Dynamics of phase transitions to gapped and ungapped quantum states

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Since the production of the first atomic Bose-Einstein condensate in 1995, studies of fundamental many-body physics with ultracold atomic gases have been highly successful. They have resulted in a substantial increase of knowledge about quantum fluids and have addressed questions that have been pondered for decades. Their applicability to a better understanding of real materials will facilitate the controllable design of new functional materials in the future.Up to now most of this research has focused on equilibrium systems; however quantum gases are perhaps even better suited to studying non-equilibrium phenomena. In particular, they have the following advantages: (i) Hamiltonian parameters can be controlled in real time by external means, such as laser light or magnetic fields; (ii) near perfect isolation from the environment makes them ideal for studying intrinsic quantum dynamics; (iii) the relevant timescales are generally favourable (millisecond scale) for time resolved studies. These unique features allow for experimentally realizing quantum quench experiments , during which Hamiltonian parameters, such as the interaction strength, are changed either effectively instantaneously ("instantaneous quench") or slowly ("slow quench"). This leaves the system in a state that is not an eigenstate of the Hamiltonian and which subsequently time-evolves and relaxes into a new (possibly stationary) state through many-body quantum interference effects. Quantum quench experiments are the cornerstones of the scientific understanding of non-equilibrium phenomena because they are conceptually very clean and, in the case of an instantaneous quench, best describable theoretically (even though usually still unsolvable). Consider, for example, an isolated many-body quantum system quenched through a phase transition - there are many questions that are still far from being answered: What determines whether the quantum system will equilibrate? How does the quantum system equilibrate? Does equilibration always lead to thermalisation? What are the roles of temperature and energy gaps in the spectrum? How do different processes like density ordering and the establishment of off-diagonal long-range order compete? Of course, formally the unitary time evolution of an isolated quantum mechanical state is known. However, strong interactions and/or long evolution times make the problem theoretically intractable. Additionally, the presence of dissipation complicates matters and even for weak dissipation only very few special cases, such as Markovian dissipation or harmonic oscillator baths, have been thoroughly studied. For crossing a classical phase transitions into an ordered phase, the dynamics of defect formation has been predicted to obey universal behaviour according to the Kibble-Zurek mechanism but the applicability of the mechanism to quantum systems is highly debated. Therefore, answering the above, fairly generic, questions using well-controlled model systems of ultracold atoms will provide crucial benchmarks for establishing possibly general laws of equilibration and thermalisation, which has been considered one of the Grand Challenges of Physics. In our experiments, we will investigate Bose gases quenched through the BEC phase transition as well as Fermi gases quenched into pseudogap or superfluid phases. For the bosonic part, the establishment of off-diagonal long-range order after a quench will be the prime focus in order to establish a firm and general physical picture of this process. In the Fermi case we will explore the relation between local (pair formation) and global (off-diagonal long-range) order. In the limit of preformed local pairs (molecules) we will be in a unique position to directly compare the results with our own measurements with Bose gases. This will then provide an excellent benchmark for gradually moving (by tuning the interactions) towards the more convolved limit of non-local Cooper pairs.