Why PeV scale left–right symmetry is a good thing

We report the results of in-situ characterization of ⁸⁷Rb atom cloud in a quadrupole Ioffe configuration (QUIC) magnetic trap after a radio-frequency (RF) evaporative cooling of the trapped atom cloud. The in-situ absorption images of the atom cloud have shown clear bimodal optical density (OD) profiles which indicate the Bose–Einstein condensation (BEC) phase transition in the trapped gas. Also, we report here, for the first time, the measured variation in the sizes of the condensate and thermal clouds with the final frequency selected in the frequency scan of the RF-field for evaporative cooling. These results on frequency-dependent sizes of the clouds are consistent with the theoretical understanding of the BEC phenomenon in the trap.     

QUIC阱中紧束缚状态下87Rb原子气体的玻色-爱因斯坦凝聚体相变的直接观测

在QUIC阱中经蒸发冷却获得了2×10⁵个|F=2,m_F=2〉态的⁸⁷Rb原子气体的玻色-爱因斯坦凝聚.验证了紧束缚状态下原子云的轴向尺寸的变化作为BEC相变的判据，观察了从热原子气体到玻色-爱因斯坦凝聚的相变过程，测量了自由膨胀过程中BEC的纵横比变化，并和理论预言进行了对比. 关键词： 玻色-爱因斯坦凝聚 激光冷却与囚禁     

Quantum-degenerate gases of Ytterbium atoms

Evaporative cooling of ultracold Yb atoms near the quantum-degenerate regime was experimentally studied. Three bosons of ¹⁷⁰Yb, ¹⁷²Yb, ¹⁷⁶Yb and two fermions of ¹⁷¹Yb and ¹⁷³Yb were evaporatively cooled in a crossed far-off resonant trap (FORT). We observed that ¹⁷⁰Yb and ¹⁷²Yb were not concentrated into the crossed region. We found that, in the cases of ¹⁷⁶Yb atoms, atoms were concentrated well into the crossed region. The following evaporative cooling in the crossed region, however, did not work well. We performed the simultaneous trapping and sympathetic cooling in the crossed FORT by use of ¹⁷²Yb-174Yb, ¹⁷⁴Yb-¹⁷⁶Yb, ¹⁷²Yb-¹⁷⁶Yb, and ¹⁷¹Yb-¹⁷⁴Yb pairs. We observed that evaporative cooling worked well. This result shows that we succeeded in the enhancement of the atom collision rate. Especially, by use of ¹⁷⁴Yb-¹⁷⁶Yb mixture, we obtained cold ¹⁷⁶Yb whose phase space density was 0.02. We observed a large atom loss, which limited the further sympathetic evaporative cooling. We also evaporatively cooled ¹⁷⁴Yb in a 1D optical lattice. Evaporative cooling worked very well because the atoms were initially trapped at a high density. After evaporative cooling, we obtained very cold atoms, and T/T _F was estimated to be 1.2.     

Final state interactions in Bose-Einstein correlations and source functions

We study the Bose-Einstein correlations (BEC) with the final state interactions (FSI) based on a framework of Bowler. Several new formulae including the FSI are utilized in analyses of data for π^±π^± production ine ⁺ e ^? annihilation by TPC, OPAL, DELPHI, and ALEPH Collaborations. Our results show that when the exponential and Gaussian distributions are used as the source functions the degree of coherence approaches approximately unity here. We analyse also data forK _S ⁰ K _S ⁰ pairs atZ-pole ine ⁺ e ^? annihilation and show that within the present statistical errors there is no difference between the BEC for pions and kaons. Moreover, using the same formulae we obtain a fractional degree of coherence for the data for BEC inp+p collision by NA27 Collaboration.     

All-optical Bose-Einstein condensation in a 1.06 μm dipole trap

We report the all-optical production of a ⁸⁷Rb Bose-Einstein condensate (BEC) in a simple 1.06 μm dipole trap experiment. We load a single beam dipole trap directly from a magneto-optic trap (MOT). After evaporation in the single beam, a second crossed beam is used for compression. The intensity in both beams is then reduced for evaporation to BEC. We obtain a BEC with 3.5 × 10⁴ atoms after 3 s of total evaporation time. We also give a detailed account of the thermal distribution in cross beam traps. This account highlights the possible difficulties in using shorter wavelength lasers to condense all optically.     

Bose-Einstein condensation of 87Rb in a levitated crossed dipole trap

We report an apparatus and method capable of producing Bose-Einstein condensates (BECs) of ～1 × 10^{6 87}Rb atoms, and ultimately designed for sympathetic cooling of ¹³³Cs and the creation of ultracold RbCs molecules. The method combines several elements: (i) the large recapture of a magnetic quadrupole trap from a magneto-optical trap; (ii) efficient forced RF evaporation in such a magnetic trap; (iii) the gain in phase-space density obtained when loading the magnetically trapped atoms into a far red-detuned optical dipole trap, and (iv) efficient evaporation to BEC within the dipole trap. We demonstrate that the system is capable of sympathetically cooling the |F = 1, m _F = ?1〉 and |1,0? sublevels with |1, +1〉 atoms. Finally we discuss the applicability of the method to sympathetic cooling of ¹³³Cs with ⁸⁷Rb.     

