We report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly linked mesoscopic traps. We used the interference of atoms released from the traps as a sensitive probe of these statistics. By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeezed states and coherent states of the atom field. The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions.

The intensity correlation spectrum of an ultracold 20 Ne atomic beam in the 1s 3 ͓3s : 1 P 0 ͔ state is experimentally studied. The spectrum shows a peak around the origin with the width corresponding to the kinetic energy spread of atoms in the beam source. [S0031-9007(96) PACS numbers: 32.80.Pj Various interferometric effects of neutral atomic beams have been demonstrated in recent years [1][2][3][4][5][6][7][8][9]. However, those experiments deal with the wave nature of a single atom. This is in sharp contrast to the case of optical beams, in which interesting results on many-photon correlation effects have been studied. This is partly due to the difference in the technical level of preparing samples. The invention of lasers and following development in nonlinear optics enabled us to work with optical beams with various statistical characteristics, whereas for particles with mass the only sample available for us was a beam of uncorrelated particles. For random particles the first order correlation is constant in time, and a nontrivial spectrum can be observed only in higher order correlations. Furthermore, to observe a many-particle correlation effect, at least two particles have to be found in a single external quantum state, which was prohibitively small with a conventional particle beam. This situation has changed considerably for a neutral atomic beam owing to the laser cooling technique. In a Bose-Einstein condensate of alkali gases, which has been reported recently by several groups [10][11][12], atoms are in a highly degenerate state. Even with commonly used laser-cooling techniques it is possible to achieve a density in which the probability of finding two atoms in the same mode is in an experimentally detectable range.We report in this Letter the first observation [13] of the second order correlation of a laser-cooled atomic beam, which is the atomic analogy of the Hambury Brown and Twiss experiment on an optical source [14]. An ultracold metastable 20 Ne atomic beam in the 1s 3 ͓3s : 3 P 0 ͔ state was generated by releasing atoms from a Ne trap in the 1s 5 ͓3s : 3 P 2 ͔ state by optical pumping [15]. We restricted the area of the detector to cover only the diffraction limited portion of the atomic beam source and measured the time-interval distribution between two atoms that successively hit the detector. The temporal correlation showed a peak around the origin that corresponded to the energy distribution of the atomic beam.The joint probability P͑r 1 , t; r 2 , t 1 t͒ of finding an atom at t and r 1 and then an another atom at a later time t 1 t and r 2 is P͑r 1 , t; r 2 , t 1 t͒ ͗Cjd y ͑r 1 , t͒d y ͑r 2 , t 1 t͒ 3 d͑r 2 , t 1 t͒d͑r 1 , t͒jC͘ , where d y ͑r, t͒ and d͑r, t͒ are the operators to create and annihilate the atom at r and t, respectively. The probability P͑t͒ of detecting two atoms separated in time by t is obtained by averaging the above expression on r 1 and r 2 over the detector surface and on t. In our experimental setup the evaluation of P͑t͒ is not difficult, if the atomic beam...

We demonstrate that fiber-based frequency combs with multi-branch configurations can transfer both linewidth and frequency stability to another wavelength at the millihertz level. An intra-cavity electro-optic modulator is employed to obtain a broad servo bandwidth for repetition rate control. We investigate the relative linewidths between two combs using a stable continuous-wave laser as a common reference to stabilize the repetition rate frequencies in both combs. The achieved energy concentration to the carrier of the out-of-loop beat between the two combs was 99% and 30% at a bandwidth of 1 kHz and 7.6 mHz, respectively. The frequency instability of the comb was 3.7x10(-16) for a 1 s averaging time, improving to 5-8x10(-19) for 10000 s. We show that the frequency noise in the out-of-loop beat originates mainly from phase noise in branched optical fibers.

We demonstrate a one-dimensional optical lattice clock with ultracold 171 Yb atoms, which is free from the linear Zeeman effect. The absolute frequency of the 1 S 0 ðF ¼ 1=2Þ-3 P 0 ðF ¼ 1=2Þ clock transition in 171 Yb is determined to be 518 295 836 590 864(28) Hz with respect to the SI second.

We have investigated photoassociation ͑PA͒ spectra of ultracold 88 Sr atoms near the 5s 2 1 S 0 +5s5p 1 P 1 atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be r 0 = 3.78͑18͒ nm. The PA lines also determined a precise lifetime of the 1 P 1 state to be 5.263͑4͒ ns.Precise knowledge of atom-atom interactions is of significant importance in the creation and manipulation of ultracold atoms or molecules as well as in their application to precision measurements. Investigations on light-induced atom losses in magneto-optical traps ͑MOTs͒, where collision processes are altered by the presence of near resonant photons ͓1͔, have triggered an emerging field of cold collisions with laser cooled atoms ͓2͔. The stability and dynamics of the Bose-Einstein condensates ͑BECs͒ are governed by the ultracold collisional properties ͓3-6͔. Their tunability via magnetic or optical method is utilized to produce ultracold molecules as well as molecular BECs ͓7-10͔. From a metrological point of view, atomic collisions introduce unwanted frequency shifts that critically limit the performance of the state-of-the-art atomic fountain clocks ͓11͔ and optical clocks ͓12͔.A two-body collision problem is most simplified for ultracold atoms. The ground-state wave function for the angular momentum l =0 ͑s-wave͒ state can be written as R͑r͒ = u g ͑r͒ / r with u g ͑r͒ the solution of an ordinary onedimensional ͑1D͒ Schrödinger equation and r the interatomic separation. The interaction is characterized by a single parameter, the s-wave scattering length a, which is associated with the last node of the scattering wave function u g ͑r͒ ͓13͔.One of the most versatile experimental techniques for probing the wave function, especially its last node, is the photoassociation ͑PA͒ spectroscopy ͓14͔ that measures the intensity modulation of the PA lines ͓15-17͔. Since the demonstration of the technique in laser-cooled Na ͓18͔ and Rb ͓19͔ atoms, there have been extensive theoretical as well as experimental studies in alkali-metal systems ͓2͔. However, analysis of these PA lines are not easy because the hyperfine structure in their ground state as well as the excited state gives rise to complicated molecular potentials. In contrast, alkaline-earth-metal system offers the simplest energy structures, i.e., the 1 S 0 ground state and the 1 P 1 excited state, which allows straightforward interpretation of PA spectra. Recently a PA line profile was obtained for Ca, which determined the possible range of the scattering length ͓20͔. A predissociation process was revealed through the broadening of the PA line profiles in Yb atoms ͓21͔. PA spectra near the dissociation limit was investigated for Sr, which determined the 1 P 1 excited state lifetime ͓22͔.In this Rapid Communication we report on the determination of the last node of the scattering wave function for the 5s 2 1 S 0 state of 88 Sr atoms by reconstructing the wave function through PA spectroscop...