Negative Frequency at the Horizon: Theoretical Study and Experimental Realisation of Analogue Gravity Physics in Dispersive Optical Media (Springer Theses)

This book is part of a large and growing body of work on the observation of analogue gravity effects, such as Hawking radiation, in laboratory systems. The book is highly didactic, skillfully navigating between concepts ranging from quantum field theory on curved space-times, nonlinear fibre optics and the theoretical and experimental foundations in the physics of optical analogues to the Event Horizon. It presents a comprehensive field-theoretical framework for these systems, including the kinematics governing the fields. This allows an analytical calculation of the all-important conversion of vacuum fluctuations into Hawking radiation. Based on this, emission spectra are computed, providing unique insights into the emissions from a highly dispersive system. In an experimental part, the book develops a clear and systematic way to experimentally approach the problem and demonstrates the construction of an experimental setup and measurements of unprecedented sensitivity in the search for stimulation of the Hawking effect. Supervisor’s Foreword 6 Abstract 9 Acknowledgments 10 Contents 11 1 Introduction 14 References 24 2 Theory of Spacetime Curvature in Optical Fibres 26 2.1 From Astrophysics to the Laboratory 26 2.1.1 Curvature of Spacetime 26 2.1.2 The Schwarzschild Spacetime 30 2.1.3 Laboratory Event Horizons 35 2.2 Developments in Optical Event Horizon Realisation 40 2.2.1 Fiber Optics 40 2.2.2 Fibre-Optical Analogue of the Event Horizon 50 2.3 Equations of the Optical Spacetime 56 2.3.1 Action in an Optical Medium as an Analogue Metric 56 2.3.2 A Black Hole Horizon for Light 58 2.3.3 Conclusion and Discussion 59 References 60 3 Spontaneous Emission of Light Quanta from the Vacuum 62 3.1 Quantum Field Theory in Curved Spacetime 62 3.1.1 Gravity and Thermodynamics: The Failure of Classical Physics 62 3.1.2 Black Hole Evaporation 70 3.1.3 Conclusion and Discussion 82 3.2 Quantum Field Theory in a Condensed Matter System 82 3.2.1 Quantum Vacuum Emission from a Refractive Index Front 82 3.2.2 Light-Matter Interactions in a Dispersive Medium 85 3.2.3 Mode Configurations at a Refractive-Index Front 92 3.2.4 Scattering of the Quantum Vacuum at the RIF 100 3.2.5 Conclusion and Discussion 105 References 106 4 Analytics and Numerics 109 4.1 Analytical Description of Scattering at the RIF 110 4.1.1 Scattering Matrix 111 4.1.2 Matching Local Amplitudes to Calculate Global Ones 113 4.2 Algorithmic of Laboratory Frame Emission 122 4.2.1 Journeying Along the Optical Branch 123 4.2.2 Rate of Particle Production in a Mode 125 4.3 Emission Spectra and Photon Flux 126 4.3.1 Emission in the Moving Frame 127 4.3.2 Emission in the Laboratory Frame 133 4.3.3 Conclusion and Discussion 137 References 139 5 Experimental Observation of Scattering at a Moving RIF 141 5.1 Stimulated Scattering 141 5.2 A Journey, at the Speed of Light, on an Optical Table 144 5.2.1 Pulse and Probe Sources 145 5.2.2 Polarisation and Coupling of Input Light 148 5.2.3 Optical Fibre 150 5.2.4 Strong Output Measurements Setup 154 5.2.5 Probing the Invisible 155 5.2.6 Spectral Sensitivity of the Setup in the UV 158 5.3 Scattering to a Positive-Norm Mode 165 5.3.1 Positive-Norm Scattering Efficiency 166 5.3.2 Tunnelling Model for Probe-Pulse Interaction 167 5.3.3 Visible Frequency Shifts at the Horizon 168 5.4 Scattering to a Negative-Norm Mode 170 5.4.1 Signal to Noise Ratio in the UV 173 5.4.2 UV Spectra 177 5.5 Conclusion and Discussion 184 5.5.1 Stimulated and Spontaneous Scattering at the Horizon 184 5.5.2 Calculation of Spontaneous Emission Around the Group-Velocity-Matched Wavelength 185 5.5.3 The Case for Optical Horizons 187 References 188 6 Conclusion 190 References 193 Appendix A Positive and Negative Frequency 194 Appendix B Modelling of a Change in the Dielectric Constant 196 Appendix C Scattering at a Smooth Profile in a Nondispersive Medium 201 Appendix Author Biography 207 Front Matter ....Pages i-xv Introduction (Maxime J. Jacquet)....Pages 1-12 Theory of Spacetime Curvature in Optical Fibres (Maxime J. Jacquet)....Pages 13-48 Spontaneous Emission of Light Quanta from the Vacuum (Maxime J. Jacquet)....Pages 49-95 Analytics and Numerics (Maxime J. Jacquet)....Pages 97-128 Experimental Observation of Scattering at a Moving RIF (Maxime J. Jacquet)....Pages 129-177 Conclusion (Maxime J. Jacquet)....Pages 179-182 Back Matter ....Pages 183-198