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| [[File:Lithium levels.png|thumb|right|300px|'''Figure 1:''' Energy levels in atomic [[lithium]] showing the Rydberg series of the lowest 3 values of [[Angular momentum#Angular momentum in quantum mechanics|orbital angular momentum]] converging on the first ionization energy.]]
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| A '''Rydberg atom''' is an [[excited state|excited atom]] with one or more [[electron]]s that have a very high [[principal quantum number]].<ref name="Gallagher">{{cite book |title=Rydberg Atoms |last=Gallagher |first=Thomas F. |authorlink= |coauthors= |year=1994 |publisher=[[Cambridge University Press]] |isbn=0-521-02166-9 |pages= }}</ref> These [[atom]]s have a number of peculiar properties including an exaggerated response to [[Electric field|electric]] and [[magnetic field]]s,<ref name="Metcalf">{{cite web |url=http://www.sunysb.edu/metcalf/rydbergprint.htm |title=Rydberg Atom Optics |accessdate=2008-07-30 |author=Metcalf Research Group |date=2004-11-08 |work= |publisher=[[Stony Brook University]]}} {{Dead link|date=October 2010|bot=H3llBot}}</ref> long decay periods and [[electron]] [[wavefunction]]s that approximate, under some conditions, [[Classical physics|classical]] orbits of electrons about the [[Atomic nucleus|nuclei]].<ref name="Classical">{{cite journal |author=J. Murray-Krezan |title=The classical dynamics of Rydberg Stark atoms in momentum space |journal=[[American Journal of Physics]] |volume=76 |issue=11 |pages=1007–1011 |year=2008 |url= |doi=10.1119/1.2961081|bibcode = 2008AmJPh..76.1007M }}</ref> The core electrons shield the [[Valence electron|outer electron]] from the electric field of the nucleus such that, from a distance, the [[electric potential]] looks identical to that experienced by the electron in a [[hydrogen atom]].<ref name="Nolan">{{cite web |url=http://webphysics.davidson.edu/alumni/jimn/Final/Pages/FinalRydberg.htm |title=Rydberg Atoms and the Quantum Defect |accessdate=2008-07-30 |last=Nolan |first=James |coauthors= |date=2005-05-31 |work= |publisher=[[Davidson College]]}}</ref>
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| In spite of its shortcomings, the [[Bohr model]] of the atom is useful in explaining these properties. Classically an electron in a circular orbit of radius ''r'', about a hydrogen [[Atomic nucleus|nucleus]] of charge +''[[Elementary charge|e]]'', obeys [[Newton's laws of motion|Newton's second law]]:
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| | | 相关的主题文章： |
| :<math> \mathbf{F}=m\mathbf{a} \Rightarrow { ke^2 \over r^2}={mv^2 \over r}</math>
| | <ul> |
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| where ''k'' = 1/(4π[[Permittivity of free space|ε<sub>0</sub>]]).
| | <li>[http://www.xiyanggift.com/news/html/?22432.html http://www.xiyanggift.com/news/html/?22432.html]</li> |
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| Orbital momentum is [[Quantization (physics)|quantized]] in units of ''[[Reduced Planck constant|ħ]]'':
| | <li>[http://www.hayfa-factory.com/hayfafourm/viewtopic.php?f=3&t=5754 http://www.hayfa-factory.com/hayfafourm/viewtopic.php?f=3&t=5754]</li> |
| | | |
| :<math> mvr=n\hbar </math>.
| | <li>[http://222.243.160.155/forum.php?mod=viewthread&tid=7988863 http://222.243.160.155/forum.php?mod=viewthread&tid=7988863]</li> |
| | | |
| Combining these two equations leads to [[Niels Bohr|Bohr]]'s expression for the orbital radius in terms of the [[principal quantum number]], ''n'':
| | <li>[http://www.rzyy.com.cn/news/html/?52172.html http://www.rzyy.com.cn/news/html/?52172.html]</li> |
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| :<math> r={n^2\hbar^2 \over ke^2m}. </math>
| | </ul> |
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| It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as ''n''<sup>2</sup> (the ''n'' = 137 state of hydrogen has an atomic radius ~1 µm) and the geometric cross-section as ''n''<sup>4</sup>. Thus Rydberg atoms are extremely large with loosely bound [[Valence shell|valence]] electrons, easily perturbed or [[Ionization potential|ionized]] by collisions or external fields.
