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- Single electron-photon pair creation from a single polarization-entangled photon pair
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- Single-photon emission from single-electron transport in a SAW-driven lateral light-emitting diode

*Andersen 1 and P.*

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How a Photon is Created or Absorbed is an electronic version of a paper by the same title published in this Journal in J. Only minor revisions have been made in the text, but the electronic medium allows interactive graphics and animations that illustrate the points being made much more effectively than could be done in the print medium.

A transition is usually depicted as a vertical arrow between two quantum states with emphasis on conservation of energy, i. At this point, the natural questions of the student are, "How is a photon created or absorbed? What is the mechanism of this process and how long does it take? The stage is set for the cycle to repeat itself for the upcoming generation of students.

The state of affairs has been greatly influenced by over 40 years of popular belief that since a bound system exhibits only certain discrete energies and a transition from one to another cannot proceed through any observable intermediate levels, then the corresponding wavefunction must also evolve in a similar discontinuous manner.

This interpretation has been shown to be incorrect 1. To illustrate the problem, consider a two-state system described by the stationary state functions 1 q , t and 2 q , t where q and t correspond to the spatial and temporal variables, respectively. It is perhaps unfortunate that the time dependence has been highly neglected in the traditional undergraduate texts.

This is undoubtedly a consequence of the importance of the eigenvalues and probability function to most problems of interest. Since 1 q and 2 q are eigenfunctions of the Hamiltonian i. However, it will be shown in this paper that the time dependence of the wavefunction is of crucial importance to understanding the nature of quantum transitions. The formal description of our system during this period of perturbation is given by a linear combination of the stationary state functions sometimes called a superposition function 4 :.

Figure 1. The internal electronic energy of an ensemble of noncolliding atoms subjected to resonance interactions with a monochromatic radiation source. Equation 2 describes a nonstationary state that evolves in time and is not an eigenfunction of the Hamiltonian operator. Therefore the energy is not a constant of motion during the transition period. A common interpretation is that an instantaneous quantum jump in the energy occurred at some unpredictable time during the transition period.

This interpretation may in turn suggest that the superposition function is merely a mathematical formalism; if one could observe the evolution of the state, it would also exhibit an abrupt discontinuity or change from i to j or vice versa.

The first experimental measurements of bulk samples undergoing spectroscopic transitions were obtained from nuclear magnetic resonance observations of the transient nutation effect 6 and spin echoes 7 , 8 using coherent radiation produced by a single radio frequency oscillator.

More recently, the analogous transient nutation effect 9 , 10 and so called "photon echoes" 11 - 13 have been observed in molecular spectra using pulsed coherent laser radiation. These experiments confirm that there are no "quantum jumps" in the non-stationary state; rather there are smooth, continuous periodic changes in the magnetic and electric properties of a system undergoing a transition. In view of these observations it is clear that the superposition function eq.

However, since a superposition function is not an eigenfunction of the Hamiltonian, it is improper to expect that an energy measurement will give an intermediate, time dependent result.

The measurement itself will cause the system to change to either its initial or final stationary state with probabilities consistent with and.

We can, however, ask for the expectation value of the energy which does change monotonically with time during the transition period Fig. This result can be interpreted as the energy of an individual atom or molecule at a specified time during its transition period. Of course, neither a single atom nor the energy of an ensemble of transient species can be observed directly. What can be experimentally observed is the distribution of a macroscopic collection of atoms or molecules over the stationary eigenstates.

Therefore, a different but equivalent interpretation is that and may be regarded as the probability of observing E 1 and E 2 from a single measurement of an ensemble of atoms or molecules at a specific time during the transition period. Accordingly, the spectroscopic perrturbation to first order will couple only states derivable from i and j.

This process is just reversed for emission. In the case of atoms undergoing absorption or stimulated emission, the coefficents c i and c j have been obtained 5. In the limit of large mean free path, low collision frequency,and high electromagnetic field intensities, the dynamics of spectroscopic transitions are dominated by induced absorption and emission processes characterized by eqs. As collision frequencies increase, or the electromagnetic field intensities decrease, collisional dephasing, spontaneous emission, and radiationless energy transfer begin to compete with the absorption and stimulated emission.

Thus, in the typical laboratory measurement where low-power, incoherent sources are used to observe atomic absorption, the non-stationary state is unimportant and optical nutation and other coherent effects are not observed. These effects can be observed in experiments where the radiation source is replaced by an intense laser and the sample is maintained at low pressure or in an atomic beam, effectively eliminating collision-induced processes.

Under these circumstances, a laser with a frequency that matches the transition will drive the atoms periodically from their ground state to the excited state as the system absorbs light and from the excited state back to the ground state as the system is stimulated to emit light. This periodic fluctuation is called transient nutation 6 , 9 , Experimentally, one observes the laser beam growing alternately dimmer and brighter with a period after it has passed through the collision free atomic sample.

