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Neptune584 (talk | contribs) Adding a brief theoritical explanation of the concept. |
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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 ==
Consider an atom interact with electromagnetic radiaiton which produces an oscillation electric field <ref>{{Cite book|title=Atomic Physics|author=Foot, CJ|year=2004|
publisher=Oxford University Press|isbn=978-0-19-850696-6}}</ref>:
{{NumBlk|:|<math> E(t) = |\textbf{E}_0| Re( e^{-i{\omega}t} \hat{\textbf{e}}_{rad} )</math>|{{EquationRef|1}}}}
with amplitude <math>|\textbf{E}_0|</math>, angular frequency <math>\omega</math> and polarization vector <math>\hat{\textbf{e}}_{rad}</math>. Note that the actual phase of wave should be <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 approximation allow us to replace <math> E(r, t) </math> with <math> E(0, t) </math> in ({{EquationNote|1}}). Atom can also interact with oscilation magnetic field produced in the radiaiton with the interaction being much weaker.
The Hamiltonian for this interaction is <math> H_I = e \textbf{r} \cdot \textbf{E}(t) </math>, analogous to the energy of a classical dipole in a electric field. [[Time-dependent perturbation theory]] is required for calculating the stimulate transition rate. However, the result can be summarized with Fermi's Golden rule:
<math display="block">
Rate \propto |eE_0|^2 \times | \lang 2 |
\textbf{r} \cdot \hat{\textbf{e}}_{rad} |1 \rang |^2
</math>
The dipole matrix element can be decompose 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 rule]] for allowed atomic transitions.
== Recent discoveries ==
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