Signatures of partial distinguishability in the dynamics of interacting bosons

The collective state of perfectly indistinguishable bosons is required to be fully symmetric under the exchange of any two bosons. As a consequence of the symmetrization, alternative paths for a given initial many-boson state evolving into a measured final state can interfere, which was first observed experimentally via the transmission of two indistinguishable photons through a fair beam splitter, and was subsequently generalized (mostly theoretically) to larger optical setups with more photons. The relation between (in)distinguishability and occurring many-particle interference was so far studied almost exclusively for (photonic) noninteracting particles, since in this case an analytical prediction of the many-particle dynamics is possible in terms of the evolution of single particles. However, in general many-particle systems, interaction among particles is commonly present, which inhibits a reduction to the single-particle level. And although it is clear that interference between evolution paths also strongly influences the many-particle dynamics of interacting indistinguishable particles, the interrelation between interaction and occurring interference has so far not been systematically investigated. Only for two particles, it was found, in theory and an experiment, that interaction diminishes the amount of observable interference, as if the particles became more distinguishable. Whether this qualitative relation also applies in general to larger systems was unclear, since interaction does not directly change the distinguishability of the particles and it increases in general the number of alternative many-particle paths from an initial to a final state. This is the question we are exploring in this dissertation: How does interaction influence the occurrence of interference in systems with partially distinguishable bosons? We choose to study this question in the Bose-Hubbard model, which describes ultracold atoms in optical lattices, as an exemplary system where interaction naturally occurs. To enable systematic investigations, a measure of the degree of indistinguishability of initial Fock states is proposed, which is shown to be correlated with the time-averaged variance of single-mode densities in the absence of interaction. The correlation also prevails for weak interaction and in certain identified cases also for arbitrary interaction strengths. With the help of a perturbative expansion of the time-evolution for weak interaction strength, we reveal how interaction induces a hierarchy of additional interference which leads to the high complexity of the interacting many-particle dynamics. Furthermore, group-theoretical arguments are used to show that the Hilbert space for partially distinguishable particles decomposes into subspaces associated with different permutation symmetries. Since every subspace induces in general a unique dynamics, which overlays with the dynamics from other subspaces, more distinguishable particles that probe more different subspaces show less pronounced interference on average, for any interaction strength.