View source for Atomic, molecular, and optical physics

{{Short description|Study of matter-light interactions at small scales}}{{quantum mechanics}}
'''Atomic, molecular, and optical physics (AMO)''' is the study of [[matter]]-matter and [[light]]-matter interactions; at the scale of one or a few [[atom]]s<ref name=nap>{{cite book|title=Atomic, molecular, and optical physics|year=1986|publisher=National Academy Press|isbn=978-0-309-03575-0|url=https://archive.org/details/atomicmolecularo00nati_0}}</ref> and energy scales around several [[electron volt]]s.<ref name=Drake>{{Cite book|title=Handbook of atomic, molecular, and optical physics|author=Editor: Gordon Drake (Various authors)|year=1996|edition=|publisher=[[Springer Science+Business Media|Springer]]|isbn=978-0-387-20802-2}}</ref>{{rp|1356}}<ref name=chen>{{cite book|last=Chen|first=L. T. (ed.)|title=Atomic, Molecular and Optical Physics: New Research|year=2009|publisher=Nova Science Publishers|isbn=978-1-60456-907-0}}</ref>  The three areas are closely interrelated.  AMO theory includes [[classical physics|classical]], [[Semiclassical physics|semi-classical]] and [[quantum physics|quantum]] treatments.  Typically, the theory and applications of [[Emission spectrum|emission]], [[Absorption (electromagnetic radiation)|absorption]], [[scattering]] of [[electromagnetic radiation]] (light) from [[Excited state|excited]] [[atom]]s and [[molecule]]s, analysis of spectroscopy, generation of [[laser]]s and [[maser]]s, and the optical properties of matter in general, fall into these categories.

== Atomic and molecular physics ==
{{main|Atomic physics|Molecular physics}}
'''Atomic physics''' is the subfield of AMO that studies atoms as an isolated system of [[electron]]s and an [[atomic nuclei|atomic nucleus]], while '''molecular physics''' is the study of the physical properties of [[molecule]]s. The term ''atomic physics'' is often associated with [[nuclear power]] and [[nuclear bomb]]s, due to the [[synonym]]ous 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 nucleus|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]].<ref>{{Cite book|chapter=|page=[https://archive.org/details/mcgrawhillencycl1993park/page/803 803]|title=McGraw Hill Encyclopaedia of Physics|author=C.B. Parker|year=1994|edition=2nd|publisher=McGraw Hill|isbn=978-0-07-051400-3|url=https://archive.org/details/mcgrawhillencycl1993park/page/803}}</ref>

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.<ref>{{Cite book|chapter=chapter 9|page=|title=Chemistry, Matter, and the Universe|author1=R. E. Dickerson |author2=I. Geis |year=1976|edition=|publisher=W.A. Benjamin Inc. (USA)|isbn=978-0-19-855148-5}}</ref> 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 level]]s. The smallest energy differences exist between different rotational states, therefore pure rotational [[Spectrum|spectra]] are in the far [[infrared]] region (about 30 - 150 [[µm]] [[wavelength]]) of the [[electromagnetic spectrum]]. [[Vibrational spectroscopy of linear molecules|Vibrational spectra]] are in the near infrared (about 1 - 5&nbsp;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.<ref>{{Cite book|chapter=chapters 12, 13, 17|page=|title=The Light Fantastic – Introduction to Classic and Quantum Optics|author=I.R. Kenyon|year=2008|edition=|publisher=Oxford University Press|isbn=978-0-19-856646-5}}</ref>

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 ==
{{see also|Optics}}
<!-- Deleted image removed: [[File:OptLat.jpg|thumb|right|200px|An [[optical lattice]] formed by [[laser]] interference. Optical lattices are used to simulate interacting [[condensed matter physics|condensed matter systems]].]] -->
'''Optical physics''' is the study of the generation of [[electromagnetic radiation]], the properties of that radiation, and the interaction of that radiation with [[matter]],<ref>{{Cite book|chapter=chapters 3|page=|title=Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers|author=Y. B. Band|year=2010|edition=|publisher=, John Wiley & Sons|isbn=978-0-471-89931-0}}</ref> especially its manipulation and control.<ref>{{cite web
 | title =Optical Physics
 | publisher =University of Arizona
 | url =http://www.optics.arizona.edu/research/faculty-specialties/optical-physics
 | accessdate = Apr 23, 2014}}</ref> 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]].<ref>{{cite web |url=http://sciencewatch.com/nobel/predictions/slow-light |title=Slow Light |website=Science Watch |accessdate=Jan 22, 2013}}</ref><ref>{{Cite book|chapter=chapters 9,10|page=|title=Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers|author=Y.B. Band|year=2010|edition=|publisher=John Wiley & Sons|isbn=978-0-471-89931-0}}</ref>

