The interference of the beams of light led to the foundations of wave optics and this motivated founding fathers of quantum mechanics to arrive at the wave equation for quantum particles like electrons. With the advent of quantum theory of light by Planck, Dirac pondered over how the interference would arise with single photons as these fundamental entities could not be broken in two parts like light waves. He introduced the idea of the quantum amplitudes for the paths which needed to be summed up coherently before finding the intensity or the photon detection probability. I will present a very important application of the interference among several paths to understand in clear physical terms the phenomena of super radiance ie the emergence of enhanced radiation from a system initially prepared in a collective state. I will show how how a collective state leads to several paths along which photon can be emitted. A constructive interference of these paths leads to super radiance where as a destructive interference leads to sub radiance.
The interference of the beams of light led to the foundations of wave optics and this motivated founding fathers of quantum mechanics to arrive at the wave equation for quantum particles like electrons. With the advent of quantum theory of light by Planck, Dirac pondered over how the interference would arise with single photons as these fundamental entities could not be broken in two parts like light waves. He introduced the idea of the quantum amplitudes for the paths which needed to be summed up coherently before finding the intensity or the photon detection probability. I will present a very important application of the interference among several paths to understand in clear physical terms the phenomena of super radiance ie the emergence of enhanced radiation from a system initially prepared in a collective state. I will show how how a collective state leads to several paths along which photon can be emitted. A constructive interference of these paths leads to super radiance where as a destructive interference leads to sub radiance.
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.
The puzzles of quantum mechanics are: 1. what is the medium for the photon and for the electron wave? i.e. what is waving? 2. particle interference pattern 3. observer effect. 4. entanglement. In Quantum Erasure and Double-Slit experiments, how does the emitter know to direct the photon two both slits or only to one slit? And how does the detector know where to detect the photons to form an interference pattern and not a bell-shaped (Gaussian) pattern or vice versa? This paper proposes a few, closely related, simple and subtle laws of nature governing quantum phenomena. Some of the findings in this paper are: 1. A photon is emitted in two steps: the creation of photon path and the emission of the photon 2. Although (almost) all of the energy of the photon is localized in space, the photon extends to infinity. An extremely small energy of the photon, which we call the 'precursor wave' in this paper, extends to infinity. The instant the photon is emitted, its precursor wave creates a path to infinity; it appears instantaneously in all its path to infinity, with infinitely small energy density. The precursor wave serves as the 'highway' for the propagation of the main energy packet. However, to conserve the principle of causality, we assume that the tip of the photon propagates at a speed billions times the speed of light. Thus, there are two speeds associated with the photon: the speed we know as c and the speed at which the photon length increases. 2. A photon will be emitted only towards an absorber. A photon is emitted by the interaction of the emitter and a detector. It is obvious that a photon will not be emitted if there is no emitter. Nor will a photon be emitted if there is no detector . Once a photon is emitted, however, it exists objectively, autonomously. The photon is emitted only after its path is determined by the interaction of the emitter and the absorber, at the instant of emission. 3. The photon energy will be concentrated where there is higher wave amplitude, i.e higher intensity of oscillation of electric and magnetic fields. This results in 'dragging' of the electromagnetic energy by the wave, hence eliminating the need for any medium. It is also proposed that single photon interference is a quantum phenomenon whereas two photon interference is a classical phenomenon. Similar laws hold for the electron. The 'medium' for the electron wave is the electron (the electron mass density field) itself. Where there is higher intensity of electron wave/oscillation, there will be higher electron mass density. This means that the electron wave 'drags' the electron with itself. Therefore, no exotic 'medium' is required for the photon and for the electron wave.
Although interferenceis intrinsically a classical wave phenomenon, the superposition principle whichunderlies all interference is also at the heart of quantum mechanics. Feynmanhas referred to interference as really “the only mystery” of quantum mechanics.Furthermore, in some interference experiments we encounter the idea of quantumentanglement, which has also been described as really the only quantum mystery.Clearly interference confronts us with some quite basic questions ofinterpretation. Despite its long history, going back to Thomas Young at thebeginning of the 19th century, optical interference still challenges ourunderstanding, and the last word on the subject probably has not yet beenwritten. With the development of experimental techniques for fast and sensitivemeasurements of light, it has become possible to carry out many of the Gedankenexperiments whose interpretation was widely debated in the 1920s and 1930s inthe course of the development of quantum mechanics. Although this articlefocuses entirely on experiments with light, interference has also been observedwith many kinds of material particles like electrons, neutrons, and atoms. For a given metal, there exists a certain minimum frequency of incidentradiation below which no photoelectrons are emitted. This frequency is calledthe threshold frequency. Increasing the frequency of the incident beam andkeeping the number of incident photons fixed increases the maximum kineticenergy of the photoelectrons emitted. The number of electrons emitted alsochanges because the probabilitythat each impacting photon results in an emitted electron is a function of thephoton energy. However, if just the intensity of the incident radiation isincreased, there is no effect on the kinetic energies of the photoelectrons.Ifthe photon energy is too low, the electron is unable to escape the material.Increasing the intensity of the light increases the number of photons in thebeam of light and thus increases the number of electrons excited but does notincrease the energy that each electron possesses. The energy of the emittedelectrons does not depend on the intensity of the incoming light (the number ofphotons), only on the energy or frequency of the individual photons. It isstrictly an interaction between the incident photon and the outermost electron.
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
Classical theory asserts that several electromagnetic waves cannot interact with matter if they interfere destructively to zero, whereas quantum mechanics predicts a nontrivial light-matter dynamics even when the average electric field vanishes. Here, we show that in quantum optics, classical interference emerges from collective bright and dark states of light, i.e., particular cases of two-mode binomial states, which are entangled superpositions of multimode photon-number states. This makes it possible to explain wave interference using the particle description of light and the superposition principle for linear systems only. It also sheds new light on an old debate concerning the origin of complementarity.