It has long been predicted that the scattering of ultracold atoms can be altered significantly through a so-called 'Feshbach resonance'. Two such resonances have now been observed in optically trapped Bose-Einstein condensates of sodium atoms by varying an external magnetic field. They gave rise to enhanced inelastic processes and a dispersive variation of the scattering length by a factor of over ten. These resonances open new possibilities for the study and manipulation of Bose-Einstein condensates.Bose-Einstein condensates of atomic gases offer new opportunities for studying quantum-degenerate fluids 1-5 . All the essential properties of Bose condensed systems-the formation and shape of the condensate, the nature of its collective excitations and statistical fluctuations, and the formation and dynamics of solitons and vortices-are determined by the strength of the atomic interactions. In contrast to the situation for superfluid helium, these interactions are weak, allowing the phenomena to be theoretically described from 'first principles'. Furthermore, in atomic gases the interactions can be altered, for instance by employing different species, changing the atomic density, or, as in the present work, merely by varying a magnetic field.At low temperatures, the interaction energy in a cloud of atoms is proportional to the density and a single atomic parameter, the scattering length a which depends on the quantum-mechanical phase shift in an elastic collision. It has been predicted that the scattering length can be modified by applying external magnetic 6-10 , optical 11,12 or radio-frequency 13 (r.f.) fields. Those modifications are only pronounced in a so-called ''Feshbach resonance'' 14 , when a quasibound molecular state has nearly zero energy and couples resonantly to the free state of the colliding atoms. In a timedependent picture, the two atoms are transferred to the quasibound state, 'stick' together and then return to an unbound state. Such a resonance strongly affects the scattering length (elastic channel), but also affects inelastic processes such as dipolar relaxation 6,7 and threebody recombination. Feshbach resonances have so far been studied at much higher energies 15 by varying the collision energy, but here we show that they can be 'tuned' to zero energy to be resonant for ultracold atoms. The different magnetic moments of the free and quasibound states allowed us to tune these resonances with magnetic fields, and as a result, minute changes in the magnetic field strongly affected the properties of a macroscopic system.Above and below a Feshbach resonance, the scattering length a covers the full continuum of positive and negative values. This should allow the realization of condensates over a wide range of interaction strengths. By setting a Ϸ 0, one can create a condensate with essentially non-interacting atoms, and by setting a Ͻ 0 one can make the system unstable and observe its collapse. Rapid tuning of an external magnetic field around a Feshbach resonance will lead to sudden changes of t...

Interference between two freely expanding Bose-Einstein condensates has been observed. Two condensates separated by approximately 40 micrometers were created by evaporatively cooling sodium atoms in a double-well potential formed by magnetic and optical forces. High-contrast matter-wave interference fringes with a period of approximately 15 micrometers were observed after switching off the potential and letting the condensates expand for 40 milliseconds and overlap. This demonstrates that Bose condensed atoms are "laser-like"; that is, they are coherent and show long-range correlations. These results have direct implications for the atom laser and the Josephson effect for atoms.

Bose-Einstein condensates of dilute atomic gases, characterized by a macroscopic population of the quantum mechanical ground state, are a new, weakly interacting quantum fluid [1,2,3]. In most experiments condensates in a single weak field seeking state are magnetically trapped. These condensates can be described by a scalar order parameter similar to the spinless superfluid 4 He. Even though alkali atoms have angular momentum, the spin orientation is not a degree of freedom because spin flips lead to untrapped states and are therefore a loss process. In contrast, the recently realized optical trap for sodium condensates [4] confines atoms independently of their spin orientation. This opens the possibility to study spinor condensates which represent a system with a vector order parameter instead of a scalar. Here we report a study of the equilibrium state of spinor condensates in an optical trap. The freedom of spin orientation leads to the formation of spin domains in an external magnetic field. The structure of these domains are illustrated in spin domain diagrams. Combinations of both miscible and immiscible spin components were realized.A variety of new phenomena is predicted [5,6,7] for spinor condensates, such as spin textures, propagation of spin waves and coupling between superfluid flow and atomic spin. To date such effects could only be studied in superfluid 3 He, which can be described by Bose-Einstein condensation of Cooper pairs of quasi particles having both spin and orbital angular momentum [8]. Compared to the strongly interacting 3 He, the properties of weakly interacting BoseEinstein condensates of alkali gases can be calculated by mean field theories in a much more straightforward and simple way.Other systems which go beyond the description with a single scalar order parameter are condensates of two different hyperfine states of 87 Rb confined in magnetic traps. Recent experimental studies have explored the spatial separation of the two components [9,10] and their relative phase [11]. Several theoretical papers describe their structure [12,13,14,15,16,17,18] and their collective excitations [19,20,21,22].Compared to these two-component condensates, spinor condensates have several new features including the vector character of the order parameter and the changed role of spin relaxation collisions which allow for population exchange among hyperfine states without trap loss. In contrast, for 87 Rb experiments trap loss due to spin relaxation severely limits the lifetime.We consider an F = 1 spinor condensate subject to spin relaxation, in which two m F = 0 atoms can collide and produce an m F = +1 and an m F = −1 atom and vice versa. We investigate the distribution of hyperfine states and the spatial distribution in equilibrium assuming conservation of the total spin. The ground state spinor wave function is found by minimizing the free energy [5]where kinetic energy terms are neglected in the ThomasFermi approximation which is valid as long as the dimension of spin domains (typically 50 µm) is ...

Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than five million condensed atoms were transferred into the optical trap. Densities of up to $3 \times 10^{15} cm^{-3}$ of Bose condensed atoms were obtained, allowing for a measurement of the three-body decay rate constant for sodium condensates as $K_3 = (1.1 \pm 0.3) \times 10^{-30} cm^6 s^{-1}$. At lower densities, the observed 1/e lifetime was more than 10 sec. Simultaneous confinement of Bose-Einstein condensates in several hyperfine states was demonstrated.Comment: 5 pages, 4 figure

Sound propagation has been studied in a magnetically trapped dilute Bose-Einstein condensate. Localized excitations were induced by suddenly modifying the trapping potential using the optical dipole force of a focused laser beam. The resulting propagation of sound was observed using a novel technique, rapid sequencing of nondestructive phase-contrast images. The speed of sound was determined as a function of density and found to be consistent with Bogoliubov theory. This method may generally be used to observe high-lying modes and perhaps second sound.[S0031-9007(97)03665-X]

Bose-Einstein condensates have been prepared in long-lived metastable excited states. Two complementary types of metastable states were observed. The first is due to the immiscibility of multiple components in the condensate, and the second to local suppression of spin-relaxation collisions. Relaxation via re-condensation of non-condensed atoms, spin relaxation, and quantum tunneling was observed. These experiments were done with F = 1 spinor Bose-Einstein condensates of sodium confined in an optical dipole trap.Metastable states of matter, excited states which relax only slowly to the ground state, are commonly encountered. This slow relaxation often arises from the presence of free-energy barriers that prevent a system from directly evolving toward its ground state; if the thermal energy to overcome this barrier is not available, the metastable state may be long-lived.Many properties of Bose-Einstein condensates in dilute atomic gases [1][2][3][4] arise from metastability; indeed, such condensates are themselves metastable, since the true equilibrium state is a solid at these low temperatures. Bose-Einstein condensates in gases with attractive interactions (scattering length a < 0) [3] are metastable against collapse due to a kinetic energy barrier [5]. The persistence of rotations in condensates with repulsive interactions (a > 0) hinges on whether vortices are metastable in singly- [6] or multiply-connected [7,8] geometries. Similarly, dark solitons in restricted geometries are predicted to be long-lived [9] akin to the recently observed metastable states in superfluid 3 He-B [10]. Finally, Pu and Bigelow discussed spatial distributions of two-species condensates which are metastable due to mean-field repulsion between the two species [11].In this Letter, we report on the observation of two complementary types of metastability in F = 1 spinor Bose-Einstein condensates of sodium. In one, a twocomponent condensate in the |F = 1, m F = 1, 0 hyperfine states was stable in spin composition, but spontaneously formed a metastable spatial arrangement of spin domains. In the other, a single component |m F = 0 condensate was metastable in spin composition with respect to the development of |m F = ±1 ground-state spin domains. In both cases, the energy barriers which caused the metastability (as low as 0.1 nK) were much smaller than the temperature of the gas (about 100 nK) which would suggest a rapid thermal relaxation. However, this thermal relaxation was slowed considerably due to the high condensate fraction and the extreme diluteness of the non-condensed cloud.Spinor Bose-Einstein condensates were created as in previous work [12]. Condensates in the |F = 1, m F = −1 state were created in a magnetic trap [13] and then transfered to an optical dipole trap formed by a single infrared laser beam [14]. The beam was weakly focused, producing cigar-shaped traps with depths of 1 -2 µK, radial trap frequencies of about 500 Hz, and aspect ratios of about 70. After transfer, Landau-Zener rf-sweeps placed the optically trappe...

Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An outof-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.

The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, this is accompanied by a strong increase in the rate of inelastic collisions. The observed three-body loss rate in a sodium Bose-Einstein condensate increased when the scattering length was tuned to both larger or smaller values than the off-resonant value. This observation and the maximum measured increase of the loss rate by several orders of magnitude are not accounted for by theoretical treatments. The strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates. A new Feshbach resonance in sodium at 1195 G was observed.