# Atomic, molecular, and optical physics

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Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms [1] and energy scales around several electron volts. [2] :1356 [3] The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments. Typically, the theory and applications of emission, absorption, scattering of electromagnetic radiation (light) from excited atoms and molecules, analysis of spectroscopy, generation of lasers and masers, and the optical properties of matter in general, fall into these categories.

## Atomic and molecular physics

Atomic physics is the subfield of AMO that studies atoms as an isolated system of electrons and an atomic nucleus, while molecular physics is the study of the physical properties of molecules. The term atomic physics is often associated with nuclear power and nuclear bombs, due to the synonymous use of atomic and nuclear in standard English. However, physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone. The important experimental techniques are the various types of spectroscopy. Molecular physics, while closely related to atomic physics, also overlaps greatly with theoretical chemistry, physical chemistry and chemical physics. [4]

Both subfields are primarily concerned with electronic structure and the dynamical processes by which these arrangements change. Generally this work involves using quantum mechanics. For molecular physics, this approach is known as quantum chemistry. One important aspect of molecular physics is that the essential atomic orbital theory in the field of atomic physics expands to the molecular orbital theory. [5] Molecular physics is concerned with atomic processes in molecules, but it is additionally concerned with effects due to the molecular structure. Additionally to the electronic excitation states which are known from atoms, molecules are able to rotate and to vibrate. These rotations and vibrations are quantized; there are discrete energy levels. The smallest energy differences exist between different rotational states, therefore pure rotational spectra are in the far infrared region (about 30 - 150 µm wavelength) of the electromagnetic spectrum. Vibrational spectra are in the near infrared (about 1 - 5 µm) and spectra resulting from electronic transitions are mostly in the visible and ultraviolet regions. From measuring rotational and vibrational spectra properties of molecules like the distance between the nuclei can be calculated. [6]

As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics. Physics research groups are usually so classified.

## Optical physics

Optical physics is the study of the generation of electromagnetic radiation, the properties of that radiation, and the interaction of that radiation with matter, [7] especially its manipulation and control. [8] It differs from general optics and optical engineering in that it is focused on the discovery and application of new phenomena. 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. E. Harris and of slow light by Harris and Lene Vestergaard Hau. [9] [10]

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. Major study in optical physics is also devoted to quantum optics and coherence, and to femtosecond optics. [1] In optical physics, support is also provided in areas such as the nonlinear response of isolated atoms to intense, ultra-short electromagnetic fields, the atom-cavity interaction at high fields, and quantum properties of the electromagnetic field. [11]

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. [12]

## History

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. [13]

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. [14]

From that time to the 1920s, physicists were seeking to explain atomic spectra and blackbody radiation. One attempt to explain hydrogen spectral lines was the Bohr atom model. [13]

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. [15]

### Classical oscillator model of matter

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. The superposition of these emitted waves from many oscillators would then lead to a wave which moved more slowly. [16] :4–8

### Early quantum model of matter and light

Max Planck derived a formula to describe the electromagnetic field inside a box when in thermal equilibrium in 1900. [16] :8–9 His model consisted of a superposition of standing waves. In one dimension, the box has length L, and only sinusoidal waves of wavenumber

${\displaystyle k={\frac {n\pi }{L}}}$

can occur in the box, where n is a positive integer (mathematically denoted by ${\displaystyle \scriptstyle n\in \mathbb {N} _{1}}$). The equation describing these standing waves is given by:

${\displaystyle E=E_{0}\sin \left({\frac {n\pi }{L}}x\right)\,\!}$.

where E0 is the magnitude of the electric field amplitude, and E is the magnitude of the electric field at position x. From this basic, Planck's law was derived. [16] :4–8,51–52

In 1911, 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 1913, 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. [16] :9–10

These results, based on a discrete set of specific standing waves, were inconsistent with the continuous classical oscillator model. [16] :8

Work by Albert Einstein in 1905 on the photoelectric effect led to the association of a light wave of frequency ${\displaystyle \nu }$ with a photon of energy ${\displaystyle h\nu }$. In 1917 Einstein created an extension to Bohrs model by the introduction of the three processes of stimulated emission, spontaneous emission and absorption (electromagnetic radiation). [16] :11

## Modern treatments

The largest steps towards the modern treatment was the formulation of quantum mechanics with the matrix mechanics approach by Werner Heisenberg and the discovery of the Schrödinger equation by Erwin Schrödinger. [16] :12

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. [16] :14 Since the field is treated classically it can not deal with spontaneous emission. [16] :16 This semi-classical treatment is valid for most systems, [2] :997 particular those under the action of high intensity laser fields. [2] :724 The distinction between optical physics and quantum optics is the use of semi-classical and fully quantum treatments respectively. [2] :997

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. [2] :556 When considering medium to high speed collisions, the nuclei can be treated classically while the electron is treated quantum mechanically. In low speed collisions the approximation fails. [2] :754

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. [2] :871

## Isolated atoms and molecules

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.

## Electronic configuration

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.

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.