Prospect for BEC in a cesium gas: one-dimensional evaporative cooling in a hybrid magnetic and optical trap

Bose-Einstein condensation (BEC) in a atomic cesium gas prepared in a low field seeker Zeeman sublevel and confined in a magnetic trap has been thwarted by a high cross-section of inelastic spin-flip collisions. A recent experiment [1] succeeded in reaching BEC for cesium atoms using all optical methods and tuning the scattering length. We will discuss a hybrid magnetic and optical trap for cesium atoms in the true hyperfine ground state, the high field seeker Zeeman sublevel, F = m _F = 3. Although this trap allows only one-dimensional (1D) evaporative cooling, we show that a route towards BEC with such a trap should be possible. We present simulations of 1D evaporative cooling, which shows that a high phase space density (PSD) of 0.1 could be reached in less than 10 seconds.Received: 25 July 2003PACS: 03.75.Hh Static properties of condensates; thermodynamical, statistical and structural properties - 05.30.Jp Boson systems - 32.80.Pj Optical cooling of atoms; trappingLaboratoire Aimé Cotton is associated with University of Paris-Sud.     

Bose--Einstein condensation on an atom chip

This paper reports an experiment of creating Bose-Einstein condensate (BEC) on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fast production of BEC. After a 4.17-s forced radio frequency evaporative cooling, a condensate with about 3000 atoms appears. The transition temperature is about 300~nK. This compact system is quite robust, allowing for versatile extensions and further studying of BEC.     

全光学冷却与囚禁133Cs原子玻色-爱因斯坦凝聚的可能性

综述了近年来有关蒸发冷却¹³³Cs原子样品的实验进展,分析了磁囚禁¹³³Cs原子玻色爱因斯坦凝聚(BEC)的困难,并在此基础上提出了一个全光型冷却与囚禁¹³³Cs原子BEC的新方案.该方案主要由一个来自半导体激光(λ=0852μm)的倒金字塔形中空光束重力光学囚禁(pyramidal-hollow-beam gravito-optical trap,缩写为PHB GOT)和一个来自Ar⁺激光(λ=05013μm)的圆锥形中空光束重力光学囚禁(conical-hollow-beam gravito-optical trap,缩写为CHB GOT)组成.在PHB GOT中,冷原子经历了一个有效的中空光束感应的Sisyphus冷却(也即强度梯度冷却)和抽运光感应的几何冷却,原子温度将被从磁光囚禁(MOT)温度(约为60μK)冷却至几个光子反冲极限(约为2μK);而在Ar⁺中空光束囚禁(CHB GOT)中,冷原子将被Raman冷却或速度选择相干粒子数囚禁技术(velocity-selection coherent population trap,缩写为VSCPT)进一步冷却至光子反冲极限以下,并被激光频率高于原子共振频率的(也即蓝失谐的)covering光束压缩.我们就PHB冷却的动力学过程进行了Monte-Carlo模拟,并计算了Ar⁺中空光束囚禁¹³³Cs原子的光学势.研究结果表明,实现一个全光学冷却与囚禁的¹³³Cs原子BEC是可能的 关键词： 倒金字塔型中空光束重力光学囚禁 强度梯度冷却 氩离子中空光束囚禁 喇曼冷却 铯原子BEC     

Atom chip based fast production of Bose–Einstein condensate

We have developed a simple method for the fast and efficient production of a Bose–Einstein condensate (BEC) on an atom chip. By using a standard six-beam magneto-optical trap and light-induced atom desorption for loading, 3×10^{7 87}Rb atoms are collected within 1 s and loaded into a small-volume magnetic potential of the chip with high efficiency. With this method, a BEC of 3×10³ atoms is realized within a total time of 3 s. We can realize a condensate of up to 2×10⁴ atoms by reducing three-body collisions. The present system can be used as a fast and high-flux coherent matter-wave source for an atom interferometer. PACS 03.75.Be; 32.80.Pj; 39.25.+k     

Simultaneous magneto-optical trapping of lithium and ytterbium atoms towards production of ultracold polar molecules

We have successfully implemented the first simultaneous magneto-optical trapping (MOT) of lithium (⁶Li) and ytterbium (¹⁷⁴Yb) atoms towards production of ultracold polar molecules of LiYb. For this purpose, we developed the dual atomic oven which contains both atomic species as an atom source and successfully observed the spectra of the Li and Yb atoms in the atomic beams from the dual atomic oven. We constructed the vacuum chamber including the glass cell with the windows made of zinc selenium (ZnSe) for the CO₂ lasers, which are the useful light sources of optical trapping for evaporative and sympathetic cooling. Typical atom numbers and temperatures in the compressed MOT are 7×10³ atoms, 640 μK for ⁶Li, 7×10⁴ atoms, and 60 μK for ¹⁷⁴Yb, respectively.     