It is now very instructive to examine the time dependence of the non-stationary probability function. David McMillin 15 has recently shown that this approach clearly reveals the origin of an oscillating dipole moment during an electronic transition of a one-electron atom. The probability function is obtained from the superposition wavefunction in the usual manner. The first two terms in eq.

However, the last term arises as an interference from the superposition of 1 and 2 and exhibits periodic oscillations at their beat frequency. Since this term is modulated by the product of c 1 and c 2 the beat amplitudes will systematically build during the beginning of a transition reaching a maximum when and then decay during the end of the transition period see Fig.

It is this interference term which gives rise to charge oscillations precisely in resonance with the electromagnetic radiation absorbed or emitted during the transition. Figure 2. The contribution of the interference term to the dynamic probability function is governed by the product of the time-dependent coefficients. Thus the amplitude of the beat frequency increases during the beginning and decays during the end of the transition period. Three simple model systems will be considered: the rigid rotor, the harmonic oscillator, and the hydrogen atom.

In each case dynamic probability functions will be computed for transitions from the respective ground state to the first excited state. For convenience, we will assume a transition period t equal to ten times the period of the electromagnetic radiation. Three dimensional computer graphics 17 were used to plot the dynamic probability as a function of the spatial and temporal variables Fig.

Figure 3. The spatial orientation of a rigid rotor is defined by the conventional spherical polar coordinates, and. We are clearly observing a quantum mechanical, statistically favored trajectory predicting a clockwise rotation in the direction of increasing.

There is also another exactly symmetrical set of diagonal ridges which cross the surface in the opposite direction describing equally probable counterclockwise rotation. Thus the analysis confirms a resonance condition in which the frequency of the radiation is exactly equal to the rotational frequency of the rigid rotor. If the rotating molecule possesses a permanent dipole moment there is clearly a mechanism for the oscillating electric field component of the microwave energy to impart a torque on the molecule.

The resonance condition will insure a constant phase coherence between the oscillating field and the rotating dipole.

The statistical quantum trajectory can be compared directly with the classical trajectory shown as diagonal lines in the , time plane directly below the probability surface in Figure 4. In this case a photon an electromagnetic wave of finite duration is "created" at the expense of molecular rotational energy by the periodic rotation of an electric dipole, not unlike radiowaves created by the periodic oscillation of charge in an antenna.

The frequency of the radiation is equal to the angular frequency of the rotor. It might also be noted that the radiation will be composed of an equal mixture of right and left circularly polarized components corresponding to equally probable clockwise and counter-clockwise molecular rotations. Figure 4a. The period of rotation is shown to equal the period of the interacting microwave radiation.

The classical trajectories are shown as diagonal lines in the , time plane. Figure 4b. Chart from the Rigid Rotor spreadsheet. Harmonic Oscillator The methods described above can also be applied to the harmonic oscillator. For this case the wavefunctions used in eq.

The vibrational period is shown to equal the period of the interacting infrared radiation t. The classical trajectory is shown as a solid line in the q , time plane. Figure 5b. Chart from the Harmonic Oscillator spreadsheet.

The resulting time dependent probability function clearly reveals periodic molecular vibrations. A maximum probability highest elevation journey takes us periodically back and forth to negative and positive values of q. An obvious prerequisite for this resonance interaction is an oscillating molecular dipole.

Again we can correlate the quantum trajectory with the classical trajectory shown in the q , time plane of Figure 5. In both the quantum and classical description, the amplitude of the oscillations increases during an absorption transition as the molecule's vibrational energy or more properly, the expectation value of the molecule's vibrational energy increases, consistent with the increase in separation of the classical turning points.

However, before and after the transition period, the quantum description is very different from the classical description. In contrast, the quantum description of the stationary states gives a time independent probability of bond length and provides no specific details about the dynamics of trajectories.

If we neglect spin, the stationary state wavefunctions of interest include The l selection rule can be rationalized on the basis of inversion symmetry considerations 3 or on the basis of conservation of angular momentum The temporal behavior of the superposition function can also provide a useful insight to the origin of the dipole selection rule Individual animation frames were obtained by evaluating eq.

Each frame of the right side animation was produced by calculating a rendered isosurface at a selected electron density level using a ray-tracing algorithm. This interesting phenomenon shows the electric charge density in the outer region periodically growing at the expense of the inner charge and then the process reversing. The amplitudes of these oscillations are largest during the middle part of the transition period.

The fluctuations in charge are smallest near the beginning and end of the transition period. This merely reflects the magnitude of the product of the coefficients c 1 c 2 of the interference term in the superposition function in eq.

This animation confirms that although the charge density and polarizability is modulated at the correct resonance frequency, there is no oscillating dipole moment in these states. The net charge density is spherically symmetrical for all compositions of the superposition function and therefore there is no mechanism for an external oscillating field to mix these states or to cause this transition by the usual electric dipole interactions.