Researchers in optical physics use and develop light sources that span the [[electromagnetic spectrum]] from [[microwave]]s to [[X-ray]]s. The field includes the generation and detection of light, linear and [[nonlinear optics|nonlinear]] optical processes, and [[spectroscopy]]. [[Laser]]s and [[laser spectroscopy]] have transformed optical science.  Major study in optical physics is also devoted to [[quantum optics]] and [[Coherence (physics)|coherence]], and to [[femtosecond]] optics.<ref name="nap"/> 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.<ref>{{Cite book|chapter=|pages=[https://archive.org/details/mcgrawhillencycl1993park/page/933 933–934]|title=McGraw Hill Encyclopaedia of Physics|author=C.B. Parker|year=1994|edition=2nd|publisher=McGraw Hill|isbn=978-0-07-051400-3|url=https://archive.org/details/mcgrawhillencycl1993park/page/933}}</ref>

Other important areas of research include the development of novel optical techniques for nano-optical measurements, [[diffractive optics]], [[Interferometry|low-coherence interferometry]], [[optical coherence tomography]], and [[Near-field scanning optical microscope|near-field microscopy]].  Research in optical physics places an emphasis on ultrafast optical science and technology. The applications of optical physics create advancements in [[telecommunication|communications]], [[medicine]], [[manufacturing]], and even [[entertainment]].<ref>{{Cite book|chapter=5, 6, 10, 16|page=|title=The Light Fantastic – Introduction to Classic and Quantum Optics|author=I. R. Kenyon|year=2008|edition=2nd|publisher=Oxford University Press|isbn=978-0-19-856646-5}}</ref>

==History==
{{Main|Atomic theory|Basics of quantum mechanics}}
[[File:Bohr-atom-PAR.svg|thumb|right|200px|The [[Bohr model]] of the [[Hydrogen atom]]]]
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 Alexander Reina Newlands|John Newlands]] and [[Dmitri Mendeleyev]] around the mid to late 19th century.<ref name="R.E. Dickerson, I. Geis 1976">{{Cite book|chapter=chapters 7, 8|page=|title=Chemistry, Matter, and the Universe|author1=R. E. Dickerson |author2=I. Geis |year=1976|edition=|publisher=W.A. Benjamin Inc. (USA)|isbn=978-0-19-855148-5}}</ref>

Later, the connection between atomic physics ''and'' optical physics became apparent, by the discovery of [[spectral line]]s and attempts to describe the phenomenon - notably by [[Joseph von Fraunhofer]], [[Fresnel]], and others in the 19th century.<ref>{{Cite book|chapter=|pages=4–11|title=Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers|author=Y.B. Band|year=2010|edition=|publisher=John Wiley & Sons|isbn=978-0-471-89931-0}}</ref>

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]].<ref name="R.E. Dickerson, I. Geis 1976"/>

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]].<ref>{{Cite book|chapter=chapter 34|page=|title=Physics for Scientists and Engineers - with Modern Physics|author1=P. A. Tipler |author2=G. Mosca |year=2008|edition=|publisher=Freeman|isbn=978-0-7167-8964-2}}</ref>

===Classical oscillator model of matter===
Early models to explain the origin of the [[refractive index|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 [[Oscillation|oscillate]]. The [[amplitude]] of the oscillation would then have a relationship to the [[frequency]] of the incident electromagnetic wave and the [[Resonance|resonant]] frequencies of the oscillator. The [[Superposition principle|superposition]] of these emitted waves from many oscillators would then lead to a wave which moved more slowly.
<ref name=Haken>{{cite book|last=Haken|first=H.|title=Light|year=1981|publisher=North-Holland Physics Publ.|location=Amsterdam u.a.|isbn=978-0-444-86020-0|edition=Reprint.}}</ref>{{rp|4–8}}
<!-- Integrate these into the history section, remove as they are mentioned 
; Pre quantum mechanics
* [[Joseph von Fraunhofer]]
* [[Johannes Rydberg]]
* [[J.J. Thomson]]
; Post quantum mechanics
* [[Alexander Dalgarno]]
* [[David Bates (physicist)|David Bates]]
* [[Max Born]]
* [[Clinton Joseph Davisson]]
* [[Enrico Fermi]]
* [[Charlotte Froese Fischer]]
* [[Vladimir Fock]]ii
* [[Douglas Hartree]]
* [[Harrie Massey|Harrie S. Massey]]
* [[Nevill Mott]]
* [[M. J. Seaton|Mike Seaton]]
* [[John C. Slater]]
* [[George Paget Thomson]]
* [[Ernest M. Henley]]
* [[Peter Zoller]]
* Fano
* [[Peter Lambropoulos]]
 -->

