Quantum phase engineering is demonstrated with two techniques that allow the spatial phase distribution of a Bose-Einstein condensate (BEC) to be written and read out. A quantum state was designed and produced by optically imprinting a phase pattern onto a BEC of sodium atoms, and matter-wave interferometry with spatially resolved imaging was used to analyze the resultant phase distribution. An appropriate phase imprint created solitons, the first experimental realization of this nonlinear phenomenon in a BEC. The subsequent evolution of these excitations was investigated both experimentally and theoretically.

We have observed Bragg diffraction of a Bose-Einstein condensate of sodium atoms by a moving, periodic, optical potential. The coherent process of Bragg diffraction produced a splitting of the condensate with unidirectional momentum transfer. Using the momentum selectivity of the Bragg process, we separated a condensate component with a momentum width narrower than that of the original condensate. By repeatedly pulsing the optical potential while the atoms were trapped, we observed the trajectory of the split atomic wave packets in the confining magnetic potential.

letters to nature 218 NATURE | VOL 398 | 18 MARCH 1999 | www.nature.com optimizing the performance of the interferometers at low frequencies, where both equations (4) and (6) become more signi®cant. It appears natural to perform such studies in the quiet environment of space, perhaps through future re®nements of LISA-type set-ups 27 .The above discussion of gravity-wave interferometers shows that the smallness of the Planck length does not preclude the possibility of direct investigations of space-time fuzziness. This complements the results of studies 28,29 which have shown that indirect evidence of quantum space-time¯uctuations could be obtained by testing the predictions of theories consistent with a given picture of thesē uctuations. Additional encouragement for experiment-driven progress in understanding the interplay between gravity and quantum mechanics comes from recent studies 30,31 in the area of gravitationally induced phases, the signi®cance of which has been emphasized in refs 32 and 33. M

Extraction of sodium atoms from a trapped Bose-Einstein condensate (BEC) by a coherent, stimulated Raman process is demonstrated. Optical Raman pulses drive transitions between trapped and untrapped magnetic sublevels, giving the output-coupled BEC fraction a well-defined momentum. The pulsed output coupling can be run at such a rate that the extracted atomic wave packets strongly overlap, forming a highly directional, quasi-continuous matter wave.