Heinz-Peter Breuer

Understanding how strong coupling and memory effects influence the energy levels of open quantum systems is a complex and challenging problem. Here, we show these effects by probing the transition frequency of an open two-level system within the Jaynes-Cummings model, experimentally realised using Ramsey interferometry in a single trapped 25Mg+ ion. Measurements of the system, coupled to a single-mode environment, reveal a time-dependent shift in the system's energy levels of up to 15% of the bare system frequency. This shift, accurately predicted using an open system ansatz of minimal dissipation, results purely from ultra-strong system-mode interactions and the buildup of correlations. Time-averaged measurements converge to the dispersive Lamb shift predictions and match dressed-state energies, indicating that this observed shift represents a generalised Lamb shift applicable across all coupling and detuning regimes. Our findings provide direct evidence of dynamic energy level renormalisation in strongly coupled open quantum systems, although the total system-environment Hamiltonian is static; this underscores the significance of memory effects in shaping the reduced system's energy landscape. These results offer more profound insights into Hamiltonian renormalisation, essential for strong-coupling quantum thermodynamics and advancements in all quantum platforms.

How can we detect that our local, controllable quantum system is correlated with some other inaccessible environmental system? The local detection method developed in recent years allows to realize a dynamical witness for correlations without requiring knowledge of or access to the environment that is correlated with the local accessible quantum system. Here, we provide a brief summary of the theoretical method and recent experimental studies with single photons and trapped ions coupled to increasingly complex environments.

Trapped atomic ions enable a precise quantification of the flow of information between internal and external degrees of freedom by employing a non-Markovianity measure [H.-P. Breuer et al., Phys. Rev. Lett. 103, 210401 (2009)]. We reveal that the nature of projective measurements in quantum mechanics leads to a fundamental, nontrivial bias in this measure. We observe and study the functional dependence of this bias to permit a demonstration of applications of local quantum probing. An extension of our approach can act as a versatile reference, relevant for understanding complex systems.

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding of nonequilibrium many-body physics. Here we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

We show that the ground-state quantum correlations of an Ising model can be detected by monitoring the time evolution of a single spin alone, and that the critical point of a quantum phase transition is detected through a maximum of a suitably defined observable. A proposed implementation with trapped ions realizes an experimental probe of quantum phase transitions which is based on quantum correlations and scalable for large system sizes.