Testing Quantum Theory with Higher-Order Interference in Many-Particle Correlations (Springer Theses)

✍ Scribed by Marc-Oliver Pleinert

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 209
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Supervisor’s Foreword
Abstract
Publications Related to This Thesis
Contents
1 Introduction
References
2 Foundations
2.1 Non-relativistic Classical Mechanics
2.2 Classical Electrodynamics
2.3 Non-relativistic Quantum Mechanics
2.4 Comparison: The Double-Slit Experiment
References
3 Path Integral Approach to Quantum Interference
3.1 Principle of Least Action in Classical Mechanics
3.2 Path Integral Formalism
3.2.1 Classical Limit
3.2.2 Equivalence to the Schrödinger Equation
3.3 Spatial Propagator and Maupertui's Principle
3.4 Double-Slit Experiment Revisited
3.4.1 Notions and Derivation of the Pattern
3.4.2 Wave Function Evolution and Mode Transformation
3.4.3 Phase Convention
3.4.4 Final Remarks
References
4 Quantum Theory of Light
4.1 Quantization of the Electromagnetic Field
4.1.1 Canonical Field Quantization
4.1.2 Quanta of Light—Photons and the Number States
4.2 Pure States, Mixed States and the Density Operator
4.3 Photon Detection Process and Correlation Functions
4.4 Mutual Coherence
References
5 A Family of Sorkin Parameters to Test Born's Rule Using Mutually Coherent Sources
5.1 Single-Particle Interference Phenomena
5.1.1 General Interference Patterns
5.1.2 Interference Orders and Hierarchy
5.1.3 Sorkin Parameter and Single-Particle Tests
5.2 Two-Particle Interference Phenomena
5.2.1 Interference Patterns
5.2.2 Classical Contributions
5.2.3 Interference Hierarchy and Two-Particle Sorkin Parameter
5.3 Many-Particle Interference Phenomena
5.3.1 Higher-Order Classical Terms
5.3.2 M-Particle Fock States
5.3.3 Interference Hierarchy
5.3.4 Number of Contributions and Family of Sorkin Parameters
5.4 The Family of Sorkin Parameters as a Test of Born's Rule
References
6 Measuring the Interference Hierarchy of Single- and Two-Particle Correlations with Coherent Light
6.1 Interference Hierarchy of Coherent States
6.2 Experimental Setting
6.2.1 Preparation: Laser and Propagation to the Slit Mask
6.2.2 Manipulation: Slit Masks and Their Alignment
6.2.3 Detection: Data Acquisition and Evaluation
6.2.4 Measurement Process
6.3 Results
6.3.1 Single-Particle Correlations: Relative Intensity and Alignment
6.3.2 Interference Hierarchy and Sorkin Parameter up to Two-Particle Correlations
References
7 Many-Particle Interference Hierarchy of Mutually Incoherent Sources
7.1 Mutually Incoherent Sources
7.1.1 Single-Photon Emitters
7.1.2 Thermal Light Sources
7.2 Single- and Many-Particle Interference Phenomena
7.2.1 Interference Hierarchy
7.2.2 Incoherent Family of Sorkin Parameters
7.3 Experimental Setting
7.3.1 Generation of (Pseudo-)Thermal Light
7.3.2 Setup Adjustments
7.3.3 Data Acquisition and Evaluation
7.3.4 Measurement Process
7.4 Interference Hierarchy and Sorkin Parameter up to Four-Particle Correlations
References
8 Contributions of Exotic Looped Paths to the Sorkin Parameter
8.1 Single-Particle Correlations
8.1.1 Straight and Looped Paths in Slit Setups
8.1.2 Impact on the Single-Particle Sorkin Parameter
8.1.3 Impact on Interference of Higher Orders
8.2 Extension to Two-Particle Correlations
8.2.1 Two-Particle Propagator
8.2.2 Looped Paths in Two-Particle Experiments
8.2.3 Impact on the Two-Particle Sorkin Parameter
8.3 Implications for the Many-Particle Sorkin Parameter
References
9 Summary and Outlook
References
Appendix Evaluation of the Wave Function Evolutions and Cross Moments
A.1 M-Photon Fock State
A.1.1 Total Evolution and Interference Patterns
A.1.2 Calculation of the Cross-Moments of a Spread M-Particle Fock State
A.1.2.1 Evaluation of the First-Order Cross Moments
A.1.2.2 Evaluation of the Mth-Order Cross Moments
A.2 Coherent States
A.2.1 Wave Function Evolution and Photon Correlations
A.2.2 Correlation Functions and Intensity Correlations
A.3 Set of Single-Photon Emitters
Reference