ANNUAL REPORT 2006

Annual report 2006 24
we have constructed the effective actions that incorporate the one-loop effects in the
presence of an NS five-brane and membrane respectively. We have restricted ourselves
to the study of these nonperturbative effects in the case of the universal hypermultiplet.
In the case of the NS five-brane we have performed an instanton calculation by
constructing the one-loop measure in the presence of the NS five-brane. This measure
can then be used to compute correlation functions and thereby construct the effective
action. The effects of the membrane have been computed by making use of knowledge
of the isometries that are preserved and/or broken by this object. Gauging the unbroken
isometry of the universal hypermultiplet produces a potential. We have shown
that the nonperturbative membrane effects to the effective action make it possible for
this potential to have a (meta-)stable de Sitter vacuum.
Dickerscheid, D.B.M. (UU)
thesis title: Quantum phases in optical lattices
advisors: prof. dr. ir. H.T.C. Stoof
co-advisor: dr. P.J.H. Denteneer
date: 6 February 2006
present position: postdoctoral fellow, Tokyo Institute of Technology, Japan
An important new development in the field of ultracold atomic gases is the study
of the properties of these gases in a so-called optical lattice. An optical lattice is a
periodic trapping potential for the atoms that is formed by the interference pattern
of a few laser beams. A reason for the interest in these systems is that the effects of
the interatomic interactions can be strongly enhanced. More specifically, it has been
shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-
Einstein condensate into an optical lattice it is possible for the system to undergo a
quantum phase transition to a new quantum phase of matter, the so-called Mott insulator
phase. Within this Mott insulator phase each lattice site is occupied by exactly
one atom. This makes the Mott insulator phase especially well suited for applications
in the field of quantum computation and quantum information processing. We have
theoretically investigated the above mentioned quantum phase transition and our formalism
allows for a description of the Mott insulator phase at nonzero temperatures.
Another important experimental development in the field of ultracold atomic gases is
the use of Feshbach resonances to control the interatomic interactions. Such a resonance
occurs whenever two colliding atoms form a long-lived molecule for some time.
The crucial point of a Feshbach resonance is that the above mentioned molecule has a
magnetic moment that is not equal to twice the magnetic moment of the atom. As a
consequence the energy difference between the two atoms and the molecule and hence
the interactions between the atoms can be controlled by using an external magnetic
field. By combining these two techniques, i.e, by trapping ultracold atomic gases in
an optical lattice and by tuning a magnetic field near a Feshbach resonance there can
be a new quantum phase transition between two superfluid phases.
We gave derived the the theory for the description of these Feshbach Resonances in
optical lattices and applied it to various systems. To be a bit more precise, if we tune
the external magnetic field such that the energy difference between a molecule and
two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate