No abstract

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 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

Abstract-It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.