There is no strong distinction, however, between optical physics, applied optics, and optical engineering, since the devices of optical engineering and the applications of applied optics are necessary for basic research in optical physics, and that research leads to the development of new devices and applications.

Often the same people are involved in both the basic research and the applied technology development, for example the experimental demonstration of electromagnetically induced transparency by S. Harris and of slow light by Harris and Lene Vestergaard Hau. Researchers in optical physics use and develop light sources that span the electromagnetic spectrum from microwaves to X-rays. The field includes the generation and detection of light, linear and nonlinear optical processes, and spectroscopy.

Lasers and laser spectroscopy have transformed optical science.

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Major study in optical physics is also devoted to quantum optics and coherence , and to femtosecond optics. Other important areas of research include the development of novel optical techniques for nano-optical measurements, diffractive optics , low-coherence interferometry , optical coherence tomography , and near-field microscopy.

Research in optical physics places an emphasis on ultrafast optical science and technology. The applications of optical physics create advancements in communications , medicine , manufacturing , and even entertainment. One of the earliest steps towards atomic physics was the recognition that matter was composed of atoms , in modern terms the basic unit of a chemical element. This theory was developed by John Dalton in the 18th century. At this stage, it wasn't clear what atoms were - although they could be described and classified by their observable properties in bulk; summarized by the developing periodic table , by John Newlands and Dmitri Mendeleyev around the mid to late 19th century.

Later, the connection between atomic physics and optical physics became apparent, by the discovery of spectral lines and attempts to describe the phenomenon - notably by Joseph von Fraunhofer , Fresnel , and others in the 19th century. From that time to the s, physicists were seeking to explain atomic spectra and blackbody radiation. One attempt to explain hydrogen spectral lines was the Bohr atom model. Experiments including electromagnetic radiation and matter - such as the photoelectric effect , Compton effect , and spectra of sunlight the due to the unknown element of Helium , the limitation of the Bohr model to Hydrogen, and numerous other reasons, lead to an entirely new mathematical model of matter and light: quantum mechanics.

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Early models to explain the origin of the index of refraction treated an electron in an atomic system classically according to the model of Paul Drude and Hendrik Lorentz. The theory was developed to attempt to provide an origin for the wavelength-dependent refractive index n of a material. In this model, incident electromagnetic waves forced an electron bound to an atom to oscillate.

The amplitude of the oscillation would then have a relationship to the frequency of the incident electromagnetic wave and the resonant frequencies of the oscillator.

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The superposition of these emitted waves from many oscillators would then lead to a wave which moved more slowly. Max Planck derived a formula to describe the electromagnetic field inside a box when in thermal equilibrium in In one dimension, the box has length L , and only sinusoidal waves of wavenumber. The equation describing these standing waves is given by:. From this basic, Planck's law was derived.

In , Ernest Rutherford concluded, based on alpha particle scattering, that an atom has a central pointlike proton. He also thought that an electron would be still attracted to the proton by Coulomb's law, which he had verified still held at small scales. As a result, he believed that electrons revolved around the proton. Niels Bohr , in , combined the Rutherford model of the atom with the quantisation ideas of Planck. Only specific and well-defined orbits of the electron could exist, which also do not radiate light. In jumping orbit the electron would emit or absorb light corresponding to the difference in energy of the orbits.

His prediction of the energy levels was then consistent with observation. These results, based on a discrete set of specific standing waves, were inconsistent with the continuous classical oscillator model. In Einstein created an extension to Bohrs model by the introduction of the three processes of stimulated emission , spontaneous emission and absorption electromagnetic radiation. There are a variety of semi-classical treatments within AMO. Which aspects of the problem are treated quantum mechanically and which are treated classically is dependent on the specific problem at hand.

The semi-classical approach is ubiquitous in computational work within AMO, largely due to the large decrease in computational cost and complexity associated with it. For matter under the action of a laser, a fully quantum mechanical treatment of the atomic or molecular system is combined with the system being under the action of a classical electromagnetic field.

