The properties of the ground state change dramatically at a quantum phase transition and competing processes usually generate complex dynamical features close to a quantum critical point. We study quantum phase transitions and their analogs in the excitation spectrum with semiclassical methods.

We are further interested in the generation of highly sensitive quantum states and macroscopic superpositions in spinor Bose-Einstein condensates, making use of the properties of different quantum phases and the transitions between them.

• P. Feldmann et al., Phys. Rev. Lett. 126, 230602 (2021).

• P. Feldmann et al., Phys. Rev. A 97, 032339 (2018).

• L. Pezzè et al., Phys. Rev. Lett. 123, 260403 (2019).

• M. Gessner, V. M. Bastidas, T. Brandes, and A. Buchleitner, Phys. Rev. B 93, 155153 (2016).

• M. Gessner, M. Ramm, H. Häffner, A. Buchleitner, and H.-P. Breuer, Europhys. Lett. 107, 40005 (2014).

Trapped-ion quantum simulators provide controlled access to vibrational and electronic degrees of freedom as well as the couplings between them. The electronic decay rates in the long-time limit depend on the precise interplay of these parameters, in analogy to the electron transfer rate in molecular systems. This allows us to study Marcus theory (a standard model for nonadiabatic electron transfer) with a degree of control that is impossible to achieve in state-of-the-art molecular systems. By changing the parameters, we can further cross over into adiabatic or deep quantum regimes and study the conditions for electron transfer under unusual conditions.

• F. Schlawin, M. Gessner, A. Buchleitner, T. Schätz, and S. S. Skourtis, PRX Quantum 2, 010314 (2021).

A powerful tool for the characterization of complex dynamical processes can be achieved by analyzing multi-time correlation functions. Nonlinear spectroscopy is a method based on a sequence of phase-coherent laser pulses that allows to follow a dynamical excitation process in time. The information provided by 2D spectroscopy has shown to be extremely useful for chemical systems. We study applications and extensions of these methods in the context of increasingly complex quantum many-body systems.

• M. Gessner, F. Schlawin, H. Häffner, S. Mukamel, and A. Buchleitner, New J. Phys. 16, 092001 (2014).

• F. Schlawin, M. Gessner, S. Mukamel, and A. Buchleitner, Phys. Rev. A 90, 023603 (2014).

• M. Gessner, F. Schlawin, and A. Buchleitner, J. Chem. Phys. 142, 212439 (2015).

In many cases it is important to know whether the quantum system at hand is correlated with other, possibly unknown systems. For example, to verify the presence of correlations with another party in a quantum communication setup or to identify an unwanted eavesdropper. In open quantum systems, the presence of initial system-environment correlations can have a significant impact on the dynamics. In all these cases, measurements are usually limited to the local quantum system. We developed a method that allows to detect discord-type correlations with another, possibly unknown system, without ever requiring access to that system.

• M. Gessner and H.-P. Breuer, Revealing correlations between a system and an inaccessible environment in Advances in Open Systems and Fundamental Tests of Quantum Mechanics (Springer Nature Switzerland, 2019), pp. 59-71.

• M. Gessner, H.-P. Breuer, and A. Buchleitner, The local detection method: Dynamical detection of quantum discord with local operations in Lectures on General Quantum Correlations and their Applications, (Springer International Publishing, 2017), pp. 275–307.

• A. Abdelrahman et al., Nat. Commun. 8, 15712 (2017).

• J.-S. Tang et al., Optica 2, 1014 (2015).

• M. Gessner et al., Europhys. Lett. 107, 40005 (2014).

• M. Gessner, M. Ramm, T. Pruttivarasin, A. Buchleitner, H.-P. Breuer, and H. Häffner, Nature Phys. 10, 105 (2014).

• M. Gessner and H.-P. Breuer, Phys. Rev. A 87, 042107 (2013).

• M. Gessner and H.-P. Breuer, Phys. Rev. Lett. 107, 180402 (2011).