[abbreviated:]
We will adapt and extend theoretical methods for strongly
correlated quantum many body systems and apply them to
{\em dipolar Bose} quantum gases. Dipolar quantum gases have recently
been realized using atoms with large magnetic moments, and
experimental efforts are currently under way to understand quantum
gases of heteronuclear molecules with electric dipole moments, like RbCs or RbK.
Numerous research
groups working on the latter problem made progress to generate
ultracold gases of ground state molecules. Since their
electric dipole moments are much
larger than magnetic moments, dipole-dipole interactions are not
weak anymore. For example, we have shown that at sufficiently
high density a two-dimensional system of fully polarized dipoles can
exhibit a phonon-roton excitation spectrum, very similar to the
dense Bose liquid helium-4 [F. Mazzanti et al., Phys. Rev. Lett.
{\bf 102}, 110405 (2009)]. We expect to find a wealth of new phenomena
when we lift the restriction of two dimensions and of full
polarization of the dipoles. Reliable predictions and
better understanding of instabilities due to strongly attracting
``head-to-tail'' configuration of dipoles, as found already in mean field theory,
calls for theories valid also for strong correlations. Adding molecule {\em rotation}
of dipolar molecules as an internal degree of freedom may open the
door to completely new ways to study Bose-Einstein condensation.
We will investigate the properties of these dipolar quantum gases
using the {\em hypernetted-chain Euler-Lagrange} (HNC-EL) method and
{\em quantum Monte Carlo} (QMC) methods, both of which are capable
to accurately describe strongly interacting systems,
thus freeing us from the restrictions of the mean field approach
that is used in the majority of past theoretical work.
We will use the mean field approach only for
the purpose of comparing with the above methods.
Forschungs-