerical simulations are in good qualitative agreement with the experimental results. Received 3 September 2002 / Received in final form 25 October 2002 Published online 11 February 2003     

Direct measurement of fine structure changing collisional losses in cold trapped 85Rb

Using a technique that consists in ionizing atoms out of the 5P _1/2 fragments originated in the cold collision process, we have measured the contribution of the fine structure changing collision (FS) to the total trap loss rate of cold ⁸⁵Rb. Our results show that FS contribution is responsible for about 4% of the total trap loss. This result should stimulate new theoretical discussions involving exoergic cold collisions. Received 26 October 1998 and Received in final form 2 February 1999     

Mixing of wavefunctions in rectangular microwave billiards

A set-up is described allowing the automatic registration of wavefunctions of quasi-two-dimensional microwave billiards of arbitrary shape. Tests of the apparatus with rectangular shaped billiards showed that a precision of some percent in the wavefunction amplitudes can be obtained, as far as isolated resonances are considered. For the case of overlapping resonances, however, the measurement yields wavefunctions which are close to a symmetric and an antisymmetric linear combination of the original rectangle eigenfunctions. The cause for this at first sight surprising result is discussed. Received 21 January 2000     

Numerical calculation of energies of some excited states in a helium atom

The energies of some excited states with the total angular momentum L=0, 1 and 2. the total spin of two electrons S=0 and 1, and the even and odd parities are precisely calculated directly from the Schrödinger equation where the mass of the helium nucleus is finite. Moreover, we find that the solutions to the equation for the excited states have some more nodes, which can be used to distinguish the states with the same spectral term.     

Photoionization cross-sections of the first excited states of sodium and lithium in a magneto-optical trap

A two element magneto-optical trap (MOT) for Na and ⁷Li or ⁶Li is used to cool and trap each of them separately. A fraction of the cold atoms is maintained in the first ²P_3/2 excited state by the cooling laser. These excited state atoms are ionized by laser light in the near-UV region, giving rise to a smaller number of trapped atoms and to different loading parameters. Photoionization cross-sections were derived out of these data. They are in reasonable agreement with data previously obtained using thermal samples and with theoretical predictions. Received 21 March 2001 and Received in final form 3 August 2001     

Anharmonic oscillators energies via artificial perturbation method

A new pseudoperturbative (artificial in nature) methodical proposal [#!ref15!#] is used to solve for Schr?dinger equation with a class of phenomenologically useful and methodically challenging anharmonic oscillator potentials . The effect of the [#!ref4!#,#!ref5!#] Padé approximant on the leading eigenenergy term is studied. Comparison with results from numerical (exact) and several eligible (approximation) methods is made. Received 2 July 1999 and Received in final form 18 November 1999     

Atomic probes of electromagnetic and weak interactions with trapped radioactive atoms

The alkali element francium has a simple electronic structure, and copious amounts of a wide range of isotopes can be produced in present and future rare isotope facilities. The atomic parity violating weak interaction in Fr is 18 times larger than in Cs, which makes it one of the best candidates to search for the effects of the weak interaction and its isotopic dependence. Atomic trapping methods now offer new ways to study these atoms with precision, and we will discuss some of our recent measurements with trapped Fr atoms. Future measurements of the spin-independent weak interaction can be used to test the standard model, but advances in atomic theory and improved understanding of the neutron distribution in nuclei are needed to make progress. We have made precise hyperfine-anomaly measurements in Fr and have shown that they are sensitive to the radial distribution of the neutron magnetization. Measurements of this type can help to constrain the neutron distributions. Future measurements of the spin-dependent weak interaction should allow extraction of the nuclear anapole moments for a sequence of isotopes, and allow separation of the neutron and proton weak interactions between hadrons. Received: 1 May 2001 / Accepted: 4 December 2001     

Two body loss rate in a magneto-optical trap of metastable He

We have measured the two body loss rate in a magneto-optical trap containing triplet metastable He atoms. We find a rate constant cm³/s at a -8 MHz detuning, with an uncertainty of a factor 2. This measurement is in disagreement with a recent experiment which measures the absolute, ion-producing collision rate, but agrees with several other published measurements. Received 20 April 1999 and Received in final form 12 July 1999     

Effect of ordering ambiguity in constructing the Schrödinger equation on perturbation theory

This work explores the application of perturbation formalism, developed for isotropic velocity-dependent potentials, to three-dimensional Schr?dinger equations obtained using different orderings of the Hamiltonian. It is found that the formalism is applicable to Schr?dinger equations corresponding to three possible ordering ambiguities. The validity of the derived expressions is verified by considering examples admitting exact solutions. The perturbative results agree quite well with the exactly obtained ones.     

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.     

Flux enhancement model for cold cesium fine-structure changing collisions

The measurements of fine-structure changing collisions in a cesium magneto-optical trap, reported in a previous work [A. Fioretti et al., Phys. Rev. A 55, R3999 (1997)], are reanalyzed within a model based on the flux enhancement effect, which takes place in cold atomic collisions. In the present analysis, we consider the cooperative effect of the long-range and the shorter-range excitation by the strong trap laser. We evidence also the important role of the hyperfine structure of the Cs₂ molecular levels asymptotically connected to the ground-state and excited-state dissociation limits. Received 22 July 1999 and Received in final form 4 May 2000     

Differential measurement of the ultracold Cs radiative escape and fine structure changing collision rates

We present direct measurements of the overall trap loss rate and the fine structure changing collision rate for ultracold cesium atom confined in a magneto-optical trap over an intensity range of 5 mW/cm² to 200 mW/cm². This set of simultaneous measurements allows the accurate extraction and separation of the fine structure changing rate and the radiative escape rate as these two processes compete with one another to determine the overall trap loss rate. Received 4 December 1998 and Received in final form 18 March 1999