===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.<ref name=Haken />{{rp|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]]
:<math> k = \frac{n\pi}{L} </math>
can occur in the box, where ''n'' is a positive [[integer]] (mathematically denoted by <math>\scriptstyle n \in \mathbb{N}_1</math>). The equation describing these standing waves is given by:

:<math>E=E_0 \sin\left(\frac{n\pi}{L}x\right)\,\!</math>.

where ''E''<sub>0</sub> 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.<ref name=Haken />{{rp|4–8,51–52}}
<!-- It's in the energy density form in the book -->

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.<ref name=Haken />{{rp|9–10}}

These results, based on a ''discrete'' set of specific standing waves, were inconsistent with the ''continuous'' classical oscillator model.<ref name=Haken />{{rp|8}}

Work by [[Albert Einstein]] in 1905 on the [[photoelectric effect]] led to the association of a light wave of frequency <math>\nu</math> with a photon of energy <math>h\nu</math>. 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)]].<ref name=Haken />{{rp|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]].<ref name=Haken />{{rp|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.<ref name=Haken />{{rp|14}} Since the field is treated classically it can not deal with [[spontaneous emission]].<ref name=Haken />{{rp|16}} This semi-classical treatment is valid for most systems,<ref name=Drake />{{rp|997}} particular those under the action of high intensity laser fields.<ref name=Drake />{{rp|724}} The distinction between optical physics and quantum optics is the use of semi-classical and fully quantum treatments respectively.<ref name=Drake />{{rp|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.<ref name=Drake />{{rp|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.<ref name=Drake />{{rp|754}}<!-- Expand from here, weaknesses of the particular approximation are also described -->

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.<ref name=Drake />{{rp|871}}

==Isolated atoms and molecules==
Atomic, Molecular and Optical physics frequently considers atoms and molecules in isolation<!-- not always, there are some multi-particle groups -->. 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 [[excited state|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 (physics)|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)|plasma physics]] and [[atmospheric physics]] even though both deal with huge numbers of molecules.

==Electronic configuration==
Electrons form notional [[Electron shell|shells]] around the nucleus. These are naturally in a [[ground state]] but can be excited by the absorption of energy from light ([[photon]]s), 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 (physics)|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.

==See also==
{{portal|Physics}}
{{col div|colwidth=20em}}
* [[Born–Oppenheimer approximation]]
* [[Second-harmonic generation|Frequency doubling]]
* [[Diffraction]]
* [[Hyperfine structure]]
* [[Interferometry]]
* [[Isomeric shift]]
* [[Metamaterial cloaking]]
* [[Molecular energy state]]
* [[Molecular modelling|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]]
{{colend}}

