Optical interference is regarded as a classical phenomenon and is usually completely described in classical terms, in which optical fields are represented by classical waves. Does it mean that optical interference, which is fundamentally ascribable to the phenomenon of a superposition of wave amplitudes, cannot be applied to test quantum phenomena? The superposition principle is at the heart of quantum physics and one could expect that it should distinguish the quantum nature of light from thewave nature. Our experience based on extensive theoretical analysis and experimental observations shows that classical and quantum theories of optical interference readily explain the presence of an interference pattern resulting from the first-order coherence. However, there are interference effects involving the higher order (second-order) coherence that distinguish the quantum (photon) nature of light from the wave nature. Quantum interference has recently returned to prominence because of its utility in manipulating spontaneous emission and other radiative properties of atomic systems. In this chapter, we present elementary concepts and definitions of both the classical and quantum theory of optical interference and discuss similarities and differences between these two approaches [80].
Authored by a highly regarded international researcher and pioneer in the field, An Introduction to Quantum Optics: Photon and Biphoton Physics is a straightforward overview of basic principles and experimental evidence for the quantum theory of light. This book introduces and analyzes some of the most exciting experimental research to date in the field of quantum optics and quantum information, helping readers understand the revolutionary changes occurring in optical science. Paints a picture of light in terms of general quantum interference, to reflect the physical truth behind all optical observations Unlike most traditional books on the subject, this one introduces fundamental classical and quantum concepts and measurement techniques naturally and gradually as it explores the process of analyzing typical experimental observations. Separating itself from other books with this uncommon focus on the experimental part of analysis, this volume: Provides a general overview of the optical coherence of light without quantization Introduces concepts and tools of field quantization and quantum optics based on the principles and rules of quantum mechanics Analyzes similarities and differences between classical and quantum coherence Concentrates on key research topics in quantum optics Explains photon and biphoton physics by examining the devices and experimental procedures used to test theories This book is basic enough for students, but it also covers a broad range of higher-level concepts that will benefit scientists and other professionals seeking to enhance their understanding of practical and theoretical aspects and new experimental methods of measurement. This material summarizes exciting developments and observations and then helps readers of all levels apply presented concepts and tools to summarize, analyze, and resolve quantum optical problems in their own work. It is a great aid to improve methods of discovering new physics and better understand and apply nontraditional concepts and interpretations in both new and historical experimental discoveries.
The nature of light, extending from the optical to the x-ray regime, is reviewed from a diffraction point of view by comparing field-based statistical optics and photon-based quantum optics approaches. The topic is introduced by comparing historical diffraction concepts based on wave interference, Dirac’s notion of photon self-interference, Feynman’s interference of space–time photon probability amplitudes, and Glauber’s formulation of coherence functions based on photon detection. The concepts are elucidated by a review of how the semiclassical combination of the disparate photon and wave concepts have been used to describe light creation, diffraction, and detection. The origin of the fundamental diffraction limit is then discussed in both wave and photon pictures. By use of Feynman’s concept of probability amplitudes associated with independent photons, we show that quantum electrodynamics, the complete theory of light, reduces in lowest order to the conventional wave formalism of diffraction. As an introduction to multi-photon effects, we then review fundamental one- and two-photon experiments and detection schemes, in particular the seminal Hanbury Brown–Twiss experiment. The formal discourse of the paper starts with a treatment of first-order coherence theory. In first order, the statistical optics and quantum optics formulations of coherence are shown to be equivalent. This is elucidated by a discussion of Zernike’s powerful theorem of partial coherence propagation, a cornerstone of statistical optics, followed by its quantum derivation based on the interference of single-photon probability amplitudes. The treatment is then extended to second-order coherence theory, where the equivalence of wave and particle descriptions is shown to break down. This is illustrated by considering two photons whose space–time probability amplitudes are correlated through nonlinear birth processes, resulting in entanglement or cloning. In both cases, the two-photon diffraction patterns are shown to exhibit resolution below the conventional diffraction limit, defined by the one-photon diffraction patterns. The origin of the reduction is shown to arise from the interference of two-photon probability amplitudes. By comparing first- and second-order diffraction, it is shown that the conventional first-order concept of partial coherence with its limits of chaoticity and first-order coherence has the second-order analogue of partial entanglement, with its limits corresponding to two entangled photons (“entangled biphotons”) and two cloned photons (“cloned biphotons”), the latter being second-order coherent. The concept of cloned biphotons is extended to the case of
n cloned photons, resulting in a
1/n reduction of the diffraction limit. In the limit of
nth-order collective state are shown to propagate on particle like trajectories, reproducing the 0th-order ray-optics picture. These results are discussed in terms of the linearity of quantum mechanics and Heisenberg’s space–momentum uncertainty principle. Finally, a general concept of coherence based on photon density is developed that in first order is equivalent to the conventional wave-based picture.
We wish to report an experimental observation of anti-correlation from first-order incoherent classical chaotic light. We explain why the classical statistical theory does not apply and provide a quantum interpretation. In quantum theory, either correlation or anti-correlation is a two-photon interference phenomenon, which involves the superposition of two-photon amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of producing a joint-photodetection event.
