Verschränkung und Interferenz ununterscheidbarer Teilchen
Malte C. Tichy
The present thesis deals with the interrelation between entanglement of identical particles and many-particle interference in multimode scattering scenarios. The processes that govern the scattering are shown to characterize the quantum correlations that result from coherent deletion of many-particle which-way information. Part I treats the constitutive situation of two identical particles which are measured by two detectors to provide a consistent definition of identical-particle entanglement. The key quantities that determine the strength and nature of correlations are diagnosed, which allows a formulation of the problem as scattering scenario. Quite counter-intuitively, the effective indistinguishability of the particles is not necessarily reflected monotonically by the strength of quantum correlations, which is explained by an interplay of the entanglement encoded in the initial state with measurement-induced correlations. The subject of Part II is the scattering of many non-interacting particles that are initially injected in an arbitrary number of modes. A comparison of bosons, fermions and distinguishable particles reveals that the dichotomy of bosons and fermions, known from the two-particle case, does, surprisingly, not prevail for many particles: A given output event can be suppressed or enhanced for bosons and fermions simultaneously. Consequently, the bunching behavior of bosons is not apparent at the level of single counting events, where dynamical many-particle interference dominates, and it is only reflected in more coarse-grained quantities that are related to the occupation statistics, for which efficient approximate treatments are derived. The general complexity of the many-particle problem is overcome for the special case of a Fourier multiport beam splitter. The exploitation of its scattering matrix’ symmetries yields a systematic event suppression law for, both, bosons and fermions, which provides a generalization of the two-photon Hong-Ou-Mandel effect to an arbitrary number of particles and modes. As a further characteristic trait of many-particle interference, the transition between indistinguishable and distinguishable particles is reflected non-monotonically by the event probabilities, which is also confirmed by an experiment that was suggested by the present work. Part III combines the formalism for identical-particle entanglement and the tools and notions developed in the context of many-particle scattering for a description of those multipartite entangled states that can be created via the scattering of many identical particles. The formalism is general enough to include virtually any possible scheme for the multipartite entanglement creation with single photons. An analytical treatment reveals fundamental constraints for the set of accessible states. In particular, an intuitive combinatorial bound for the Schmidt number of the target state follows from the finite number of combinations to distribute the particles among the output modes. Furthermore, bosons and fermions have very distinct potential for entanglement creation: Fewer states are accessible for fermions, whereas the success probability of entanglement production is strongly enhanced with respect to bosons.
•Jan 1, 2011•0 citations