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.     

An Enriched ^40K Source for Atomic Cooling

We have developed an enriched ⁴⁰K source used in ⁴⁰K--⁸⁷Rb atomic mixture cooling experiment. The enriched ⁴⁰K source is a home-made dispenser which releases ⁴⁰K atoms by the redox reaction between ⁴⁰K enriched KCl and calcium. It is efficient and easy to be made and used. We collect 10⁷ ～10^{8 40}K atoms in collection magneto-optical trap. With this dispenser, we perform a quantum degenerate Fermi gas experiment.     

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.     

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.     

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

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

Tunneling dynamics between two-component Bose–Einstein condensates

We present a mean-field model to study the tunneling dynamics between initially separated two-component Bose condensates in a time-dependent double-well potential. We solve the model in terms of a completely numerical procedure. In contrast to the usual Josephson effect between two coherently separated single-component condensates, we find that this system sustains a macroscopic quantum self-trapping even for sufficiently weak interatomic interactions and small initial population imbalance far below the critical value.     

Coherent Scattering of Light by Bose-Einstein Condensation in a Tight Confinement

We have observed strong scattering of a probe light by dilute Bose-Einstein condensate （BEC） ^87Rb gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.     

Free expansion of a Bose–Einstein condensate from an Ioffe–Pritchard magnetic trap

5 rubidium-87 atoms released from an Ioffe–Pritchard magnetic trap is investigated experimentally. The expansion dynamics depend only on the trap frequencies, which are determined independently. The data are in good agreement with the expected expansion of a condensate, and are clearly distinct from the behaviour of a classical gas in the hydrodynamic regime. Received: 3 June 1998/Final version: 25 September 1998     

Phase Diagram and Phase Separation of a Trapped Interacting Bose-Fermi Gas Mixture

In six different regimes for a spatial phase diagram of a trapped interacting Bose-Fermi gas mixture at low temperatures, we present the conditions for the spatial demixing and separation of bosons and fermions. Starting from a semiclassically thermodynamic model for the local density functional of thermal bosons and fermions,the explicit analytical expressions for the fugacities of bosons and fermions are derived in different regimes by means of a first-order perturbation method in a local-density approximation. The critical values of the fermionboson interaction strength as a function of the fractional composition of fermions have a general feature: increase,extreme and decrease with increasing the fermionic composition slightly above Bose-Einstein critical temperature.     

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.     

Bose–Einstein condensation of lithium

7 Li has been studied in a magnetically trapped gas. Many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms because of the effectively attractive interactions between ⁷Li atoms. Using a versitile phase-contrast imaging technique, we experimentally observe the condensate number to be consistent with this limit. We discuss our measurements, the current theoretical understanding of BEC in a gas with attractive interactions, and future experiments we hope to perform. Received: 4 June 1997     

Characterization and control of phase fluctuations in elongated Bose–Einstein condensates

Quasi-one-dimensional Bose–Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time of flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that, under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. We also discuss our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BECs in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations. Received: 17 August 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +49-511/762-3023, E-mail: Helge.Kreutzmann@ITP.uni-hannover.de     

Phase fluctuations in Bose–Einstein condensates

We demonstrate the existence of phase fluctuations in elongated Bose–Einstein condensates (BECs) and study the dependence of these fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase-coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed. Received: 13 July 2001 / Revised version: 28 September 2001 / Published online: 23 November 2001     

BEC from a time-dependent variational point of view

We use the time-dependent variational principle of Balian and Vénéroni to derive a set of equations governing the dynamics of a trapped Bose gas at finite temperature. We show that this dynamics generalizes the Gross-Pitaevskii equations in that it introduces a consistent dynamical coupling between the evolution of the condensate density, the thermal cloud, and the “anomalous” density.     

Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

Experimental Improvement of Signal of a Single Laser-Cooled Trapped ^40Ca^＋ Ion

A single ^40Ca^＋ ion is loaded in a miniature Paul trap and the probability of directly loading a single ion is above 50%. The signal-to-noise ratio and the storage time for a single ion have been improved by minimizing the ion micromotion and locking a 397nm cooling laser to a Fabry-Perot interferometer and optogalvanic signal. From the fluorescence spectrum, the ion temperature is estimated to be about 5mK.     

Bose–Einstein condensates in 1D- and 2D optical lattices

Bose–Einstein condensates of rubidium atoms are transferred into one- and two-dimensional optical lattice potentials. The phase coherence of the condensate wavefunction in the lattice potential is studied by suddenly releasing the atoms from the trapping potential and observing the multiple matter-wave interference pattern of several thousand expanding quantum gases. We show how arbitrary phase gradients can be mapped onto the periodic wavefunction through the application of a potential gradient. Furthermore, the experimentally measured strength of the momentum components is compared to a theoretical model of the condensate wavefunction in the lattice. Received: 3 July 2001 / Revised version: 26 September 2001 / Published online: 23 November 2001     

Bogolyubov approximation for diagonal model of an interacting Bose gas

We study, using the Bogolyubov approximation, the thermodynamic behavior of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying μ>λ(0)$\mu >\lambda (0)$, where λ(0)?0$\lambda (0)?0$ is the lowest energy value, the system undergoes Bose–Einstein condensation.     

Ground-State Properties of Charged Bosons Confined in a One-Dimensional Harmonic Double-Well Trap： Diffusion Monte Carlo Calculations

The diffusion Monte Carlo method is applied to study the ground-state properties of charged bosons in one dimension confined in a harmonic double-well trap. The particles interact repulsively through a Coulombic 1/r potential. Numerical results show that the well separation has significant influence on the ground-state properties of the system. When the interaction of the system is weak, ground-state energy decreases with the increasing well separation and has a minimal value. If the well separation increases continually~ the ground-state energy increases and approaches to a constant gradually. This effect will be abatable in the strong interacting system. In addition, by calculating the density of the systems for different interaction strengths with various well separations, we find that the density increases abnormally when the well separation is large at the centre of the system.