== Notes ==
{{Reflist}}

==References==
{{refbegin}}
* {{Cite book|title=Physics of Atoms and Molecules|author=Bransden, B. H.|author2=Joachain, CJ|
    year=2002|publisher=Prentice Hall|edition=2nd|isbn=978-0-582-35692-4}}
* {{Cite book|title=Atomic Physics|author=Foot, C. J.|year=2004|
    publisher=Oxford University Press|isbn=978-0-19-850696-6}}
*{{Cite book|author=Herzberg, G.|title=Atomic Spectra and Atomic Structure
    |year= 1979|origyear=1945 |publisher=Dover|isbn=978-0-486-60115-1}}
* {{Cite book|title=The Theory of Atomic Spectra|author1=Condon, E. U.  |author2=Shortley, G. H. |lastauthoramp=yes |year=1935|
    publisher=Cambridge University Press|isbn=978-0-521-09209-8}}
* {{Cite book|title=The Theory of Atomic Structure and Spectra|author=Cowan, Robert D.|year=1981|
    publisher=University of California Press|isbn=978-0-520-03821-9}}
* {{Cite book|title=Atomic Many-Body Theory|author1=Lindgren, I.  |author2=Morrison, J. |lastauthoramp=yes |year=1986|
    edition=Second|publisher=Springer-Verlag|isbn=978-0-387-16649-0}}
* {{Cite book|title=Solid State Physics|author1=J. R. Hook |author2=H. E. Hall |year=2010|
    edition=2nd|publisher=Manchester Physics Series, John Wiley & Sons|isbn=978-0-471-92804-1}}
* {{Cite book|title=Physical chemistry|author=P. W. Atkins|year=1978|
    edition=|publisher=Oxford University Press|isbn=978-0-19-855148-5}}
* {{Cite book|title=Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers|author=Y. B. Band|year=2010|
    edition=|publisher=John Wiley & Sons|isbn=978-0-471-89931-0}}
* {{Cite book|title=The Light Fantastic – Introduction to Classic and Quantum Optics|author=I. R. Kenyon|year=2008|
    edition=|publisher=Oxford University Press|isbn=978-0-19-856646-5}}
* {{Cite book|title=The New Quantum Universe|author=T.Hey, P.Walters|year=2009|
    edition=|publisher=Cambridge University Press|isbn=978-0-521-56457-1}}
* {{Cite book|title=The Quantum Theory of Light|author=R. Loudon|year=1996|
    edition=|publisher=Oxford University Press (Oxford Science Publications)|isbn=978-0-19-850177-0}}
* {{Cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles|author1=R. Eisberg|author2=R. Resnick|year=1985|edition=2nd|publisher=John Wiley & Sons|isbn=978-0-471-87373-0|url=https://archive.org/details/quantumphysicsof00eisb}}
* {{Cite book|title=Quanta: A handbook of concepts|author=P.W. Atkins|year=1974|
    edition=|publisher=Oxford University Press|isbn=978-0-19-855493-6}}
* {{Cite book|title=Quantum Mechanics|author=E. Abers|year=2004|
    edition=|publisher=Pearson Ed., Addison Wesley, Prentice Hall Inc|isbn=978-0-13-146100-0}}
* {{Cite book|title=Molecular Quantum Mechanics Parts I and II: An Introduction to QUANTUM CHEMISTRY (Volume 1)|author=P.W. Atkins|year=1977|
    edition=|publisher=Oxford University Press|isbn=978-0-19-855129-4}}
* {{Cite book|title=Molecular Quantum Mechanics Part III: An Introduction to QUANTUM CHEMISTRY (Volume 2)|author=P.W. Atkins|year=1977|
    edition=|publisher=Oxford University Press|isbn=978-0-19-855129-4}}
* ''Solid State Physics (2nd Edition)'', J.R. Hook, H.E. Hall, Manchester Physics Series, John Wiley & Sons, 2010, {{ISBN|978 0 471 92804 1}}
* ''Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers'', Y.B. Band, John Wiley & Sons, 2010, {{ISBN|978-0471-89931-0}}
* ''The Light Fantastic – Introduction to Classic and Quantum Optics'', I.R. Kenyon, Oxford University Press, 2008, {{ISBN|978-0-19-856646-5}}
*''Handbook of atomic, molecular, and optical physics'', Editor: Gordon Drake, [[Springer Science+Business Media|Springer]], Various authors, 1996, {{ISBN|0-387-20802-X}}
*{{cite book | last=Fox | first=Mark | title=Optical properties of solids | publisher=Oxford University Press | publication-place=Oxford New York | year=2010 | isbn=978-0-19-957336-3 | ref=harv}}
{{refend}}

==External links==
{{Commonscat|Atomic, molecular, and optical physics}}

*[https://web.archive.org/web/20140304074633/http://emlab.utep.edu/ee5390em21.htm Lorentz and Drude Models (see and listen to Lecture 2)]
*[https://web.archive.org/web/20140304074633/http://emlab.utep.edu/ee5390em21.htm Nonlinear and Anisotropic Materials (see and listen to Lecture 3)]
*[http://www.sciencedirect.com/science/bookseries/1049250X ScienceDirect - Advances In Atomic, Molecular, and Optical Physics]
*[http://iopscience.iop.org/0953-4075/ Journal of Physics B: Atomic, Molecular and Optical Physics]

=== Institutions ===

* [http://www.aps.org/units/damop/ American Physical Society - Division of Atomic, Molecular & Optical Physics]
* [https://web.archive.org/web/20090927053332/http://ampd.epsdivisions.org/ European Physical Society - Atomic, Molecular & Optical Physics Division]
* [https://www.nsf.gov/funding/pgm_summ.jsp?pims_id=13622 National Science Foundation - Atomic, Molecular and Optical Physics]
* [http://cuaweb.mit.edu/ MIT-Harvard Center for Ultracold Atoms]
* [https://jila.colorado.edu/research/atomic-molecular-physics/atomic-molecular-physics JILA - Atomic and Molecular Physics]
* [http://jqi.umd.edu/ Joint Quantum Institute at University of Maryland and NIST]
*[http://www.phy.ornl.gov/ ORNL Physics Division]
*[http://web.am.qub.ac.uk/ctamop/ Queen's University Belfast - Center for Theoretical, Atomic, Molecular and Optical Physics,]
*[http://physics.berkeley.edu/research/atomic-molecular-and-optical-physics University of California, Berkeley - Atomic, Molecular and Optical Physics]
{{Physics-footer}}

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