Quantum mechanics does neither give information on details of the emission of a photon from a single atom or molecule nor on the physical size of a photon. Experiments to get answers to such questions have, at least in principle, become possible only recently with the advent of single molecule photon sources. If diffraction of light at wavelength sized apertures is already a property of individual photons, some clear statements on emisission can be made: The energy of an individual photon, which at the start of the process is concentrated in an Angstrom sized atom or molecule, is diluted to micrometer dimensions, i.e. by many orders of magnitude. Since single photons can still be detected at least 18 m after their emission, the dilution must be terminated at some point. A photon model presented in an accompanying paper suggests a size for a photon of λ / 2π and explains what does stop and revert the expansion process, thus starting an oscillation.
Quantum mechanics does neither give information on details of the emission of a photon from a single atom or molecule nor on the physical size of a photon. Experiments to get answers to such questions have, at least in principle, become possible only recently with the advent of single molecule photon sources. If diffraction of light at wavelength sized apertures is already a property of individual photons, some clear statements on emisission can be made: The energy of an individual photon, which at the start of the process is concentrated in an Angstrom sized atom or molecule, is diluted to micrometer dimensions, i.e. by many orders of magnitude. Since single photons can still be detected at least 18 m after their emission, the dilution must be terminated at some point. A photon model presented in an accompanying paper suggests a size for a photon of λ / 2π and explains what does stop and revert the expansion process, thus starting an oscillation.
The statistical properties of photon sequences originating from single-molecule emitters differ from those produced by generic light sources. Let us start with the latter. A typical light source (such as a lightbulb) is composed of numerous independent lightemitting atoms or molecules. A sufficiently sensitive photodetector may be used to record the arrival time of each individual photon. The simplest assumption one could adopt to describe this kind of measurement is that the arrival times for different photons are completely uncorrelated (see, however, the discussion at the end of this section). If the properties of the light source (such as, e.g., its brightness) do not depend on time then we should expect that the probability of detecting a photon during an infinitesimal time interval dt is proportional to dt , with the proportionality constant being independent of time or the arrival times of other photons. Let us call this probability λdt , where λ is the probability of detecting a photon per unit time (which will be referred to as the photon count rate). To estimate λ we could measure the number of photons n detected over a certain period of time t and divide it by t : λ ≈ n/t. (7.1) But, since photon arrival times are random, the exact number of photons found during any finite time interval t will fluctuate around its mean value λt , as illustrated in Fig.7.1. A complete description of this process thus requires the probability wn(t) that a specified number of photons, n, is observed during the time interval t . To obtain this probability, it is helpful to think of the number of detected photons, n, as the “state” of the system at time t . At t = 0 we have n = 0. Each time a new photon is detected, the system undergoes a first-order irreversible “reaction” n → n + 1. The overall process thus can be described by the kinetic scheme: 0 λ→ 1 λ→ 2 λ→ 3 λ→ 4 → · · · . Accordingly, wn(t) is described by a system of differential equations of the form dwn(t)/dt = λwn−1(t) − λwn(t), n > 0 (7.2) and dw0(t)/dt = −λw0(t), (7.3) with the initial conditions wn(0) = 0, n > 0 and w0(0) = 1. The solution to Eq. 7.3 is w0(t) = e−λt . (7.4) Substituting this into the differential equation for w1 (Eq. 7.2) we can find the time dependence of w1(t), then substitute the result into the equation for w2(t) and so on. Suppose we have found wn−1(t) and now wish to solve for wn(t). It is convenient to use the ansatz wn(t) = ρn(t)e−λt .
Crucial experiments of physics, such as the quantum mechanical version of the double slit experiment, have so far not been performed with true single (antibunching) photons. Instead, attenuated classical light sources such as bulbs or lasers have been suggested to provide the photons in these experiments. Since attenuators do not change photon statistics, i.e. do not convert classical into non - classical light, reliable single photon beams cannot be generated on this way. Antibunching sources, for example single molecules, are required. Due to the lack of such sources in the past, some extrapolations from the many - photon case to the one photon case have remained speculative, for example the long wavetrain model for a single photon. Alternative hypotheses, elaborated by considering details of the emission of single photons by single molecules are equally probable. Arguments are presented which disfavour the wavetrain model and favour the short pulse as a model for a photon.
