Kinetic Energy of Trapped Ions Cooled by Buffer Gas

The average kinetic energy of 40 Ca＋ ions is measured by the method of evaporating ions in an rf ion trap. The kinetic energy of the ion 40Ca＋ varies from 0.5eV to 0.2eV with changing buffer gas pressure from 10^-7 mbar to 10^-5 mbar. The Brownian motion model is also introduced to calculate the average kinetic energy of the trapped ions.     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

Quantum Degenerate Fermi--Bose Mixtures of 40K and 87Rb Atoms in a Quadrupole-Ioffe Configuration Trap

We report on the attainment of quantum degeneracy of 40^K by means of efficient thermal collisions with the evaporatively cooled 87^Rb atoms. In a quadrupole-Ioffe configuration trap, potassium atoms axe cooled to 0.5 times the Fermi temperature. We obtain up to 7.59 × 10^5 degenerate fermions 40^K.     

Superfluid-Mott-Insulator Phase Transition Phases of Bosons in an and Collective Fluctuations in both Optical Lattice

The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean t~eld theory based on a constraint SU（3） pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mort phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.     

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross-Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 （1996） 2477] This new method is simple compared to other methods used to solve numerically the Gross-Pitaevskii equation, and one can obtain analytic and reliable results.     

Simultaneous Magneto-Optical Trapping of Fermionic ^40K and Bosonic ^87Rb Atoms

We report on simultaneous magneto-optical trapping of fermionic ^40K and bosonic 87Rb atoms. This trap is the first step towards quantum degenerate fermi gas ^40K. Laser lights for the two-species magneto-optical trap （MOT） are generated from diode lasers and tapered amplifier. The enriched ^40K dispenser is utilized in the experimental setup. We obtain up to 10^7 -10^8 ^40K and 10^8 -10^9 ^87Rb atoms respectively in the steady-state single-species MOT.     

Effects of traps on dynamics of two coupled Bose-Einstein condensates

Effects of the traps are investigated on the dynamics of two coupled Bose-Einstein condensates, and the atom population transfer between the two condensates is discussed. It is found that the traps and the initial condition determine the switching and self-trapping effects on the atom population imbalance. There are the critical potential amplitude and the critical potential width, by which the oscillation manner of the population transferring ratio can be analyzed as time changes.     

Reflection of cold atoms by a cobalt single crystal

We have demonstrated that a cobalt single crystal can be used to make a remarkably smooth retro-reflector for cold paramagnetic atoms. The crystal is cut so that its surface lies in the (0001) plane and the atoms are reflected by the magnetic field above the surface due to the self-organized pattern of magnetic domains in the material. We find that the reflectivity for suitably polarized atoms exceeds 90% and may well be unity. We use the angular spread of a reflected atom cloud to measure the roughness of the mirror. We find that the angular variation of the equivalent hard reflecting surface is (3.1±0.3°)rms for atoms dropped onto the mirror from a height of 2 cm. Received: 29 November 1999 / Revised version: 24 February 2000 / Published online: 5 April 2000     

Scalable Generation of Cluster State for Multiple Hot Trapped Ions

We propose an alternative scheme for preparing N-qubit cluster state by using a frequency-modulated laser field to simultaneously illuminate the trapped ions. Selecting the index of modulation yields the selective mechanisms of coupling and decoupling between the internal and external states of the ions. Based on the selective mechanisms, the highly entangled cluster state is achieved. In our scheme, the vibration mode is only virtually excited. Thus the quantum operations are insensitive to the heating and lead to the high-fidelity quantum information processing.     

Directly Trapping Atoms in a U-Shaped Magneto-Optical Trap Using a Mini Atom Chip

We experimentally demonstrate the trapping of ^85Rb atoms directly on a chip-size U-shaped magneto-optical trap （U-MOT）. The trap includes a U-shaped wire on the chip, two bias magnetic field coils and laser beams. The capture volume of the U-MOT is theoretically calculated, and the trap is experimentally realized. With 2 A current applied to the U-shaped wire and 2-Gauss horizontal bias field, more than 2 × 10^6 atoms are trapped. In contrast with an ordinary mirror-MOT, this U-MOT captures atoms directly from the background, thus the trap size is greatly reduced. Based on this mini trap scheme, it is possible to realize a chip-size atom trap array for quantum information processing.     