Electromagnetic Wave Theory and Measurement of Light Electromagnetic Wave Theory of Light Classical Superposition Measurement of Light Intensity of Light: Expectation and Fluctuation Measurement of Intensity: Ensemble Average and Time Average Coherence Property of Light-The State of the Radiation Coherence Property of Light Temporal Coherence Spatial Coherence Diffraction and Propagation Diffraction Field Propagation Optical Imaging A Classic Imaging System Fourier Transform via a Lens First-Order Coherence of Light First-Order Temporal Coherence First-Order Spatial Coherence Second-Order Coherence of Light Second-Order Coherence of Coherent Light Second-Order Correlation of Chaotic-Thermal Radiation and the HBT Interferometer The Physical Cause of the HBT Phenomenon Near-Field Second-Order Spatial Coherence of Thermal Light Nth-Order Coherence of Light Nth-Order Near-Field Spatial Coherence of Thermal Light Homodyne Detection and Heterodyne Detection of Light Optical Homodyne and Heterodyne Detection Balanced Homodyne and Heterodyne Detection Balanced Homodyne Detection of Independent and Coupled Thermal Fields Quantum Theory of Light: Field Quantization and Measurement The Experimental Foundation-Part I: Blackbody Radiation The Experimental Foundation-Part II: Photoelectric Effect The Light Quantum and the Field Quantization Photon Number State of Radiation Field Coherent State of Radiation Field Density Operator and Density Matrix Composite System and Two-Photon State of Radiation Field A Simple Model of Incoherent and Coherent Radiation Source Pure State and Mixed State Product State, Entangled State, and Mixed State of Photon Pairs Time-Dependent Perturbation Theory Measurement of Light: Photon Counting Measurement of Light: Joint Detection of Photons Field Propagation in Space-Time Quantum Theory of Optical Coherence Quantum Degree of First-Order Coherence Photon and Effective Wavefunction Measurement of the First-Order Coherence or Correlation Quantum Degree of Second-Order Coherence Two-Photon Interference vs. Statistical Correlation of Intensity Fluctuations Second-Order Spatial Correlation of Thermal Light Photon Counting and Measurement of G(2) Quantum Entanglement EPR Experiment and EPR State Product State, Entangled State, and Classically Correlated State Entangled States in Spin Variables Entangled Biphoton State EPR Correlation of Entangled Biphoton System Subsystem in an Entangled Two-Photon State Biphoton in Dispersive Media Quantum Imaging Biphoton Imaging Ghost Imaging Ghost Imaging and Uncertainty Relation Thermal Light Ghost Imaging Classical Simulation of Ghost Imaging Turbulence-Free Ghost Imaging Two-Photon Interferometry I: Biphoton Interference Is Two-Photon Interference the Interference of Two Photons? Two-Photon Interference with Orthogonal Polarization Franson Interferometer Two-Photon Ghost Interference Delayed Choice Quantum Eraser Two-Photon Interferometry II: Quantum Interference of Chaotic Light Two-Photon Young's Interference Two-Photon Anticorrelation with Incoherent Chaotic Light Two-Photon Interference with Incoherent Orthogonal Polarized Chaotic Light Bell's Theorem and Bell's Inequality Measurement Hidden Variable Theory and Quantum Calculation for the Measurement of Spin 1/2 Bohm State Bell's Theorem and Bell's Inequality Bell States Bell State Preparation
From the point of view of classical theory and our everyday experience, quantum phenomena are surprising and the concepts of quantum mechanics are incomprehensible. Since the beginning of quantum theory scientists questioned its very basic concepts, such as locality, reality, and complementarity, and proposed gedankenexperiments , or thought experiments, to probe its foundations. In the light of new optical technology we have been able to realize some of these experiments. This chapter will focus on three of them: (1) EPR-Bohm-Bell correlation and Bell’s inequality; (2) Scully’s quantum eraser; (3) Popper’s experiment. The results of these experiments are very interesting. On one hand, the experimental observations confirm the predictions of EPR-Bell, Scully, and Popper. On the other hand, the calculations from quantum theory perfectly agree with the experimental data. Moreover, apparently, the experimental observations do not lead to any “violations” of the principles of quantum mechanics. One important conclusion we may draw from these optical tests is that all the observations are the results of multi-photon interference: a group of photons interferes with the group itself at distance. The nonlocal multi-photon interference phenomena may never be understood in classical theory, however, it is legitimate in quantum mechanics. The superposition principle of quantum theory supports the superposition of multi-photon amplitudes, whether the photons are entangled or randomly grouped and despite the distances between these individual photodetection events. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Photons are discrete particles of light, yet they undergo interference, a phenomenon typically demonstrated by waves. This phenomenon, known as “wave-particle duality,” is inexplicable in classical physics. In this chapter, we discuss two experiments. The first experiment demonstrates how photons can undergo interference and how measurement can force photons to give up their wave nature and behave like particles that cannot interfere. The second experiment adds to the surprise, showing that it is not only the measurement of the photon under consideration that can force it to change its nature but also that of its entangled twin.