Within collision dynamics and using the semi-classical treatment, the internal degrees of freedom may be treated quantum mechanically, whilst the relative motion of the quantum systems under consideration are treated classically. In low speed collisions the approximation fails. Classical Monte-Carlo methods for the dynamics of electrons can be described as semi-classical in that the initial conditions are calculated using a fully quantum treatment, but all further treatment is classical.

Atomic, Molecular and Optical physics frequently considers atoms and molecules in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons, whilst molecular models are typically concerned with molecular hydrogen and its molecular hydrogen ion. It is concerned with processes such as ionization , above threshold ionization and excitation by photons or collisions with atomic particles. While modelling atoms in isolation may not seem realistic, if one considers molecules in a gas or plasma then the time-scales for molecule-molecule interactions are huge in comparison to the atomic and molecular processes that we are concerned with.

This means that the individual molecules can be treated as if each were in isolation for the vast majority of the time. By this consideration atomic and molecular physics provides the underlying theory in plasma physics and atmospheric physics even though both deal with huge numbers of molecules. Electrons form notional shells around the nucleus. These are naturally in a ground state but can be excited by the absorption of energy from light photons , magnetic fields, or interaction with a colliding particle typically other electrons.

Electrons that populate a shell are said to be in a bound state. The energy necessary to remove an electron from its shell taking it to infinity is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy. The atom is said to have undergone the process of ionization.

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In the event that the electron absorbs a quantity of energy less than the binding energy, it may transition to an excited state or to a virtual state. After a statistically sufficient quantity of time, an electron in an excited state will undergo a transition to a lower state via spontaneous emission. The change in energy between the two energy levels must be accounted for conservation of energy.

In a neutral atom, the system will emit a photon of the difference in energy. However, if the lower state is in an inner shell, a phenomenon known as the Auger effect may take place where the energy is transferred to another bound electrons causing it to go into the continuum. This allows one to multiply ionize an atom with a single photon. There are strict selection rules as to the electronic configurations that can be reached by excitation by light—however there are no such rules for excitation by collision processes. From Wikipedia, the free encyclopedia.

Study of matter-light interactions at small scales. Classical mechanics Old quantum theory Bra—ket notation Hamiltonian Interference. Advanced topics. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics.

Main articles: Atomic physics and Molecular physics. See also: Optics. Main articles: Atomic theory and Basics of quantum mechanics. Physics portal. Born—Oppenheimer approximation Frequency doubling Diffraction Hyperfine structure Interferometry Isomeric shift Metamaterial cloaking Molecular energy state Molecular modeling Nanotechnology Negative index metamaterials Nonlinear optics Optical engineering Photon polarization Quantum chemistry Rigid rotor Spectroscopy Superlens Stationary state Transition of state Vector model of the atom.

National Academy Press. Handbook of atomic, molecular, and optical physics. Nova Science Publishers. Parker McGraw Hill Encyclopaedia of Physics 2nd ed. McGraw Hill. Dickerson; I. Geis Chemistry, Matter, and the Universe. Benjamin Inc. Kenyon Curator: Daniel Baye. Pierre Descouvemont. Daniel Baye , Physique Quantique, C.

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Cross sections in atomic and nuclear physics may present rapid variations that are known as resonances. The shapes of these resonances often differ strongly and a parametrization of the cross sections in their vicinity as a function of energy and scattering angle is impossible without understanding the underlying physics. The basic idea was introduced by Kapur and Peierls : the configuration space is divided into two regions. The external region allows satisfying scattering properties. The internal region simplifies the treatment of the wave functions at short distances by the use of a square-integrable basis.

The basis proposed by Kapur and Peierls however suffered from a complicated energy dependence. The boundary between these regions is a parameter known as the channel radius. This radius is chosen large enough so that, in the external region, the different parts of the studied system interact only through known long-range forces and antisymmetrization effects due to the identity of some particles can be neglected.

The scattering wave function is approximated in the external region by its asymptotic expression which is known except for coefficients related to the scattering matrix. In the internal region, the system is considered as confined. Its eigenstates thus form a discrete basis. A well chosen square-integrable basis can provide accurate approximations of scattering wave functions over the internal region.

