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.

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.

Storage and retrieval of a squeezed vacuum was successfully demonstrated using electromagnetically induced transparency. The squeezed vacuum pulse having a temporal width of 930 ns was incident on the laser cooled 87Rb atoms with an intense control light in a coherent state. When the squeezed vacuum pulse was slowed and spatially compressed in the cold atoms, the control light was switched off. After 3 mus of storage, the control light was switched on again, and the squeezed vacuum was retrieved, as was confirmed using the time-domain homodyne method.

We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation Dt are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on Dt and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate. PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Qk Since the first demonstrations of Bose-Einstein condensation in dilute atomic gases [1], there have been many efforts to explore the nature of such condensates [2,3]. The phase properties of Bose-Einstein condensates are of particular interest because they affect how BECs interfere. The characterization of atoms extracted from a BEC as constituting an "atom laser" beam is related to these phase properties. In this Letter we present direct measurements and theoretical calculations of phase variations across a BEC, a property related to spatial coherence. For a trapped, pure BEC one expects the phase to be spatially uniform because the condensate is in a stationary state of the system with no angular momentum. On the other hand, in an incompletely formed BEC, one might expect differences in the phase between different regions of the condensate [4]. A released BEC, composed of atoms with a positive scattering length, develops phase variations as it explosively expands due to the atom-atom (mean-field) interaction [2]. Understanding these phase variations is essential for characterizing condensates as sources of coherent matter waves.Matter-wave interference between two condensates was reported in 1997 [5] where two condensates initially localized in different regions of a double-well potential were released and allowed to spread and overlap. That experiment, equivalent to a Young's double slit experiment, showed that two independent condensates interfere, as do two separate lasers [6]. Here we describe a novel method of self-interfering a BEC to extract information about its phase.We measure the spatial coherence of the BEC by creating and interfering two spatially displaced, coherently diffracted "copies" of the original BEC in the same momentum state. An optical standing wave pulse diffracts [7-9] a small fraction of the condensate into momentum states 62nh k, where n is an integer and k ͑2p͞l͒ẑ is the optical wave vector. For our conditions, a negligible fraction is diffracted into momentum states with n . 1. (Because the process is symmetric, the discussion that follows refers to only the 12hk copy.) A second diffraction pulse, applied Dt after the first pulse, creates a second overlapping 2hk copy displaced from the first by D z ͑2hkDt͞m͒ẑ 2y r Dtẑ, with m the atomic mass and y r the recoil velocity. The amplitudes of the wave functions rep...