Quantum transport of ultracold atoms in an accelerating optical potential

Received: 8 July 1997     

Topological phase shift in a cold-atom interferometer

Matter-wave interferences in a four-pulse version of a Ramsey-Bordé atom interferometer have been utilized to study phase shifts. A topological phase shift analogous to the scalar Aharonov-Bohm effect proposed for charged-particle interferences in the presence of a pulsed electrostatic potential has been investigated. The time-dependent potential has been generated by the interaction of a laser field with an induced atomic dipole without spatial variation along the interferometer arms. The atom interferometer has been run with laser-cooled magnesium atoms stored in a magneto-optical trap.Dedicated to H. Walther on the occasion of his 60th birthday     

Effects of the Scattering Length on the Yrast Spectrum for a Two-Component Bose-Einstein Condensates

We study the energy eigenvalue and the yrast states for a harmonically two-component weak-interacting Bose-Einstein condensate (BEC) when the intra-species and interspecies scattering length are different. The energy shift for different energy eigenvalues related to intra-and interspecies scattering lengths is calculated with the perturbation method. The actual yrast spectrum is more complicated than that when intra-species and interspecies scattering length are equal. The degenerated features disappear and so do the perfect symmetric features.     

Magnetic resonance imaging of Bose–Einstein condensates

As a new method for measuring the spatial distribution of Bose–Einstein condensates, the magnetic resonance imaging (MRI) method is proposed and studied in detail. The basic concepts, the resolution limit and the formalism of the MRI method are presented. It is expected that a resolution higher than that in optical imaging methods can be obtained by using the MRI method. Results of simulation of expected MRI signals for Bose–Einstein condensates containing dark solitons are also presented. Received: 27 September 2001 / Revised version: 24 October 2001 / Published online: 17 January 2002     

Guiding Neutral Atoms with Two Current-Carrying Wires and a Vertical Bias Field on the Atom Chip

We demonstrate the guiding of neutral atoms with two parallel microfabricated current-carrying wires on the atom chip and a vertical magnetic bias field. The atoms are guided along a magnetic field minimum parallel to the current-carrying wires and confined in the other two directions. We describe in detail how the precooled atoms are efficiently loaded into the two-wire guide. We present a detailed experimental study of the motional properties of the atoms in the guide and the relationship between the location of the guide and the vertical bias field. This two-wire guide with vertical bias field can be used to realize large area atom interferometer.     

Collision dynamics of two Bose–Einstein condensates in the presence of Raman coupling

A collision of two-component Bose-Einstein condensates in the presence of Raman coupling is proposed and studied by numerical simulations. Raman transitions are found to be able to reduce collision-produced irregular excitations by forming a time-averaged attractive optical potential. Raman transitions also support a kind of dark soliton pair in two-component Bose-Einstein condensates. Soliton pairs and their remnant single solitons are shown to be controllable by adjusting the initial relative phase between the two colliding condensates or the two-photon detuning of Raman transitions. Received: 5 February 2001 / Published online: 27 April 2001     

Bragg spectroscopy and superradiant Rayleigh scattering in a Bose–Einstein condensate

Two sets of studies concerning the interaction of off-resonant light with a sodium Bose–Einstein condensate are described. In the first set, properties of a Bose–Einstein condensate were studied using Bragg spectroscopy. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum distribution of the condensate. Depending on the momentum transfer, both the phonon regime as well as the free-particle regime could be explored. In the second set of studies, the cigar-shaped condensate was exposed to a single off-resonant laser beam and highly directional scattering of light and atoms was observed. This collective light scattering was caused by the long coherence time of the quasi-particles in the condensate and resulted in a new form of matter wave amplification. Received: 26 June 1999 / Revised version: 21 September 1999 / Published online: 10 November 1999     

Matter-wave amplification and collective internal excitations in a trapped Bose gas

Received: 23 May 1997/Revised version: 29 July 1997     

Nanoscale focusing of atoms with a pulsed standing wave

We have theoretically and experimentally investigated the focusing properties of a detuned pulsed standing wave onto a beam of neutral atoms. In close analogy to the continuous-wave situation the dipole force leads to a periodic focusing of atoms with a period of λ/2, provided an adiabatic condition is fulfilled. Pulsed laser light is conveniently converted to short wavelengths and hence offers advantages in the application of atom lithography with elements of technological interest having blue or UV resonance lines. Received: 6 October 1999 / Revised version: 3 February 2000 / Published online: 5 April 2000     

Cold atomic beam from a rubidium funnel

We report an experimental demonstration of a continuous, slow and cold beam of rubidium atoms from a two-dimensional magneto-optic trap or atomic funnel. Typically 7.3(7)×10⁸ atoms/s are ejected from the funnel with a variable velocity in the range 2–8 m/s and a temperature of 45–55 μK in the moving frame. This represents the first demonstration of sub-Doppler laser cooling in an atomic beam and temperatures as low as ≈25 μK have been observed. Received: 30 September 1999 / Published online: 5 April 2000