Atomic electron transition: Difference between revisions

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{{short description|Change of an electron between energy levels within an atom}}

[[File:Bohr-atom-electron-to-jump.svg|thumb|228x228px|An electron in a [[Bohr model]] atom, moving from [[Quantum number|quantum level]] {{math|1=''n'' = 3}} to {{math|1=''n'' = 2}} and releasing a [[photon]]. The energy of an electron is determined by its orbit around the atom, The n = 0 orbit, commonly referred to as the [[ground state]], has the lowest energy of all states in the system. ]]

{{About||the TV series|Quantum Leap|the sculpture|The Quantum Leap}}

[[File:Bohr-atom-electron-to-jump.svg|thumb|228x228px|An electron in a [[Bohr model]] atom, moving from [[Quantum number|quantum level]] {{math|1=''n'' = 3}} to {{math|1=''n'' = 2}} and releasing a [[photon]].]]

{{Use mdy dates|date=February 2016}}

In [[atomic physics]] and [[chemistry]], an '''atomic electron transition''' (also called an '''electronicatomic (de-)excitation'''transition, '''atomicquantum transition'''jump, or '''quantum jump'''leap) is a change (or jump) of an [[electron]] changing from one [[energy level]] to another within an [[atom]]<ref>Schombert, James. [http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html "Quantum physics"] University of Oregon Department of Physics</ref> or [[artificial atom]].<ref>{{Cite journal |arxiv = 1009.2969|bibcode = 2011PhRvL.106k0502V|title = Observation of Quantum Jumps in a Superconducting Artificial Atom|journal = Physical Review Letters|volume = 106|issue = 11|pages = 110502|last1 = Vijay|first1 = R|last2 = Slichter|first2 = D. H|last3 = Siddiqi|first3 = I|year = 2011|doi = 10.1103/PhysRevLett.106.110502|pmid = 21469850| s2cid=35070320 }}</ref> ItThe appearstime discontinuousscale asof a quantum jump has not been measured experimentally. However, the electron[[Franck–Condon "jumps"principle]] frombinds onethe quantizedupper energylimit levelof tothis another,parameter typicallyto inthe aorder fewof [[nanosecondAttosecond|attoseconds]]s.<ref>{{Cite orjournal less|last1=de la Peña |first1=L. |last2=Cetto |first2=A. M. |last3=Valdés-Hernández |first3=A. |date=2020-12-04 |title=How fast is a quantum jump? |url=https://www.sciencedirect.com/science/article/pii/S0375960120307477 |journal=Physics Letters A |volume=384 |issue=34 |pages=126880 |doi=10.1016/j.physleta.2020.126880 |issn=0375-9601|arxiv=2009.02426 |bibcode=2020PhLA..38426880D }}</ref>

Electrons can ''relax'' into states of lower energy by emitting [[electromagnetic radiation]] in the form of a photon. Electrons can also absorb passing photons, which ''excites'' the electron into a state of higher energy. The larger the energy separation between the electron's initial and final state, the shorter the photons' [[wavelength]].<ref name=":0"/>

Electron transitions cause the [[Spontaneous emission|emission]] or [[Absorption (electromagnetic radiation)|absorption]] of [[electromagnetic radiation]] in the form of quantized units called [[photon]]s. Their statistics are [[Poisson distribution|Poissonian]], and the time between jumps is [[Exponential distribution|exponentially distributed]].<ref>{{Cite web |url=http://www.mpq.mpg.de/Theorygroup/CIRAC/wiki/images/8/86/Samuel.pdf |last=Deléglise |first=S. |title=Observing the quantum jumps of light |access-date=September 17, 2010 |archive-url=https://web.archive.org/web/20101107043403/http://www.mpq.mpg.de/Theorygroup/CIRAC/wiki/images/8/86/Samuel.pdf |archive-date=November 7, 2010 |url-status=dead }}</ref> The damping time constant (which ranges from [[nanosecond]]s to a few seconds) relates to the natural, pressure, and field [[Spectral line#Line broadening and shift|broadening of spectral lines]]. The larger the energy separation of the states between which the electron jumps, the shorter the [[wavelength]] of the photon emitted.<ref name=":0" /> The emitted photon changes the [[kinetic energy]] of the atom, enabling the [[laser cooling]] technology to slow down the motion of atoms.

