Quantum Dynamics in a Ferromagnetic Atomic Gas

Bose-Einstein condensates (BECs) provide an extraordinary system to study many-body quantum effects with a high degree of control. Using such ultra-cold gases, microscopic quantum effects become visible on a macroscopic scale as thermal fluctuations are negligible. In particular, quantum phase transitions can be observed. These phase transitions can be indicated by an order parameter that abruptly changes at the critical value of a certain control parameter. Throughout this work, a spin-1 BEC with ferromagnetic interactions and zero magnetization is considered. This system exhibits three ground-state quantum phases that can be controlled by an effective magnetic field. These phases have been explored both theoretically and experimentally in the last two decades. Quantum phase transitions are by definition only applicable to the ground state of a system. However, this powerful concept can be extended to states with non-zero energy. Such excited-state quantum phase transitions (ESQPTs) can be driven by a conventional control parameter, but, interestingly, also by a variation of the excitation energy only. ESQPTs have been studied theoretically and their existence itself has been revealed, e.g., in molecular spectra. However, a thorough investigation by an order parameter and in particular the experimental mapping of the corresponding phase diagram remain an open challenge in any physical system. In this thesis, an interferometric order parameter is employed to experimentally map out an excited-state quantum phase diagram. This order parameter is based on dynamical behavior of coherent states that resemble the mean-field phase-space trajectories of excited-state phases. While a ferromagnetic spin-1 BEC with zero magnetization serves as an exemplary platform, the findings can be applied to other quantum systems with similar Hamiltonians. Importantly, the distinction of excited-state quantum phases utilizes the excitation energy as a second control parameter, which presents a key feature of ESQPTs. Our experiments therefore extend the powerful concept of quantum phases and quantum phase transitions to the entire Hilbert space of the spin-1 BEC