Figure 7 illustrates the dynamics of a transition between the 1 s 1,0,0 state and the 2 p z 2,1,0 state. During this transition the center of the electron's charge density is periodically displaced in the positive and negative z directions from the nuclear charge giving a persistent oscillating dipole moment.

The process is obviously analogous to the production of radio waves by charge oscillating back and forth at the resonance frequency of an r. In the atomic case the oscillation is driven at the expense of the electronic energy of the atom, i.

A photon is a tiny particle that comprises waves of electromagnetic radiation. As shown by Maxwell, photons are just electric fields traveling through space. Photons have no charge, no resting mass, and travel at the speed of light. Photons are emitted by the action of charged particles , although they can be emitted by other methods including radioactive decay. Since they are extremely small particles, the contribution of wavelike characteristics to the behavior of photons is significant. In diagrams, individual photons are represented by a squiggly arrow.

Online Textbook. Table of Contents. Photons x-ray and gamma end their lives by transferring their energy to electrons contained in matter. X-ray interactions are important in diagnostic examinations for many reasons. For example, the selective interaction of x-ray photons with the structure of the human body produces the image; the interaction of photons with the receptor converts an x-ray or gamma image into one that can be viewed or recorded. This chapter considers the basic interactions between x-ray and gamma photons and matter.

It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves , and the force carrier for the electromagnetic force. The photon belongs to the class of bosons. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave—particle duality , their behavior featuring properties of both waves and particles. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric effect , Einstein introduced the idea that light itself is made of discrete units of energy. In , Gilbert N.

sources for electromagnetic fields, electric charge and magnetic charge, and in probability per unit time and and unit solid angle for emission of the photon in a.

Figure references in this section are to the alternate second edition of Elementary Modern Physics. The photoelectric and Compton effects represent two mechanisms of photon absorption , the process in which a photon gives up some or all of its energy to a material particle contained usually within an atom in a solid. The intensity therefore decays exponentially within the material, as shown in Fig. We can also take x as being the entire thickness of the material, in which case I x represents the photon intensity at the exit surface. By placing radiation detectors in front and behind a sheet of material of known thickness x, the absorption coefficient can be measured.

Electron multiplication charge-coupled devices EMCCD are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. The long-distance quantum transfer between electron-spin qubits in semiconductors is important for realising large-scale quantum computing circuits.

*It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves , and the force carrier for the electromagnetic force.*

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer.

Data and processing scripts associated with this work are available at the University of Cambridge data repository The source data underlying Figs. The long-distance quantum transfer between electron-spin qubits in semiconductors is important for realising large-scale quantum computing circuits.

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measures of the probability of interaction. charged particles because photons have no electrical charge. 8 material (electron density of the absorbing matter). emit their own electromagnetic radiation and return to their.

Figure 1. In , after returning to Copenhagen, he began publishing his theory of the simplest atom, hydrogen, based on the planetary model of the atom. For decades, many questions had been asked about atomic characteristics. From their sizes to their spectra, much was known about atoms, but little had been explained in terms of the laws of physics. Niels Bohr, Danish physicist, used the planetary model of the atom to explain the atomic spectrum and size of the hydrogen atom.

How a Photon is Created or Absorbed is an electronic version of a paper by the same title published in this Journal in J. Only minor revisions have been made in the text, but the electronic medium allows interactive graphics and animations that illustrate the points being made much more effectively than could be done in the print medium. A transition is usually depicted as a vertical arrow between two quantum states with emphasis on conservation of energy, i.

*Будьте моей женой. Она подняла голову.*

Что он не мог разобрать, но все-таки кое-как прочитал первые буквы, В них не было никакого смысла. И это вопрос национальной безопасности. Беккер вошел в телефонную будку и начал набирать номер Стратмора. Не успел он набрать международный код, как в трубке раздался записанный на пленку голос: Todos los circuitos estan ocupados - Пожалуйста, положите трубку и перезвоните позднее.

* И. - Итак, ТРАНСТЕКСТ вскрывает один шифр в среднем за шесть минут.*

Только и делов - вывести человека на свежий воздух. Халохот отчаянно озирался, но Беккера нигде не было. Сотни людей стояли на коленях перед алтарем, принимая причастие.

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## 4 Comments

## Salustio S.

article in Physics Today entitled “The Concept of the Photon,”1 in which we described the “photon” as a classical electromagnetic detected with highest probability at the interference peaks, electric effect, stimulated emission and absorption, saturation acts like an oscillating charge density, producing an ensemble.

## Sinforoso E.

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## Bartlett D.

For a Poisson distribution with average value 16, calculate the probability to The current is the charge of each pulse times the electron charge, times the num- Solution: The CsI:Tl emits 65, scintillation photons per MeV of energy lost.

## Madeleine M.

the free electromagnetic field and the description of single photon processes. But we will also examine some magnetic current in addition to electric charge and current. In such an extended The emission probability given by Wfi. = |〈f| ˆ.