quantum interference and coherence theory and experiments

[...]... important for later discussion and present some essential mathematical approaches The experiments discussed are those that demonstrate the basic physical ideas concerning first- and second-order interference and coherence The nature of 2 1 Optical Interference and Coherence interference is so fundamental that it connects with many different aspects of atomic physics, classical and quantum optics, such as atom-field... interactions, the theory of measurement, entanglement and collective interactions 1.1 Classical Interference and Optical Interferometers Optical interference is generally regarded as a classical wave phenomenon Despite this, classical and quantum theories of optical interference readily explain the presence of an interference pattern, but there are interference effects that distinguish the quantum nature... following sections 1.2 Principles of Quantum Interference In the classical theory of optical interference and coherence, discussed in the previous sections, the electric field is represented as the sum of its positive and negative frequency parts, which we represent as the complex vectorial amplitudes E (r, t) and E ∗ (r, t), respectively In the quantum theory of interference, the classical electric... quantum mechanics [3] Although interference is usually associated with light, interference has also been observed with many kinds of material particles, such as electrons, neutrons and atoms [4] This introductory chapter concerns the basic theoretical concepts of classical and quantum interference, and elementary interference experiments with optical fields We introduce concepts and definitions that are important... demonstrations of optical interference and for all quantitative measurements of so-called first-order coherence The presence of interference fringes in the experiment may be regarded as a manifestation of first-order coherence Young’s double slit experiment has been central to our understanding of many important aspects of classical and quantum mechanics [1] The essential feature of any optical interference experiment... and no interference pattern was observed for the σ polarized scattered field [Fig 1.6(b)] The above experiments clearly demonstrated that interference and whichway information are mutually exclusive When which-way information is present, no interference pattern is observed, and vice versa: a lack of which way information results in the appearance of the interference pattern [11] 1.1.5 Second-Order Coherence. .. temporal coherence (Michelson interferometer) or spatial coherence (Young interferometer) between the two light beams Interference experiments played a central role in the early discussions of the dual nature of light, and the appearance of an interference pattern was recognized as a demonstration that light is wave-like [1] The interpretation of interference experiments changed with the birth of quantum. .. the correspondence between the classical and quantum correlation functions is not unique since ˆ (−) (R, t) and E (+) (R, t) do not commute In addition, this ˆ the operators E correspondence is true only as long as first-order correlation functions are considered, where interference effects do not distinguish between quantum 22 1 Optical Interference and Coherence and classical theories of the electromagnetic... 9.5.3 Collapses and Revivals of a Bose–Einstein Condensate 9.6 Higher Order Coherence in a BEC 377 378 386 387 389 392 393 395 395 397 401 402 References 405 Index 413 1 Classical and Quantum Interference and Coherence Interference is the simplest phenomenon... distinguishes quantum interference from classical interference is the properties of the higher order correlation functions, in particular, those of the second-order correlation function, which can differ greatly Here, we discuss separately spatial and temporal interference effects in the second-order correlations, which distinguish quantum (nonclassical) interference from the classical form Spatial Nonclassical Interference . Figures Zbigniew Ficek Stuart Swain Department of Physics School of Mathematics and Physics The University of Queensland Queen s University Belfast Brisbane, QLD 4072 Belfast, BT7 1NN Australia UK ficek@ physics.uq.edu.au. experimental results. Brisbane, Belfast, Zbigniew Ficek March 2004 Stuart Swain Contents 1 Classical and Quantum Interference and Coherence 1 1.1 ClassicalInterferenceandOpticalInterferometers 2 1.1.1. CorrelationFunctionsfor aMulti-AtomSystem 80 2.2.3 Spectral Expressions 82 XII Contents 3 Superposition States and Modification of Spontaneous Emission Rates 85 3.1 Superposition States in a Multi-Level System