In this project funded by the Villum Foundation, we examine two main topics.

The first topic concerns cold dipolar gases. These gases are predicted to exhibit a wealth of interesting phenomena including nematic phases, stripes (charge-density waves), and p-wave superfluidity. We will focus will be on the interplay between stripe order and superfluidity. A specific goal is to show that fluctuations in stripe order can significantly increase the interaction leading to superfluidity. This effect is speculated to lead to high temperature superconductivity in solid state compounds (cuprates), but there many unknown parameters in these systems and the theory is controversial. It will therefore have major impact if we can demonstrate the principle of fluctuation-enhanced interactions in a controlled system such as a dipolar gas.

The second topic concerns mixtures of bosons and fermions. New experiments are producing such mixtures, where both components are superfluid. We will examine the so-called Bose-polaron, where an “impurity” atom interacts with a Bose-Einstein condensate (BEC). The impurity atom couples to the Bogoliubov (sound) modes of the condensate. The resulting system is closely analogous to electrons coupled to phonons in a crystal forming the Fröhlich polaron. We will develop a systematic perturbative description of the Bose polaron in the Bose-Fermi interaction strength. Surprisingly, such a perturbation theory have not been performed yet in the literature. We will also examine the interplay between 3-body Efimov resonances and the Bose-polaron where interactions are strong.