Correlations and counting statistics of an atom laser

We demonstrate time-resolved counting of single atoms extracted from a weakly interacting Bose-Einstein condensate of 87Rb atoms. The atoms are detected with a high-finesse optical cavity and single atom transits are identified. An atom laser beam is formed by continuously output coupling atoms from the Bose-Einstein condensate. We investigate the full counting statistics of this beam and measure its second order correlation function g((2))(tau) in a Hanbury Brown-Twiss type experiment. For the monoenergetic atom laser we observe a constant correlation function g((2))(tau)=1.00 +/- 0.01 and an atom number distribution close to a Poissonian statistics. A pseudothermal atomic beam shows a bunching behavior and a Bose distributed counting statistics.     

A slow gravity compensated atom laser

We report on a slow guided atom laser beam outcoupled from a Bose–Einstein condensate of ⁸⁷Rb atoms in a hybrid trap. The acceleration of the atom laser beam can be controlled by compensating the gravitational acceleration and we reach residual accelerations as low as 0.0027 g. The outcoupling mechanism allows for the production of a constant flux of 4.5×10⁶ atoms per second and due to transverse guiding we obtain an upper limit for the mean beam width of 4.6 μm. The transverse velocity spread is only 0.2 mm/s and thus an upper limit for the beam quality parameter is M ²=2.5. We demonstrate the potential of the long interrogation times available with this atom laser beam by measuring the trap frequency in a single measurement. The small beam width together with the long evolution and interrogation time makes this atom laser beam a promising tool for continuous interferometric measurements.     

Experimental study of coupling Bose–Einstein condensates into weakly non-trapping and trapping states

We study the production of an atom laser from a Bose–Einstein condensate using radio-frequency out-coupling. Single frequency coupling from the Bose–Einstein condensate leads to unstable production of an atom laser due to the extreme sensitivity of this process to magnetic field fluctuations. The extent of this experimental instability is quantified. Stable, repeatable production of an atom laser is achieved by the frequency modulation of the coupling, which forms a frequency comb across the condensate. Different regimes of modulated coupling are discussed. In addition the coupling of atoms into a weakly trapping state is studied. The oscillation frequency of this state in the vertical direction is measured. Preliminary results indicating qualitative difference between condensate and thermal cloud coupling are presented.     

Time interval distributions of atoms in atomic beams

We report an experimental investigation of two-particle correlations between neutral atoms in a Hanbury Brown and Twiss experiment. Both an atom laser beam and a pseudo-thermal atomic beam are extracted from a Bose–Einstein condensate and the atom flux is measured with a single atom counter. We determine the conditional and the unconditional detection probabilities for the atoms in the beam and find good agreement with the theoretical predictions. PACS 03.75.Pp; 05.30.Jp; 07.77.Gx; 42.50.Pq     

一种新颖的全光型表面原子(分子)漏斗

提出了一种产生全光型表面原子(分子)漏斗的新方案.采用红失谐高斯激光束照明由柱面透镜组成的光学系统，可在透镜焦平面附近产生横向漏斗形光强分布，以构成一表面光波导型原子漏斗.计算了漏斗的光强分布及其光学偶极势与偶极力分布.研究结果表明：该原子漏斗可用于冷原子(分子)的表面光波导、分束器和干涉仪以及微阱囚禁的有效装载，因而在集成原子光学及其原子芯片的研究中有着重要的应用. 关键词： 原子漏斗 分子漏斗 光学偶极势 原子芯片     

All-optical formation of a Bose–Einstein condensate for applications in scanning electron microscopy

We report the production of a F=1 spinor condensate of ⁸⁷Rb atoms in a single beam optical dipole trap formed by a focused CO₂ laser. The condensate is produced 13 mm below the tip of a scanning electron microscope employing standard all-optical techniques. The condensate contains up to 120000 atoms and we achieve a duty cycle of less than 10 s. PACS 03.75.Hh; 07.79.-v     

Generating controllable atom-light entanglement with a Raman atom laser system

We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a Bose-Einstein condensate via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field and show that, with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.     

