Attraction between the atoms of a Bose-Einstein condensate renders it unstable to collapse, although a condensate with a limited number of atoms can be stabilized by confinement in an atom trap. However, beyond this number the condensate collapses. Condensates constrained to one-dimensional motion with attractive interactions are predicted to form stable solitons, in which the attractive forces exactly compensate for wave-packet dispersion. Here we report the formation of bright solitons of (7)Li atoms in a quasi-one-dimensional optical trap, by magnetically tuning the interactions in a stable Bose-Einstein condensate from repulsive to attractive. The solitons are set in motion by offsetting the optical potential, and are observed to propagate in the potential for many oscillatory cycles without spreading. We observe a soliton train, containing many solitons; repulsive interactions between neighbouring solitons are inferred from their motion.

We report the attainment of simultaneous quantum degeneracy in a mixed gas of bosons (lithium-7) and fermions (lithium-6). The Fermi gas has been cooled to a temperature of 0.25 times the Fermi temperature by thermal collisions with the evaporatively cooled bosons. At this temperature, the spatial size of the gas is strongly affected by the Fermi pressure resulting from the Pauli exclusion principle and gives clear experimental evidence for quantum degeneracy.

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold (6)Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.

Bose-Einstein condensation of7 Li has been studied in a magnetically trapped gas. Because of the effectively attractive interactions between 7 Li atoms, many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms. We observe the condensate number to be limited to a maximum value between 650 and 1300 atoms. The measurements were made using a versatile phase-contrast imaging technique. [S0031-9007(97) 7 Li atoms have a negative s-wave scattering length a, indicating that for a sufficiently cold and dilute gas the interatomic interactions are effectively attractive. Attractive interactions are thought to prevent BEC from occurring at all in a spatially homogeneous (i.e., untrapped) gas [3,4], and as recently as 1994, these interactions were believed to preclude BEC in a trap as well. Current theories predict that BEC can occur in a trap such as ours, but with no more than about 1400 condensate atoms [5][6][7][8][9][10][11]. Verification of this prediction would provide a sensitive test of many-body quantum theory. In our previous work [1], the condensate could not be directly observed, and the number of condensate atoms suggested by the measurements was overestimated. In this Letter we report quantitative measurements of the condensate number, which are consistent with the theoretical limit.The effects of interactions on a trapped condensate are studied using mean-field theory. For densities n such that na 3 ø 1, the mean-field interaction energy is given by U 4ph 2 an͞m, where m is the atomic mass. For 7 Li, a ͑214.5 6 0.4͒ Å [12]. Because a , 0, the interaction energy decreases with increasing n, so the condensate tends to collapse upon itself. When the confining potential is included in the theory, it is found that if U is sufficiently small compared to the trap energy-level spacing, the destabilizing influence of the interactions is balanced by the kinetic pressure of the gas, and a metastable condensate can form. This requirement for U leads to the prediction that the number of condensate atoms N 0 is limited. As the maximum N 0 is approached, the rate for inelastic collisions increases and the gas becomes progressively less stable with respect to thermal and quantum mechanical fluctuations [7][8][9][10].

%e present the first realization of a measurement of a "weak value, " a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This "weak measurement" is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference eAect may have application in the amplification and detection of weak eff'ects.