== History ==

Danish physicist [[Niels Bohr]] first theorized that electrons can perform quantum jumps in 1913.<ref>{{Cite news|last=Gleick|first=James|date=1986-10-21|title=PHYSICISTS FINALLY GET TO SEE QUANTUM JUMP WITH OWN EYES|language=en-US|work=The New York Times|url=https://www.nytimes.com/1986/10/21/science/physicists-finally-get-to-see-quantum-jump-with-own-eyes.html|access-date=2021-12-06|issn=0362-4331}}</ref> Soon after, [[James Franck]] and [[Gustav Ludwig Hertz]] [[Franck–Hertz experiment|proved experimentally]] that atoms have quantized energy states.<ref>{{Cite web|title=Franck-Hertz experiment {{!}} physics {{!}} Britannica|url=https://www.britannica.com/science/Franck-Hertz-experiment|access-date=2021-12-06|website=www.britannica.com|language=en}}</ref>

The observability of quantum jumps was predicted by [[Hans Dehmelt]] in 1975, and they were first observed using [[Quadrupole ion trap|trapped ions]] of [[barium]] at [[University of Hamburg]] and [[Mercury (element)|mercury]] at [[NIST]] in 1986.<ref name=":0">{{cite journal|last1=Itano|first1=W. M.|last2=Bergquist|first2=J. C.|last3=Wineland|first3=D. J.|date=2015|title=Early observations of macroscopic quantum jumps in single atoms|url=http://tf.boulder.nist.gov/general/pdf/2723.pdf|journal=International Journal of Mass Spectrometry|volume=377|page=403|bibcode=2015IJMSp.377..403I|doi=10.1016/j.ijms.2014.07.005}}</ref>

== Theory ==

An atom interacts with the oscillating [[electric field]]:

Consider an atom interact with electromagnetic radiation which produces an oscillation electric field <ref>{{Cite book|title=Atomic Physics|author=Foot, CJ|year=2004|

{{NumBlk|:|<math> E(t) = |\textbf{E}_0| Re( e^{-i{\omega}t} \hat{\textbf{e}}_\mathrm{rad} )</math>|{{EquationRef|1}}}}

publisher=Oxford University Press|isbn=978-0-19-850696-6}}</ref>:

{{NumBlk|:|with amplitude <math> E(t) = |\textbf{E}_0|</math>, Re(angular e^{-i{frequency <math>\omega}t}</math>, and polarization vector <math>\hat{\textbf{e}}_\mathrm{rad} )</math>|.<ref>{{EquationRefCite book|title=Atomic Physics|author=Foot, CJ|year=2004|1}}}}

with amplitude <math>|\textbf{E}_0|</math>, angular frequencypublisher=Oxford <math>\omega</math>University and polarization vector <math>\hat{\textbf{ePress|isbn=978-0-19-850696-6}}_{rad}</mathref>. Note that the actual phase of wave should beis <math> (\omega t - \textbf{k} \cdot \textbf{r}) </math>. However, in many cases, the variation of <math> \textbf{k} \cdot \textbf{r} </math> is small over the atom, (or equivalently, the radiation wavelength is much greater than the size of an atom. This is called dipole approximation,) and this approximationterm allowcan usbe toignored. replaceThis <math>is E(r,called t)the </math>dipole withapproximation. <math>The E(0, t) </math> in ({{EquationNote|1}}). Atomatom can also interact with oscilationthe oscillating [[magnetic field]] produced inby the radiaitonradiation, withalthough themuch interaction being muchmore weakerweakly.

The Hamiltonian for this interaction, analogous to the energy of a classical dipole in an electric field, is <math> H_I = e \textbf{r} \cdot \textbf{E}(t) </math>,. analogousThe tostimulated thetransition energyrate ofcan abe classicalcalculated dipole in a electric field.using [[Timetime-dependent perturbation theory]]; is required for calculating the stimulate transition rate. Howeverhowever, the result can be summarized withusing [[Fermi's Goldengolden rule]]:

<math display="block">

Rate \propto |eE_0|^2 \times | \lang 2 |

\textbf{r} \cdot \hat{\textbf{e}}_\mathrm{rad} |1 \rang |^2

</math>

The dipole matrix element can be decomposedecomposed into the product of the radial integral and the angular integral. The angular integral is zero unless certain condition is met, which are the [[selection rulerules]] for allowedthe atomic transitionstransition are satisfied.

== Recent discoveries ==