We use a Feshbach resonance to tune the scattering length a of a Bose-Einstein condensate of 7Li in the |F=1,mF=1> state. Using the spatial extent of the trapped condensate, we extract a over a range spanning 7 decades from small attractive interactions to extremely strong repulsive interactions. The shallow zero crossing in the wing of the Feshbach resonance enables the determination of a as small as 0.01 Bohr radii. Evidence of the weak anisotropic magnetic dipole interaction is obtained by comparison with different trap geometries for small a.

We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate ͑BEC͒ of 7 Li atoms. At moderate disorder strengths ͑V D ͒, we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher V D , the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence. The behavior of a superfluid or a superconductor in the presence of disorder is of fundamental interest. A superfluid can flow without friction around obstacles, and a superconductor can have zero resistance despite material defects. On the other hand, disorder is able to localize particles, resulting in an insulating state ͓1͔. Experimentally, disorder-induced superfluid/superconductor to insulator transitions ͑SIT͒ have been probed in many systems, including superfluid helium in porous media ͓2͔, thin-film and granular superconductors ͓3,4͔, and random Josephson junction arrays ͓5͔. While many believe that such a SIT is a quantum phase transition driven by quantum fluctuations, it remains a central task to understand exactly how the superfluid/superconducting order parameter, which consists both an amplitude and a phase, may be destroyed with increasing disorder. Numerous fundamental questions remain, such as the nature of the insulator, the fate of phase coherence throughout the transition, and the possibility of intermediate metallic phases ͓3,6,7͔.Cold atoms, with their intrinsic cleanliness coupled with remarkable controllability of physical parameters, have emerged as exceptional systems to study various condensed matter problems. Recently, several experiments ͓8-11͔ have studied 87 Rb condensates in random optical potentials and observed, for example, damping of collective excitations ͓8͔ and inhibition of expansion ͓9-11͔ due to disorder. Another experiment ͓12͔ has examined a Bose-Einstein condensate ͑BEC͒ in an incommensurate ͑quasirandom͒ optical lattice in order to investigate a possible "Bose-glass" phase ͓13͔. Experiments with disordered atomic quantum gases may provide unique insights into disordered quantum systems and may uncover a rich variety of quantum phases ͓14͔.Here we report experiments on a BEC of interacting 7 Li atoms subject to a well-controlled disordered potential. While we corroborate previous transport measurements ͓8-11͔, we have also probed the ground-state density distribution and phase coherence of the disordered BEC by performing both in situ and time-of-flight ͑TOF͒ imaging. While disorder inhibits transport of the BEC, reproducible TOF interference patterns are observed for intermediate disorder strengths V D , reflecting an underlying phase coherence in the disordered BEC. At stronger V D , the interference contrast diminishes as the BEC fragments into a "granular" condensate, which...

