Coherent Momentum State Manipulation of Matter Waves

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.