Testing Quantum Theory with Higher-Order Interference in Many-Particle Correlations

The structure of quantum theory permits interference of indistinguishable paths. At the same time, however, it also limits such interference to certain orders and any higher-order interference is prohibited. This thesis develops and studies concepts to test quantum theory with higher-order interference using many-particle correlations, the latter being generally richer and typically more subtle than single-particle correlations. It is demonstrated that quantum theory in general allows for interference up to order 2M in M-particle correlations. Depending on the mutual coherence of the particles, however, the related interference hierarchy can terminate earlier. In this thesis, we show that mutually coherent particles can exhibit interference of the highest orders allowed. We further demonstrate that interference of mutually incoherent particles truncates already at order M+1, although interference of the latter is principally more multifaceted than their coherent counterpart. We introduce two families of many-particle Sorkin parameters, whose members are expected to be all zero when quantum mechanics holds. As proof of concept, we demonstrate the disparate vanishing of such higher-order interference terms as a function of coherence in experiments with mutually coherent and incoherent sources. Finally, we investigate the influence of exotic kinked or looped quantum paths, which are permitted by Feynman's path integral approach, in such setups.

Autorentext

Marc-Oliver Pleinert is currently working as a postdoctoral researcher at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany, and as scientific coordinator of the Collaborative Research Centre Transregio TRR 306 QuCoLiMa - Quantum Cooperativity of Light and Matter. At FAU, he works in the group Quantum Optics & Quantum Information (QOQI) led by Prof. Dr. Joachim von Zanthier. He received his Ph.D. degree in the QOQI group in 2021, for which he received the "Ohm-Preis" of the Physics Department, FAU. During his doctoral studies, he was supported by the Studienstiftung des deutschen Volkes and a member of the International Max Planck Research School (IMPRS): Physics of Light. In 2019, he was elected to participate as Young Researcher at the Lindau Nobel Laureate Meeting dedicated to Physics. His research focuses on tests of quantum theory using multi-particle correlations.

Klappentext

Quantum mechanics is based on a set of only a few postulates, which can be separated into two parts: one part governing the 'inner' structure, i.e., the definition and dynamics of the state space, the wave function and the observables; and one part making the connection to experiments. The latter is known as Born's rule, which - simply put - relates detection probabilities to the modulus square of the wave function. The resulting structure of quantum theory permits interference of indistinguishable paths; but, at the same time, limits such interference to certain interference orders and any higher-order interference is prohibited. The latter would have severe consequences for quantum theory, yet the physical origin of the absence of higher-order interference is not understood.

This thesis develops and studies concepts to test quantum theory with higher-order interference using many-particle correlations, the latter being generally richer and typically more subtle than single-particle correlations. It is demonstrated that quantum theory prohibits any interference of order 2M+1 and larger in mutually coherent M-particle correlations. A family of many-particle Sorkin parameters is introduced, all expected to be zero when quantum mechanics holds. In a proof-of-concept demonstration, the di erent interference orders and the corresponding Sorkin parameters are measured in single- and two-particle correlations. It is further shown that quantum mechanics indeed allows for interference up to order 2M, but depending on the mutual coherence of the particles, the related interference hierarchy can terminate earlier. This thesis shows that interference of mutually incoherent particles is essentially more multifaceted than their coherent counterpart, but, at the same time, the related interference hierarchy truncates already at order M+1. The latter is also demonstrated in two-, three-, and four-particle experiments with thermal light sources. Finally, exotic kinked or looped quantum paths in slit setups, permitted by Feynman's path integral approach, and their contributions are investigated.

Inhalt

Introduction.- Foundations.- Path Integral Approach to Quantum Interference.- Quantum Theory of Light.- A Family of Sorkin Parameters to Test Born's Rule Using Mutually Coherent Sources.- Measuring the Interference Hierarchy of Single- and Two-Particle Correlations With Coherent Light.- Appendix.