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We demonstrate that the nonlinear mean-field shift in a multi-component Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification is achieved by, e.g., suitably engineering the environment of the condensate. We consider as an example the case of a two-component condensate in a tightly confining atom waveguide. Modification of the atom-atom interactions is then achieved by varying independently the transverse wave function of the two components. Eliminating the density dependent phase shift in a high-density atomic beam has important applications in atom interferometry and precision measurement.

We propose a scheme to measure the cross-correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.

This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now within experimental reach, has the potential to impact a number of fields of physics, including the manipulation and applications of atomic coherence, and the preparation of quantum entanglement between microscopic and macroscopic systems. Possible applications include quantum information processing, matter-wave holography, and nanofabrication., Comment: Proceedings of LPHYS'99, Budapest, to be published in Laser Physics

We study the conditions under which atomic condensates can be used as a recording media and then suggest a reading scheme which allows to reconstruct an object with atomic reading beam. We show that good recording can be achieved for flat condensate profiles and for negative detunings between atomic Bohr frequency and optical field frequency. The resolution of recording dramatically depends on the relation between the healing length of the condensate and the spatial frequency contents of the optical fields involved., Comment: 8 pages, 5 figures, Latex

We give a brief overview of the way atomic physics is now developing in a way reminiscent of the optics revolution of the 1960's. Thanks in particular to recent developments in atomic trapping and cooling, the new field of atom optics is rapidly leading to exciting new developments such as nonlinear atom optics and quantum atom optics. We illustrate these developments with examples out of our own research., Comment: 13 pages, 1 figure

In analogy to Glauber's analysis of optical coherence, we adopt an operational approach to introduce different classes of atomic coherence associated with different types of measurements. For the sake of concreteness we consider specifically fluorescence, nonresonant imaging, and ionization. We introduce definitions of coherence appropriate to them, which we call electronic, density, and field coherence, respectively. We illustrate these concepts in various descriptions of Bose-Einstein condensation, showing that each of these descriptions makes different implicit assumptions on the coherence of the system. We also study the impact of elastic collision on the field and density coherence properties of atom lasers., Comment: 12 pages, 4 figures, Revtex

We discuss a detection scheme that reveals the existence of vortex states in a cylindrically symmetric condensate trap. It relies on the measurement of the second-order correlation function of the Schr\"odinger field, and yields directly the topological charge of the vortex state., Comment: 4 pages, Latex, no figure

We analyze several models of atomic detectors in the context of the measurement of coherence properties of matter waves. In particular, we show that an ionization scheme measures normally-ordered correlation functions of the Schr\"odinger field, in analogy with the optical situation. However, it exhibits a sensitivity to exchange processes that is normally absent in optics., Comment: 4 pages, Latex, no figures

We propose and analyze a way in which effective multicomponent condensates can be created inside high-Q multimode cavities. In contrast to the situation involving several atomic species or levels, the coupling between the various components of the dressed condensates is linear. We predict analytically and numerically confirm the onset of instabilities in the quasiparticle excitation spectrum., Comment: plain tex, 20 pages, 4 figures