Cold atoms provide idealized and widely tunable model systems for the study of many-body phenomena and strong correlations. Their interaction strength is adjustable either directly by Feshbach resonances, where the scattering length is resonantly enhanced or, effectively, in optical lattices, where atoms are trapped in artificial crystals due to light forces. Current topics of research in this area are fermionic gases near the limit of infinite scattering length. In particular we study imbalanced gases where novel phases like pairing at finite momenta or a breakdown of a Fermi liquid to a polarized superfluid phase may appear. As part of the DFG Research Unit 801 we study analogs of quantum magnetism in multicomponent gases in optical lattices and the dynamics of many-body systems far from equilibrium.

The high degree of control over cold neutral atoms in optical traps and electromagnetic fields down to the single photon level create a diverse environment for the study of both fundamental physics and specific applications. On the fundamental level quantum optical many-body systems are inherently driven and dissipative, which requires the investigation of their critical behavior and classification into new classes of universality. In this area we investigate cavity systems, where long-range retarded interactions draw into question the validity of known paradigms from condensed matter.

As part of a collaboration with the group of D. Chang (ICFO) we focus on photonic crystals, in particular the novel phenomenon of many-body EIT, where photon induced atom-atom interactions create a narrow, controllable transparent frequency interval with strongly non-linear characteristics necessary for photonic quantum switches. Specifically questions regarding the realizability of a non-equilibrium crystal of light in these systems are being addressed.

For our research we combine methods from both condensed matter and quantum optics, incorporating them into computer assisted applications of non-equilibrium path integral methods.

Nanomechanical resonators are promising tools for ultra-sensitive detection of displacements and forces and for the storage and manipulation of quantum information. This requires cooling into a regime where the phonon occupancy of the quantized mechanical motion is of order one. In collaboration with the experimental group of T. Kippenberg (MPQ), we have developed quantum models for the coupling between light and the mechanical motion in optomechanical cavities, which show that ground state cooling is possible in the resolved sideband limit. In a related context, we are studying the coupling of optical cavities to Bose-Einstein Condensates. To achieve the quantum regime in nanomechanical systems it is crucial to understand the limits for mechanical dissipation in these structures. Along these lines we have developed a microscopic theory of phonon tunneling losses (clamping losses) in nanoresonators.

Phonon confinement also plays a key role in determining the limits for qubit-decoherence. In collaboration with the group of A. Imamoglu (ETH) we are currently studying the effect of 1D phonon confinement on the optical lineshape of an embedded two-level emitter.

Although microscopically condensed matter physics is about interaction between electrons, protons, neutrons and light, often the many-body nature of the problem gives rise to emergence of new degrees of freedom with intriguing collective behavior at low energies. These degrees of freedom constitute the building blocks of effective field theories that in addition are constrained by symmetries of the problem. This set-up provides a reliable micro-independent framework for non-perturbative understanding of strongly interacting quantum systems. In our group we are especially interested in the interplay of symmetries, geometry and topology in quantum phases of matter. We apply effective theories to various low-dimensional many-body topological quantum fluids, such as chiral superfluids, superconductors, quantum Hall states and Weyl loop semimetals.