Strongly Interacting Dipolar Bose Gases

[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.