DFG Research Unit FOR 5413

Prof. Dr. Sebastian Slama

The goal of this project is to study the collective behavior of a spin system under the action of collective interactions between all spins (all-to-all), simultaneously acting with long-range interactions between neighbouring spins. In order to carry out this study, we will experimentally implement a Dicke-Ising spin-boson model. Spin states will be realized by Zeeman sublevels of the ground state of cold Rubidium atoms. Collective interactions are mediated by positioning the atoms inside an optical cavity. The atoms will be optically pumped transversally to the cavity axis and collectively driven into the Dicke phase transition. At the same time, long-range interactions (on the order of micrometers) are generated by coupling one of the spin states to a Rydberg state with large detuning (Rydberg dressing), realizing an effective Ising interaction between the spins. We will first study the influence of weak, long-range interactions on the collective dynamics of the atoms and on the Dicke phase diagram. A second step will address the regime where Ising interactions are comparable and compete with the coupling strength of the Dicke model, where we will search for new phases and phase transitions. Experimental work will be supported by a collaboration with a project P2, where the Dicke-Ising model will be investigated theoretically and predictions on the expected phase diagram and on universal behavior at the phase transition will be made. Dissipative effects based on cavity mirror transmission of photons will also be studied, leading to tools that can be used within the experiment in order to identify and characterize dynamical phases and phase transitions using photons that are coupled out of the cavity.

Dr. Beatriz Olmos Sanchez, Prof. Dr. Joszef Fortagh, and Dr. David Petrosyan (Mercator fellow)

The goal of the present project is the investigation of large and small spin systems with cavity mediated all-to-all interactions. We will perform detailed theoretical studies of the so-called Dicke-Ising model, experimentally implemented in P1 of this Research Unit. Here, the infinite-range interactions induced by the collective coupling of a large atomic gas to a cavity coexist with Ising-type long-range interatomic interactions induced by off-resonant laser excitation of Rydberg states. We will explore the novel phases and phase transitions in this model and analyze its potential to create highly correlated many-body quantum states. We will then turn to the study of a few-spin system with infinite-range exchange or Ising-type interactions. This system will be realised experimentally in this project using highly-excited Rydberg atoms coupled to a microwave cavity field that plays the role of a ”quantum bus”. Strong dipole-dipole interactions between the nearby Rydberg atoms will permit the formation of Rydberg superatoms that can accommodate at most one collective excitation. Individual superatoms would represent single spins, which in turn can interact with each other via the cavity-mediated infinite-range interactions. The development of such few- and many-body quantum systems with highly-tunable arbitrary-range interactions will be of paramount importance for scalable implementations of quantum logic gates and the realization of dynamically controlled and configurable quantum simulators.

Prof. Dr. Igor Lesanovsky and Prof. Dr. Christian Lubich

The project proposed here aims to study the phases and phase transitions of an open quantum many-body system with coherent long-range interactions and an absorbing stationary state. We will investigate the temporal dynamics, stationary phases and universal behaviour near the phase transition point. Moreover, we will investigate generalisations of the above dynamics, e.g. the competition between classical and quantum processes. During the project we will develop numerical methods that are able to treat open quantum systems with long-range interactions. This will allow us to understand when and how their dynamics becomes “complex”, i.e. is hard to simulate on classical computers, an whether they can display novel forms of universal behaviour.

Prof. Dr. Daniel Braun, Prof. Dr. Joszef Fortagh, and Dr. David Petrosyan (Mercator fellow)

The project aims to study various non-equilibrium states in dynamically driven, long-range interacting quantum systems and to explore their usefulness for quantum metrology. Theoretically, we will study adiabatic and non-adiabatic (quenched) dynamics of the interacting many-body systems and examine their utility for increasing the sensitivity of measurements of external parameters, such as electromagnetic fields. We will elucidate the role of underlying phase-space structures for the sensitivity and develop and implement quantum algorithms for simulating open complex quantum systems. Experimentally, we will employ two-dimensional clouds of cold trapped atoms coupled by resonant lasers to the highly excited Rydberg states in strong electric fields. Small and fast changes of the control electric field permit dynamical tuning of the corresponding dipole-dipole interaction strength. This enables the realization of different kinds of dynamical driving schemes and tuning the relaxation and ionisation rates. Using an ion microscope with high spatiotemporal resolution, we will perform precise measurements of the spatial and temporal dynamics and correlations in this driven interacting quantum system. Proof of principle experiments for measuring the electric field with sensitivity better than the standard quantum limit will be performed using long-range interacting Rydberg atoms.

Prof. Dr. Christian Groß

In this project we aim at the experimental realization of a time-reversal protocol in twodimensional optical tweezer arrangements coupled by Rydberg-Rydberg interactions. We plan to combine microwave dressing with optical dressing to design binary interaction potentials with reversable sign. Being able to reverse the arrow of time in a generic quantum many-body system provides a powerful tool for quantum simulations. It opens novel control and benchmarking possibilities and provides access to new observables. Ultimately, a Loschmidt echo may be implemented. The new observables provide a window into the complex quantum dynamics and allow for the characterization of information spreading and thermalization rates. One prominent example are out-of-time-order correlation functions, which are useful to characterize entanglement spreading in the system. Time reversal is also a resource in quantum metrology and in systems with short ranged interactions it may allow to utilize the large Fisher information generated in during the evolution for new robust metrology protocols with enhanced sensitivity.

Prof. Dr. Stefan Teufel

Our goal is to develop a rigorous understanding of how the range of interactions and the system size affect the quality of the adiabatic approximation and the validity of linear response theory in quantum spin systems with gapped ground state. To this end, we will construct and analyze nonequilibrium almost-stationary states for perturbations of such systems and their response to adiabatic changes in the Hamiltonian. In particular, we will investigate the extent to which existing results for systems with short-range interactions can be generalized to intermediate- or long-range interactions. The focus will be on sharpening and improving mathematical tools to prove rigorous statements and error estimates. However, another important aspect is that understanding the mathematical obstacles to generalization from short- to long-range will also shed light on the question of which decay exponents can be expected to exhibit qualitatively new behavior with respect to the thermodynamic limit. The answers to these questions are relevant to all areas where adiabatic protocols are applied to many-body systems, to pre-thermalization in many-body systems, and to linear response theory.

Prof. Dr. Sabine Andergassen

The project proposed here aims to provide a functional renormalization group (fRG) based scheme for an improved construction of effective low-energy models whose precise determination is crucial for a quantitative theory. Previously introduced to determine realistic effective interactions for material systems, the fRG accounts for the renormalization of the bare interaction due to virtual transitions of particles from the low-energy bands in consideration to higher energy ones. For systems with shortrange interactions, this has been shown to lead to effective multi-body interactions which can have an important impact on emergent collective behavior and the associated low-energy phase diagram. We here aim at the extension of the fRG for effective interactions formulated for fermionic systems in order to study long-range interacting systems. We will perform a systematic analysis of the interaction structures arising from the interplay between long-range interactions and virtual transitions / renormalization effects for paradigmatic setups relevant also for the description of the experiments of the research unit, where several experimental platforms are available for benchmark and direct application. On a long-term perspective, we plan to link the fRG implementation to existing software packages for calculating Rydberg potentials.