Strongly Interacting Dipolar Bose Gases

The young research ?eld of ultra-cold quantum gases has experienced rapid growth since the ?rst real- ization of Bose-Einstein condensation of gases in 1995. Since then the ?eld has matured and spread beyond its atomic physics roots into other branches of physics. Particularly experiments where Feshbach resonances are exploited have entered the regime where interactions between particles are not necessarily a weak per- turbation that could be described by mean ?eld theories. Thus the ?eld is crossing over to condensed matter physics, where quantum many body theories applicable to strong interactions are available. We will adapt and extend theoretical methods for strongly correlated quantum many body systems and apply them to 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 suf?ciently 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. 102, 110405 (2009)]. We expect to ?nd 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" con?guration of dipoles, as found already in mean ?eld theory, calls for theories valid also for strong correlations. Adding molecule 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 hypernetted-chain Euler- Lagrange (HNC-EL) method and 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 ?eld approach that is used in the majority of past theoretical work. We will use the mean ?eld approach only for the purpose of comparing with the above methods.

In our project we studied ultra-cold dipolar quantum gases with theoretical and numerical tools, in order to understand corresponding experiments, predict their results and motivate new experiments. Unlike in a classical gas, such as the air surrounding us, the temperature in these experiments is so low (of the order of nano-Kelvin) that quantum mechanics has an essential and exciting influence on their properties.The predictions that Bose and Einstein made in 1925 that identical particles of a certain type (those with integer spin) condense into a peculiar macroscopic quantum state at sufficiently low temperature, created a new field of physics 70 years later, the field of ultra-cold quantum gases. For more than20 years now, atomic Bose-Einstein condensates are almost routinely being produced in many labs, their properties being studied and new discoveries being made. The field has matured to the point where experiments on ultra-cold gases are suggested as quantum simulators that emulate systems in completely different fields such as material science, and that one day might complement numerical calculations using condense matter theories. In all these experiments with gases of (neutral) atoms, the density is so low that the interaction between the atoms is very local and its range small; atoms interact only if they occupy almost the same point in space.In recent experiments, ultracold gases of molecules have been produced. Molecules consisting of different kinds of atoms have an electric dipole moment by default. Unlike neutral atoms, molecules with a dipole moment interact over a long range since the interaction between two dipoles falls off slowly, as the inverse third power of the distance. Furthermore the interaction between polar molecules can be quite strong, even under typical experimental conditions at low gas density. Finally, unlike atoms, molecules are not just like points moving through space, but they can also rotate.In our project we investigated the effects of strong dipolar interactions on various properties of molecular quantum gases. For example we found that under certain conditions, the anisotropy of the dipolar interaction (i.e. it depends not just on the distance but also on the orientations of the dipole moments) can lead to stripes. i.e. the quantum gas exhibits a static oscillation of the density. Of particular interest for us are dynamical properties. Regarding the example of the stripe phase, we discovered a certain type of excitation called roton the energy of which vanishes exactly when the stripes appear. Hence the system becomes soft and susceptible to getting stripes when it requires no energy to generate a roton. For these and all other investigations, we built the numerical tools grounded in theoretical physics, and advanced the theoretical background when needed.Quantum gases will eventually enter the realm of applications, such as highly accurate clocks they surpass standard atomic clocks already nowadays , and maybe quantum simulators will help the future physicist to understand phenomena in material science, cosmology or high energy physics. Such progress requires the foundation of theoretical physics for understanding experiments and for calculating and predicting their results.