Quasicontinuous atom laser in the presence of gravity

We analyze the extraction from a trapped Bose-Einstein condensate to a nontrapping state of a coherent atomic beam and its subsequent fall, at T = 0 K. Our treatment fully takes gravity into account but neglects the mean-field potential exerted on the free falling beam by the trapped atoms. We derive analytical expressions for the output rate and the output mode of the quasicontinuous "atom laser." Comparison with experimental data of Bloch et al. [Phys. Rev. Lett. 82, 3008 (1999)] is satisfactory.     

量子模型分析激光驻波原子透镜的像差

采用量子模型对近共振激光驻波原子透镜会聚Cr原子束、形成纳米量级光栅结构的物理过程进行数值模拟。为提高原子透镜的成像质量,对各种像差,如衍射像差、球差、色差、及原子束发散角、原子磁支能级、原子同位素等因素引起的像差进行了理论分析。模拟结果表明,相比粒子光学模型,量子模型能更加精确地描述原子会聚结果,且能解释原子在驻波光场中的衍射现象。在各种像差中,原子束发散角是最主要的因素,其影响大于衍射像差、球差、色差。原子的磁支能级、同位素等因素对像差影响很小,可以忽略不计。激光冷却准直原子束的方法可以减小束发散角引起的像差,压缩原子速度Vz分布范围的方法可以减小色差。     

Line width of an atom laser

We describe the measurement of the line width of an atom laser beam extracted from a Bose–Einstein condensate. Using a novel magnetic resonance imaging technique, we find that the energy width of the atom laser beam is Fourier-limited by the duration of the output-coupling process. Received: 25 July 2002 / Revised version: 28 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +41-1/633-1254, E-mail: koehl@iqe.phys.ethz.ch     

原子间相互作用对双模原子激光压缩性质的影响

研究了由单模压缩相干态光场与Ξ型三能级原子玻色爱因斯坦凝聚体(BEC)相互作用系统中耦合输出的双模原子激光的压缩特性,重点讨论了玻色爱因斯坦凝聚体原子间相互作用对原子激光压缩性质的影响,并讨论了原子激光压缩对光场初始压缩因子的依赖关系。结果表明:由光场诱导的双模原子激光呈现周期性的压缩,原子间的相互作用和光场初始压缩因子对原子的压缩性质具有重要影响。原子间的相互作用影响原子激光压缩的振荡频率而不会影响其压缩深度,而初始光场的压缩因子则对原子激光压缩深度产生调制作用,且初始光场的压缩因子越大,则原子激光压缩的时间越短。     

Interferometer-type structures for guided atoms

We experimentally demonstrate interferometer-type guiding structures for neutral atoms based on dipole potentials created by microfabricated optical systems. As a central element we use an array of atom waveguides being formed by focusing a red-detuned laser beam with an array of cylindrical microlenses. Combining two of these arrays, we realize X-shaped beam splitters and more complex systems like the geometries for Mach-Zehnder and Michelson-type interferometers for atoms.     

A Class of Two-mode Nonclassical State via Generalize Super Positions of Two-mode Coherent States

A new method is introduced to generate a elliptical hollow beam inside a cavity. Using a matrix eigenvalue method, the laser resonator with optical diffraction elements is theoretically analyzed and simulated. A elliptical hollow beam of good quality is realized experimentally. The interaction between linearly polarized elliptical hollow beam and a two-level atom is investigated theoretically. Although the linearly polarized elliptical hollow beam does not carry angular momentum, it can produce very high torque. The atoms initially at rest and located at off-beam- axis positions will rotate under the drive of the torque of the beam. The atomic motion trajectory in the field of elliptical hollow beam has been demonstrated. The study shows that the elliptical hollow beam might be a useful tool in the study of vortex property of Bose-Einstein condensate or ultra cold atom media.     