The concept of the photon , central to Einstein's explanation of the photoelectric effect, is exactly 100 years old. Yet, while photons have been detected individually for more than 50 years, devices producing individual photons on demand have only appeared in the last few years. New concepts for single-photon sources, or 'photon guns', have originated from recent progress in the optical detection, characterization and manipulation of single quantum objects. Single emitters usually deliver photons one at a time. This so-called antibunching of emitted photons can arise from various mechanisms, but ensures that the probability of obtaining two or more photons at the same time remains negligible. We briefly recall basic concepts in quantum optics and discuss potential applications of single-photon states to optical processing of quantum information: cryptography, computing and communication. A photon gun's properties are significantly improved by coupling it to a resonant cavity mode, either in the Purcell or strong-coupling regimes. We briefly recall early production of single photons with atomic beams, and the operation principles of macroscopic parametric sources, which are used in an overwhelming majority of quantum-optical experiments. We then review the photophysical and spectroscopic properties and compare the advantages and weaknesses of various single nanometre-scale objects used as single-photon sources: atoms or ions in the gas phase and, in condensed matter, organic molecules, defect centres, semiconductor nanocrystals and heterostructures. As new generations of sources are developed, coupling to cavities and nano-fabrication techniques lead to improved characteristics, delivery rates and spectral ranges. Judging from the brisk pace of recent progress, we expect single photons to soon proceed from demonstrations to applications and to bring with them the first practical uses of quantum information.
During these three years we focused on several topics in quantum otpics and quantum electrodynamics. A central theme in our investigations is that of the photon wave function. Can quantum optics and quantum electrodynamics experiments be described simply, in position space, with the help of a wave function describing the photon(s) featured in the experiment ? The answer to that question is not quite obvious: the usual description of photons takes place in the reciprocal space of wave vectors. But these experiments call for a wave mechanical description in the position representation, as is done in quantum mechanics textbooks in situations featuring massive particles. Moreover, in a recent experiment [1], single photon trajectories through a Young two-slit setup have been observed. In order to try and describe these trajectories formally, it is natural to build a wave mechanical formalism for photons. We therefore studied in detail the formal construction of the photon wave function, an object which was little studied until the 1990s. We also studied the properties of the photon wave function in the presence of sources.To do that, we considered several open (interacting) quantum systems. We saw that there exists in principle an infinite number of possibilities when defining the photon wave function. We emphasised several criteria on the basis of which it appears that only three choices for the wave function are interesting. One of them coincides with an object introduced and used by Glauber [2] to study light detection andthe correlations of the electromagnetic field in the quantum regime. We also saw that, in the absence of sources, the propagation equation for a single photon is formally equivalent to Maxwell’s equations. At low photon numbers, the wave function formalism can be very useful. We adapted it to interacting systems,first, to cavity quantum electrodynamics (QED) [3], in particular to the experiments carried out by Serge Haroche’s group [4]. We proposed a simple model to describe photons in QED cavities. With this model, and with the helpof the photon wave function, we studied the propagation of photons escaping a cavity. We also constructed the Lindblad master equation without introducing nonunitary quantum jumps (also see [5]). We finally investigated the spacetime evolution of a photon which is emitted during the decay of an atomic electron. After having carefully studied the dynamics of the electronic decay, especially at very short times [6, 7], we set out to describe the emitted electromagnetic field as rigorously as possible. This emitted field, surprisingly, does not evolve causally. Though this is not entirely unexpected in view of Hegerfeldt’s theorem, which states [8] that causality is impossible for quantum systems which are described by a Hamiltonian with a spectrum which is bounded by below, we identified [9] two other sources of non causality. One of them was predicted qualitatively by Shirokov [10], while the other one, which is completely new as far as we can tell, is still to be better understood
Throughout the development and confirmation of the photon concept, "Gedankenexperiments" have been invoked where a light source is attenuated until "only one photon is in the apparatus." Such a statement requires, however, knowledge on details of the light generation process, which were not known until the advent of true single-photon light sources such as isolated single atoms or molecules. Here, starting from a two atom light source, it is shown that probably multi-atom or multi-molecule light sources do not generate, even not in small fractions, antibunching photons and that attenuation down to one photon per time unit is not reliably possible. Thus, one of the strongest arguments in favour of the existence of single "photons" in free space, the accumulation time argument, which discusses the absorption of a single photon by a single atom or molecule, becomes questionable.