A matching with the solution in the external region provides the scattering matrix. This method can also provide the bound states of the system. In this case, the external solution behaves as a decreasing exponential. Since the exponential decrease depends on the unknown binding energy, an iteration is then necessary. Many of its practitioners often ignore the progresses about the other aspect of this double-faced method.

As already mentioned, the original goal was to provide an efficient theory for the treatment of nuclear resonances Wigner and Eisenbud, ; Lane and Thomas, An important advantage is that most of these parameters have a physical meaning. This first variant of the method is still very important and much employed, in particular to parametrize the low-energy cross sections relevant in nuclear astrophysics. Such parametrizations are useful to provide cross sections at angles and energies where they have not been measured at least at energies below the maximum energy where measurements took place.

## Atomic theory

In the context of nuclear astrophysics, it is important to reliably extrapolate measured cross sections to the very low energies encountered in stars, at which direct measurements are in general impossible. It is especially competitive in coupled-channel problems with large numbers of open channels where a direct numerical integration may become unstable. Moreover, the influence of closed channels can be taken into account in a simple way.

An additional advantage is that narrow resonances which can escape a purely numerical treatment are easily studied. Its properties are reviewed in Burke and Robb, ; Barrett et al. However, in , just before that review appeared in print, an important improvement of the method was published, which is, therefore, not used in their review.

Bloch introduced a singular operator defined on the boundary between the two regions, now known as the Bloch operator, which allows a more elegant and compact presentation of the method Bloch, References Barrett et al. For each set of good quantum numbers, i. The lowest poles are closely related to bound states at negative energies or to narrow resonances at positive energies. Nevertheless, the poles and the energies of physical states are slightly different see Eq. Because of this shift, the determination of these parameters from data requires some skill.

Contrary to the reduced width, the width is also very sensitive to the effects of transmission through the Coulomb barrier. When studying a reaction, it is necessary to consider more than one channel. The spins of the particles in the different channels play a role.

It is more difficult to adjust such a number of parameters to available data, specially when several partial waves contribute. The size of the collision matrix depends on the number of open channels. Since the shift factor weakly depends on energy, one can make the Thomas approximation Lane and Thomas, , i. In many cases, the reduced width is small and the difference between formal and observed width is negligible with respect to the experimental error bar see section XII. A counterexample can be found in Delbar et al. Data sets are available at the c.

The corresponding cross sections are shown in Figure 1. The three channel radii provide fits which are indistinguishable at the scale of the figure. This indicates that experimental widths must sometimes be considered with caution. They may depend on the way they are derived from the data. This approach is based on a delicate treatment of Coulomb functions. Among these applications, let us mention a detailed study of resonances and an extension of the method to the description of electromagnetic processes.

All these applications have been made in nuclear physics, i.

Nevertheless, using the method still revealed a number of difficulties. They also explained non-intuitive effects such as the Thomas-Ehrman shift Barker and Ferdous, , ghosts of resonances Barker et al. The approach developed by Barker and collaborators has become a standard tool for the analysis of low-energy radiative-capture reactions useful in astrophysics. These analyses essentially provide information on resonance properties spin, energy, width.

In Pellegriti et al. Other recent applications on elastic scattering can be found for example in deBoer et al. At those energies, the cross sections are too small to be measured in the laboratory. It was proposed in by Haglund and Robson and applied to a two-channel problem involving square-well potentials Haglund and Robson, An expansion over a finite basis was introduced by Buttle Buttle, A more serious problem is a discontinuity of the derivative of the wave function at the boundary between the regions that occurs with the traditional choice of basis states inspired by the original ideas in Wigner and Eisenbud, Various solutions to the lack of matching at the boundary have been suggested see Barrett et al.

This apparent problem has attracted a lot of attention even long after an efficient technique where it does not occur was introduced Lane and Robson, ; Lane and Robson, This test provides a measure of the accuracy of the calculations. Many papers impose such a condition, but it has unfavourable effects on the convergence; see Choice of basis and misconceptions and Descouvemont and Baye for a discussion.

It also depends on the channel radius. The other functions, though unphysical, are important to ensure a smooth matching between the internal and external wave functions Baye et al.

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It has an infinity of real simple poles, bounded from below.