Phase-coherent matter-wave amplification was demonstrated using Bose- Einstein-condensed rubidium-87 atoms. A small seed matter wave was created with coherent optical Bragg diffraction. Amplification of this seed matter wave was achieved by using the initial condensate as a gain medium through the superradiance effect. The coherence properties of the amplified matter wave, studied with a matter-wave interferometer, were shown to be locked to those of the initial seed wave. The active matter-wave device demonstrated here has great potential in the fields of atom optics, atom lithography, and precision measurements.

Abstract:We construct a Mach-Zehnder interferometer using Bose-Einstein condensed rubidium atoms and optical Bragg diffraction. In contrast to interferometers based on normal diffraction, where only a small percentage of the atoms contribute to the signal, our Bragg diffraction interferometer uses all the condensate atoms. The condensate coherence properties and high phase-space density result in an interference pattern of nearly 100% contrast. In principle, the enclosed area of the interferometer may be arbitrarily large, making it an ideal tool that could be used in the detection of vortices, or possibly even gravitational waves. PACS number(s): 03.75. Fi, 03.75.Dg, 39.20

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We constructed a Mach-Zehnder interferometer for Bose-Einstein condensed Rubidium atoms using optical Bragg diffraction. An interference pattern of almost 100 % visibility was obtained. This scheme permits novel studies of condensate phase properties.Recently Bragg diffraction of a Bose-Einstein condensate (BEC) with a moving optical standing wave has been demonstrated [ 13. The diffraction efficiency can be controlled from 0 to 100 % and may be used as an ideal adjustable beam splitterhirror, enabling one to construct various atomoptic elements. Here we report the first demonstration of a Mach-Zehnder interferometer using a BEC and an optical Bragg diffraction technique.We first prepare a BEC of about lo5 87Rb atoms in the 5s1,2, F = 1, mF = -1 state. We release the condensate from the trap, wait 5 ms and then apply a series of three Bragg pulses (n/2, n, and n/2-pulse) each separated in time by AT [ Fig. 11. (A n/2 (n) pulse is a one that diffracts half (all) of the BEC.) The condensate, initially in the Ip = O> momentum state, is coherently and equally split into the lpl = O> and ]pz = 2Ak> states by the first n/2-pulse. After a delay AT, a n-pulse is applied that reverses the two momentum states, i.e. Ipl = O>+(p,' = 2Ak> and Ipz = 2Ak>+lp,' = O>. After another delay AT, the two wavepackets overlap completely in space and time and a final n/2 pulse is applied. This pulse splits each of them and produces a coherent superposition with a definite relative phase. The final relative phase is controlled by shifting the phase of the third pulse with an electro-optic phase shifter.The population in each respective output port of the interferometer (momentum state) oscillates as a function of this phase shift. Figure 2(a) shows absorption images of the condensates taken 10 ms after the third Bragg pulse with 0" (left) and 180" (right) phase shifts. For this image AT=100 ps and an interference pattern with a visibility of almost 100 % is observed [ Fig. 2(b)].