We have measured the intensity dependent rate and frequency shift of a photoassociation transition in a quantum degenerate gas of 7 Li. The rate increases linearly with photoassociation laser intensity for low intensities, whereas saturation is observed at higher intensities. The measured rates and shifts agree reasonably well with theory within the estimated systematic uncertainties. Several theoretically predicted saturation mechanisms are discussed, but a theory in which saturation arises because of quantum mechanical unitarity agrees well with the data. DOI: 10.1103/PhysRevLett.91.080402 PACS numbers: 03.75.Nt, 33.20.Kf, 33.70.-w, 34.20.Cf Photoassociation (PA) of ultracold atoms has been a remarkably useful tool for determining scattering lengths characterizing ultracold atom collisions, for producing ultracold molecules, and for providing extremely precise measurements of atomic radiative lifetimes (see Refs. [1,2] for reviews). This utility is largely a consequence of the spectroscopic precision afforded by the small thermal broadening in a laser or evaporatively cooled gas. Quantum degenerate gases are especially interesting because the coherence of the atomic field may enable the formation of a molecular Bose-Einstein condensate (BEC) from an atomic one by coherent Raman transitions [3,4], stimulated Raman adiabatic passage [5], or by other coherent adiabatic population transfer schemes [6,7].There have been extensive theoretical studies of the rate of PA [8][9][10][11][12]. The rate is predicted to increase linearly with intensity at low intensities, while various mechanisms have been proposed that cause saturation of the rate at higher intensities. Among these mechanisms are the quantum mechanical unitarity limit on the rate of atomic collisions [11], a breakdown of the two-mode approximation [4,13] for PA of Bose condensates caused by coupling to noncondensed atomic modes [12,14 -16], and the depletion of the atomic pair correlation function [15]. Photoassociation resonances are also predicted to exhibit a spectral shift proportional to the light intensity caused by coupling to the continuum of free-atom states [11,[17][18][19]. In contrast to theory, there are relatively few experimental measurements, and only two that could be considered ''precise'' (which we define as measurements with uncertainties of less than a factor of 2). We previously measured the spectral light shift using quantum degenerate 7 Li and obtained good agreement with theory [20]. Both the spectral shift and the PA rate constant were recently measured in a Na condensate, and good agreement with two-body theory was found [21]. Saturation was not observed in this experiment. Saturation was observed in two other lower precision experiments [22,23], but these experiments were performed in a magneto-optical trap, where the temperatures were greater than 100 K and the corresponding unitaritylimited rates were quite small, of the order of 1 s ÿ1 or less.We report precise measurements of both the rate of PA and the spectral shift in...

We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold 7 Li. The photoassociation-induced loss-rate coefficient K p depends strongly on magnetic field, varying by more than a factor of 10 4 for fields near the FR. At sufficiently high laser intensities, K p for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field dependent and exhibits an anomalous blueshift for fields just below the FR.

Ultrafast electron diffractive imaging of nanoscale objects such as biological molecules 1,2 and defects in solid-state devices 3 provides crucial information on structure and dynamic processes: for example, determination of the form and function of membrane proteins, vital for many key goals in modern biological science, including rational drug design 4 . High brightness and high coherence are required to achieve the necessary spatial and temporal resolution, but have been limited by the thermal nature of conventional electron sources and by divergence due to repulsive interactions between the electrons, known as the Coulomb explosion. It has been shown that, if the electrons are shaped into ellipsoidal bunches with uniform density 5 , the Coulomb explosion can be reversed using conventional optics, to deliver the maximum possible brightness at the target 6,7 . Here we demonstrate arbitrary and real-time control of the shape of cold electron bunches extracted from laser-cooled atoms. The ability to dynamically shape the electron source itself and to observe this shape in the propagated electron bunch provides a remarkable experimental demonstration of the intrinsically high spatial coherence of a cold-atom electron source, and the potential for alleviation of electron-source brightness limitations due to Coulomb explosion 6 . Carbon nanotube field emitters are at present the brightest available electron sources but must operate at low currents to avoid Coulomb expansion and are therefore not suitable for ultrafast imaging. Limited bunch shaping has been demonstrated with photoemission sources 7,8 , which use high-energy laser pulses to generate electrons at high current. Combined with longitudinal bunch compression, sub-100 fs pulses have been obtained with sufficient brightness for diffraction studies of gold 8,9 . However, large increases in brightness are needed for single-shot imaging of weakly scattering materials such as biological molecules, and further increases in the brightness of intrinsically hot photoemission sources will be difficult.Recent simulations 10,11 and experiments 12 show that photoionization of a cold atom cloud can produce cold electron bunches with high coherence and current. Electrons are extracted by nearthreshold photoionization of atoms that have been laser-cooled to microKelvin temperature 13 . We demonstrate here that the extracted electron bunches have extremely small transverse momentum, and show that the source has quasi-homogeneous rather than thermal coherence properties; that is, unlike conventional photocathode sources, the transverse locations of the cold electrons remain strongly correlated to their original location at the source.In addition, the internal structure of the atoms that form the underlying electron source provides a unique tool for three-dimensional control of the electron bunch shape 5 . We show that it is possible to engineer the spatial profiles of the incident excitation and photoionization laser beams to control the shape ARC Centre of Excellence in C...