# Research

Welcome to the theoretical quantum physics group

Our research interest is the investigation of ultracold atomic gases and condensed matter system.

## Ultracold quantum gases

In recent years significant advances in the field of ultra cold atoms have facilitated the production of dilute quantum degenerate gases and have culminated in engineering quantum many-body systems with tunable interactions and geometries. The vibrant interplay between cold atomic gases and condensed matter physics has triggered a new wave of research in this field both experimentally and theoretically. Generic condensed matter systems are mimicked with atoms optical lattices, which are lattice potentials created from standing wave laser potentials.

We study particle transport through a chain of coupled sites connected to free-fermion reservoirs at both ends, subjected to a local particle loss. The transport is characterized by calculating the conductance and particle density in the steady state using the Keldysh formalism for open quantum systems. In addition to a reduction of conductance, we find that transport can remain (almost) unaffected by the loss for certain values of the chemical potential in the lattice. We show that this “protected” transport results from the spatial symmetry of single-particle eigenstates. At a finite voltage, the density profile develops a drop at the lossy site, connected to the onset of nonballistic transport.

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many-body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. In particular, for large dissipation strengths a steady state with a fully mixed atomic sector is obtained crucially different from the predicted mean-field state.

We propose how a fermionic quantum gas confined to an optical lattice and coupled to an optical cavity can self-organize into a state where the spontaneously emerging cavity field amplitude induces an artificial magnetic field. The fermions form either a chiral insulator or a chiral liquid carrying chiral currents. The feedback mechanism via the dynamical cavity field enables robust and fast switching in time of the chiral phases, and the cavity output can be employed for a direct nondestructive measurement of the chiral current.

## Solid state physics

Materials have often very complex structures. Electrons are moving on the background formed from the ion core. The interaction between electrons is of great importance. For example quasi-one dimensional strongly interacting spin structures have been found in different organic compounds and open the way to investigate the strong quantum fluctuations in low dimensions. We investigate the properties of low dimensional materials. One example is the fascinating transition of a Luttinger liquid in weakly coupled spin ladders to a Bose-Einstein condensation.

We investigate the Fermi-Hubbard model with a Floquet-driven impurity in the form of a local time-oscillating potential. For strong attractive interactions a stable formation of pairs is observed. These pairs show a completely different transmission behavior than the transmission that is observed for the single unpaired particles. Whereas in the high frequency limit the single particles show a maximum of the transition at low driving amplitudes, the pairs display a pronounced maximum transmission when the amplitude of the driving lies close to the ratio of the interaction U and the driving frequency ω. We use the distinct transmission behaviour to design filters for pairs or single particles, respectively. For example one can totally block the transmission of single particles through the driven impurity and allow only for the transmission of pairs. We quantify the quality of the designed filters.

We show the presence of Majorana edge modes in an interacting fermionic ladder with spin in a number conserved setting. The interchain single particle hopping is suppressed and only a pair hopping is present between the different chains of the ladder. Additionally, the hopping along the chains is spin imbalanced and a transverse magnetic field is applied breaking time-reversal invariance. We study the robustness of the topological phase with respect to an on-site interaction between the spin-up and spin-down fermions and the spin dependent imbalance of the hopping. The main result of the present work is that the topological phase survives for a finite region in the parameter space in the presence of interactions. The localized Majorana edge modes seems to be more stable in the case when the on-site interaction is an attraction.

## Method development

The realization of strongly correlated systems in and out of equilibrium in quantum gases and in nanostructures poses interesting questions which can be tackled theoretically only using state of the art methods. We apply different analytical and numerical methods to get insights into the physics of these systems. One method which has been developed by us is for example the numerical adaptive time-dependent density matrix renormalization group method well suited to investigate the dynamics of low dimensional systems.

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field.

We compare the efficiency of different matrix product state (MPS) based methods for the

calculation of two-time correlation functions in open quantum systems. The methods are the purification approach and two approaches based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.