## Notes

1. Atomic, molecular, and optical physics. National Academy Press. 1986. ISBN   978-0-309-03575-0.
2. Editor: Gordon Drake (Various authors) (1996). Handbook of atomic, molecular, and optical physics. Springer. ISBN   978-0-387-20802-2.CS1 maint: extra text: authors list (link)
3. Chen, L. T. (ed.) (2009). Atomic, Molecular and Optical Physics: New Research. Nova Science Publishers. ISBN   978-1-60456-907-0.CS1 maint: extra text: authors list (link)
4. C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. p.  803. ISBN   978-0-07-051400-3.
5. R. E. Dickerson; I. Geis (1976). "chapter 9". Chemistry, Matter, and the Universe. W.A. Benjamin Inc. (USA). ISBN   978-0-19-855148-5.
6. I.R. Kenyon (2008). . The Light Fantastic – Introduction to Classic and Quantum Optics. Oxford University Press. ISBN   978-0-19-856646-5.
7. Y. B. Band (2010). "chapters 3". Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers. John Wiley & Sons. ISBN   978-0-471-89931-0.
8. "Optical Physics". University of Arizona. Retrieved Apr 23, 2014.
9. "Slow Light". Science Watch. Retrieved Jan 22, 2013.
10. Y.B. Band (2010). "chapters 9,10". Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers. John Wiley & Sons. ISBN   978-0-471-89931-0.
11. C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. pp.  933–934. ISBN   978-0-07-051400-3.
12. I. R. Kenyon (2008). . The Light Fantastic – Introduction to Classic and Quantum Optics (2nd ed.). Oxford University Press. ISBN   978-0-19-856646-5.
13. R. E. Dickerson; I. Geis (1976). "chapters 7, 8". Chemistry, Matter, and the Universe. W.A. Benjamin Inc. (USA). ISBN   978-0-19-855148-5.
14. Y.B. Band (2010). Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers. John Wiley & Sons. pp. 4–11. ISBN   978-0-471-89931-0.
15. P. A. Tipler; G. Mosca (2008). "chapter 34". Physics for Scientists and Engineers - with Modern Physics. Freeman. ISBN   978-0-7167-8964-2.
16. Haken, H. (1981). Light (Reprint. ed.). Amsterdam u.a.: North-Holland Physics Publ. ISBN   978-0-444-86020-0.

## Related Research Articles

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions.

In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. After the cubical model (1902), the plum pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911) came the Rutherford–Bohr model or just Bohr model for short (1913). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation.

Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.

Physics is the natural science that studies matter, its motion and behavior through space and time, and the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid state and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. The effect has found use in electronic devices specialized for light detection and precisely timed electron emission.

Quantum chemistry, also called molecular quantum mechanics, is a branch of chemistry focused on the application of quantum mechanics to chemical systems. Understanding electronic structure and molecular dynamics using the Schrödinger equations are central topics in quantum chemistry.

Spectroscopy is the study of the interaction between matter and electromagnetic radiation as a function of the wavelength or frequency of the radiation. In simpler terms, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum; indeed, historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO).

Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation.

Ionization or ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

Photoluminescence is light emission from any form of matter after the absorption of photons. It is one of many forms of luminescence and is initiated by photoexcitation, hence the prefix photo-. Following excitation, various relaxation processes typically occur in which other photons are re-radiated. Time periods between absorption and emission may vary: ranging from short femtosecond-regime for emission involving free-carrier plasma in inorganic semiconductors up to milliseconds for Phosphorescence processes in molecular systems; and under special circumstances delay of emission may even span to minutes or hours.

Laser cooling includes a number of techniques in which atomic and molecular samples are cooled down to near absolute zero. Laser cooling techniques rely on the fact that when an object absorbs and re-emits a photon its momentum changes. For an ensemble of particles, their thermodynamic temperature is proportional to the variance in their velocity. That is, more homogeneous velocities among particles corresponds to a lower temperature. Laser cooling techniques combine atomic spectroscopy with the aforementioned mechanical effect of light to compress the velocity distribution of an ensemble of particles, thereby cooling the particles.

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a function of frequency, and this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum.

Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes Raman scattering. The effect is exploited by chemists and physicists to gain information about materials for a variety of purposes by performing various forms of Raman spectroscopy. Many other variants of Raman spectroscopy allow rotational energy to be examined and electronic energy levels may be examined if an X-ray source is used in addition to other possibilities. More complex techniques involving pulsed lasers, multiple laser beams and so on are known.

Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing.

Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics. Its most important experimental techniques are the various types of spectroscopy; scattering is also used. The field is closely related to atomic physics and overlaps greatly with theoretical chemistry, physical chemistry and chemical physics.

The Rydberg states of an atom or molecule are electronically excited states with energies that follow the Rydberg formula as they converge on an ionic state with an ionization energy. Although the Rydberg formula was developed to describe atomic energy levels, it has been used to describe many other systems that have electronic structure roughly similar to atomic hydrogen. In general, at sufficiently high principal quantum numbers, an excited electron - ionic core system will have the general character of a hydrogenic system and the energy levels will follow the Rydberg formula. Rydberg states have energies converging on the energy of the ion. The ionization energy threshold is the energy required to completely liberate an electron from the ionic core of an atom or molecule. In practice, a Rydberg wave packet is created by a laser pulse on a hydrogenic atom and thus populates a superposition of Rydberg states. Modern investigations using pump-probe experiments show molecular pathways – e.g. dissociation of (NO)2 – via these special states.

Joseph Henry Eberly is the Andrew Carnegie Professor of Physics and Professor of Optics at the University of Rochester.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

The I. I. Rabi Prize in Atomic, Molecular, and Optical Physics is given by the American Physical Society to recognize outstanding work by mid-career researchers in the field of atomic, molecular, and optical physics. The award was endowed in 1989 in honor of the physicist I. I. Rabi and has been awarded biannually since 1991.

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