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Pötting, Sierk (2004): Coherent Momentum State Manipulation of Matter Waves. Dissertation, LMU München: Faculty of Physics
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Abstract

This dissertation presents a theoretical analysis of methods to manipulate and control the momentum state of coherent matter waves. Of particular interest is the coherent acceleration of a quantum-degenerate atomic system, which, as a direct consequence of the form of the de Broglie wavelength, results in tunable source of matter waves. Such sources are of considerable importance for a number of potential applications in the field of atom optics, including the development of highly sensitive gyroscopes, accelerometers, gravity gradiometers or atom lithography and holography, as well as for potential uses in integrated atom optics. Our basic setup consists of a Bose-Einstein condensate in a moving optical lattice created by a pair of frequency-chirped counterpropagating laser beams acting as a "conveyor belt'' for ultracold atoms. Whereas the acceleration of ultracold but non-condensed atoms in such a lattice was demonstrated earlier, we extend this scheme to the case of Bose-Einstein condensates. As a first step, we investigate the acceleration efficiency for various acceleration rates and nonlinear interaction strengths. We find parameter regimes where efficient acceleration is possible, i.e. all atoms are accelerated to the same velocity and the initially sharp momentum distribution and thus its monochromaticity is preserved. However, in general we identify switch-on effects of the lattice, dynamical loss and nonlinear effects to be responsible for deterioration of the monochromaticity of the condensate: On the one hand, switch-on effects and dynamical loss induce a coupling of the initially populated momentum mode to other modes, thereby distributing the momentum over several modes. On the other hand, the nonlinear release of mean field energy during the acceleration process causes the mode profile itself to broaden, also leading to a contamination of the initial monochromaticity. As a second step, we discuss ways to improve this scheme by removing the restriction of constant accelerations. We employ genetic algorithms to optimize the time-dependent motion of the lattice. We show that with such flexibility, it is possible to achieve a fast and highly efficient coherent acceleration of condensates, even when mean-field effects cannot be neglected. The same scheme also enables the creation of arbitrary coherent superposition states in momentum space. The technique is thus suitable for building highly efficient momentum state beam splitters. In addition to simply accelerating condensates, it is desirable for many potential applications to transport atomic wave packets without dispersion over large distances. This can be achieved by launching bright atomic solitons, where the effects of the nonlinearity counterbalance the dispersion. Placing a Bose-Einstein condensate with repulsive interactions in a lattice, one can create a negative effective mass. Under these circumstances bright and stable soliton solutions exist, so-called gap solitons. After a careful analysis of the soliton properties, we use the tools we developed for condensate acceleration and demonstrate two feasible schemes to excite the solitons. Experimental data released after publication of our results demonstrating the acceleration of Bose-Einstein condensates in moving lattices and the very recent observation of atomic gap solitons indicates that our theoretical analysis was timely and indeed experimentally feasible. As an outlook, we briefly comment on a new direction in the field of atom optics that holds promise for future applications: the use of quantum degenerate Fermi gases. In atomic as well as in optical physics one often encounters situations where there exists a coupling between several modes of a system. Here, we illustrate the "toy model'' of a fermionic coupler where transitions between two internal states are induced by Raman coupling. Due to Fermi statistics and interatomic interactions, this is a simple example of a nonlinear multimode coupler. Investigation of this system consisting of only a few fermions already clearly illustrates the basic differences between bosonic and fermionic dynamics and sheds light on the role of two-body collisions. Understanding the basic mechanisms of this system is a first step towards more sophisticated coherent control of fermionic systems.