Translationally noninvariant path integral for Bose-Einstein condensate

The Bogolyubov [Hartree-Fock-Bogolyubov (HFB)] method performs the one-particle (mean-field) approximation in the theory of Bose-Einstein condensation (BEC). Various generalizations of this method are possible. Apart from a nonlinear theory, taking the correlation effects into consideration, the HFB approximation for translationally noninvariant systems describes an instructive phenomenon. This paper is devoted to the treatment of two cases: superfluid ⁴He in porous media and atomic BEC in traps subjected to the gravitational field. Both these systems show the dependence of a critical BEC temperature T _c on their nonuniform properties in space.     

An energy sum constraint of event mixing for Bose-Einstein correlations in reactions with ππX final states around 1 GeV

We present a new event mixing technique for measuring two-pion Bose-Einstein correlations(BEC)in reactions with only two identical bosons among three final state particles.This new mixing method contains a missing mass consistency(MMC)cut and an energy sum order(ESO)cut.Unlike the previous proposed pion energy cut,which abandons nearly half the original events,the ESO cut does not eliminate any original events and hence improves the statistics of both original events and mixed events.Numerical tests using theγp→π~0π~0p events around1 Ge V are carried out to verify the validity of the ESO cut.This cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects.In addition,its ability to observe BEC effects is tested by an event sample in the presence of BEC effects.Simulation results show the BEC effects can be observed clearly as an enhancement in the correlation function,and the BEC parameters extracted by this event mixing cut are consistent with the input BEC parameters.     

Bose-Einstein condensates in optical lattices: Spontaneous emission in the presence of photonic band gaps

An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of 10¹⁴ cm^-3. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics. Received 27 March 2000     

On the possibility of using dark magneto-optical lattices to achieve Bose condensation of atoms

We show that in dark magneto-optical lattices, effects associated with the Bose statistics of atoms can be observed even at laser cooling temperatures (10⁻⁴–10⁻⁶ K), which exceed evaporative cooling temperatures in magnetic traps by several orders of magnitude. Quasicondensation occurs, i.e., the wave function is formed over the distances on which atoms are localized near the bottom of a separate potential well. In addition, switching off the magnetic field adiabatically reduces the temperature significantly, as a result of which Bose condensation in the entire volume of the gas can be observed. We propose a configuration of the light and magnetic fields in which the shape of the three-dimensional magneto-optical potential is independent of the phases of the emerging light waves. Zh. éksp. Teor. Fiz. 113, 2056–2064 (June 1998)     

Dynamics of quantum liquids in nanoporous media

We sketch our recent neutron scattering measurements of the phonon-roton (P-R) modes and Bose-Einstein condensation (BEC) of liquid ⁴He in porous media. The aim is to reveal the interdependence of BEC, well-defined P-R modes and superfluidity in helium confined to nanoscales and in disorder. In all porous media investigated to date, we observe well-defined P-R modes above T_c in the normal liquid phase, up to T_λ. Since well defined P-R modes are associated with BEC, this suggests that there is BEC above T_c in porous media. We interpret this as BEC localized to favorable regions separated by regions of normal fluid. At high pressures, p ≥25 bars, well defined P-R modes are no longer observed at lower wavevectors, Q ≤1.5 ?. At p ≈39 bars a roton is no longer observed. Work is in progress to explore whether loss of modes can be associated with a recently reported Quantum Phase Transition.     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Experimental investigation of evaporative cooling mixture of bosonic 87Rb and fermionic 40K atoms with microwave and radio frequency radiation

We investigate sympathetic cooling fermions ⁴⁰K by evaporatively cooling bosonic ⁸⁷Rb atoms in a magnetic trap with microwave and radio frequency induced evaporations in detail. The mixture of bosonic and fermionic atoms is prepared in their polarized spin states |F=9/2, m_F=9/2> for ⁴⁰K and |F=2, m_F=2> for ⁸⁷Rb, which is trapped in Quadrupole--Ioffe--Configuration trap. Comparing microwave with radio frequency evaporatively cooling bosonic ⁸⁷Rb atoms with sympathetically cooling Fermi gas ⁴⁰K, we find that the presence of rubidium atoms in the |2,1> Zeeman states, which are generated in the evaporative process, gives rise to a significant loss of ⁴⁰K due to inelastic collisions. Thus, the rubidium atoms populated in the |2, 1> Zeeman states should be removed in order to effectively perform sympathetically cooling ⁴⁰K with the evaporatively cooled ⁸⁷Rb atoms.     

Calculation of Elastic Scattering Properties in an Ultra-Cold ^85Rb-^85Rb Vapour

We report the calculation of the same-species elastic scattering properties for the ultracold rubidium-rubidium (^85Rb-^85Rb) system and the results are compared with other theoretical and experimental results in detail. We present an improved potential for triplet ground states of the Rb2 molecule, and calculate the scattering lengths αt and the effective range re using WKB and Numerov methods for two rubidium-85 collisions in the triplet state. Also, we investigate the convergence of these scattering properties, i.e. the dependence on core radius and K^0 parameter using quantum defect theory and the analytic calculations of scattering length obtained by Szmytkowski. In addition, we present evaporative cooling and other results that include phase shift and cross section at zero energy limit.