基于磁悬浮大体积交叉光学偶极阱的Dimple光阱装载研究

三维拉曼边带冷却后的铯原子样品装载于一个磁悬浮的大体积交叉光学偶极阱中, 继续加载一个小体积的光学偶极阱后, 实现了Dimple光学偶极阱对铯原子的高效装载. 对不同磁场下磁悬浮大体积光阱的有效装载势能进行理论分析与实验测量, 得出最优化的梯度磁场和均匀偏置磁场, 获得了基于磁悬浮大体积光阱的Dimple光学偶极阱的装载势能曲线, 实现了Dimple光学偶极阱对经拉曼边带冷却后俘获在磁悬浮的大体积光阱中的铯原子样品的有效装载. 比较了Dimple光学偶极阱分别从拉曼边带冷却、大体积的交叉光阱和消除反俘获势后的磁悬浮大体积光阱装载的结果, 将俘获在磁悬浮大体积光阱中的铯原子样品装载到Dimple光学偶极阱, 铯原子样品的密度提高了约15倍.     

Surface excitations of a bose-einstein condensate

Surface modes in a Bose-Einstein condensate of sodium atoms have been studied. We observed excitations of standing and rotating quadrupolar and hexadecapolar modes. The modes were excited with high spatial and temporal resolution using the optical dipole force of a rapidly scanning laser beam. This novel technique is very flexible and should be useful for the study of rotating Bose-Einstein condensates and vortices.     

Bose–Einstein condensate on a persistent-supercurrent atom chip

A Bose–Einstein condensate was achieved in a stable magnetic trap on a persistent-supercurrent atom chip with a superconducting closed-loop circuit. We determined precisely the shape of the magnetic trapping potential by systematically controlling the persistent supercurrent. The condensation was verified by time-of-flight imaging and by atom number decay measurements. The measured decay rates agreed quantitatively with numerical simulations on the three-body loss process assuming all of the atoms to be a condensate. We also discuss the feasibility of creating a quasi-one-dimensional Bose gas on our atom chip.     

冷原子穿越激光束的量子隧穿时间

原子通过激光冷却技术能够被制备在低温状态，这时冷原子云会展现出量子力学的波动性.研究了一束冷原子入射到一个蓝失谐的激光束上所表现出的量子力学隧穿效应.蓝失谐的激光束相对于冷原子而言等效于一个量子力学势垒.根据二能级模型，在理论上分析了具有内部结构的原子矢量物质波穿过激光束的量子力学反射与透射，特别是对原子穿越激光束所需的时间——量子隧穿时间进行了详细的研究.量子力学波动性使得冷原子穿越一个激光束时明显地展现出与经典粒子(热原子)不同的结果. 关键词： 冷原子 原子光学 量子隧穿     

Generation of compressed sub-poisson Bose condensate by an atom laser

The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ～10⁶, the Fano factor may be as high as ?0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.     

Characterizing optical dipole trap via fluorescence of trapped cesium atoms

Optical dipole trap (ODT) is becoming an important tool of manipulating neutral atoms. In this paper ODT is realized with a far-off resonant laser beam strongly focused in the magneto-optical trap (MOT) of cesium atoms. The light shift is measured by simply monitoring the fluorescence of the atoms in the magneto-optical trap and the optical dipole trap simultaneously. The advantages of our experimental scheme are discussed, and the effect of the beam waist and power on the potential of dipole trap as well as heating rate is analyzed.     

Atom Michelson interferometer on a chip using a Bose-Einstein condensate

An atom Michelson interferometer is implemented on an "atom chip." The chip uses lithographically patterned conductors and external magnetic fields to produce and guide a Bose-Einstein condensate. Splitting, reflecting, and recombining of condensate atoms are achieved by a standing-wave light field having a wave vector aligned along the atom waveguide. A differential phase shift between the two arms of the interferometer is introduced by either a magnetic-field gradient or with an initial condensate velocity. Interference contrast is still observable at 20% with an atom propagation time of 10 ms.