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| Because the [[binding energy]] of a Rydberg electron is proportional to 1/''r'' and hence falls off like 1/''n''<sup>2</sup>, the energy level spacing falls off like 1/''n''<sup>3</sup> leading to ever more closely spaced levels converging on the first [[ionization energy]]. These closely spaced Rydberg states form what is commonly referred to as the ''Rydberg series''. '''Figure 1''' shows some of the energy levels of the lowest three values of [[Azimuthal quantum number|orbital angular momentum]] in [[lithium]].
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| == History ==
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| <!--[[File:Rydberg-Physicist(1854-1919).jpg|thumb|Swedish physicist Johannes Rydberg.]]--> | |
| The existence of the Rydberg series was first demonstrated in 1885 when [[Johann Balmer]] discovered a [[Balmer series#Balmer's formula|simple empirical formula]] for the [[wavelength]]s of light associated with transitions in atomic [[hydrogen]]. Three years later the Swedish physicist [[Johannes Rydberg]] presented a generalized and more intuitive version of Balmer's formula that came to be known as the [[Rydberg formula]]. This formula indicated the existence of an infinite series of ever more closely spaced discrete [[energy level]]s converging on a finite limit.<ref name="Rydberg">{{cite journal |author=I. Martinson and L. J. Curtis |title=Janne Rydberg – his life and work |journal=[[Nuclear Instruments and Methods in Physics Research Section B]] |volume=235 |issue=1–4 |pages=17–22 |year=2005 |doi=10.1016/j.nimb.2005.03.137|bibcode = 2005NIMPB.235...17M }}</ref>
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| This series was qualitatively explained in 1913 by [[Niels Bohr]] with his [[Bohr model|semiclassical model]] of the hydrogen atom in which [[Quantization (physics)|quantized]] values of angular momentum lead to the observed discrete energy levels.<ref name="Bohr">{{cite web |url=http://csep10.phys.utk.edu/astr162/lect/light/bohr.html |title=The Bohr Model |accessdate=2009-11-25 |author= |date=2000-08-10 |work= |publisher=[[University of Tennessee, Knoxville]]}}</ref> A full quantitative derivation of the observed spectrum was derived by [[Wolfgang Pauli]] in 1926 following development of [[quantum mechanics]] by [[Werner Heisenberg]] and others.
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| == Methods of production ==
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| The only truly stable state of a [[hydrogen-like atom]] is the ground state with ''n'' = 1. The study of Rydberg states requires a reliable technique for exciting ground state atoms to states with a large value of ''n''.
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| === Electron impact excitation ===
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| Much early experimental work on Rydberg atoms relied on the use of collimated beams of fast electrons incident on ground-state atoms.<ref name="Electron impact">{{cite journal |author=J. Olmsted |title=Excitation of nitrogen triplet states by electron impact |journal=[[Radiation Research]] |volume=31 |issue=2 |pages=191–200 |year=1967 |jstor=3572319 |doi= 10.2307/3572319|pmid=6025857}}</ref> [[Inelastic scattering]] processes can use the electron [[kinetic energy]] to increase the atoms' internal energy exciting to a broad range of different states including many high-lying Rydberg states,
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| :<math> e^- + A \rarr A^* + e^- </math>.
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| Because the electron can retain any arbitrary amount of its initial kinetic energy this process always results in a population with a broad spread of different energies.
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| === Charge exchange excitation ===
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| Another mainstay of early Rydberg atom experiments relied in charge exchange between a beam of [[ion]]s and a population of neutral atoms of another species resulting in the formation of a beam of highly excited atoms,<ref name="Charge exchange">{{cite journal |author=M. Haugh |title=Electronic excitation accompanying charge exchange |journal=[[Journal of Chemical Physics]] |volume=44 |issue=2 |pages=837–839 |year=1966 |doi=10.1063/1.1726773|bibcode = 1966JChPh..44..837H |author-separator=, |display-authors=1 |author2=<Please add first missing authors to populate metadata.> }}</ref>
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| :<math> A^+ + B \rarr A^* + B^+ </math>.
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| Again, because the kinetic energy of the interaction can contribute to the final internal energies of the constituents this technique populates a broad range of energy levels.
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| === Optical excitation ===
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| The arrival of tunable [[dye laser]]s in the 1970s allowed a much greater level of control over populations of excited atoms. In optical excitation the incident [[photon]] is absorbed by the target atom, absolutely specifying the final state energy. The problem of producing single state, mono-energetic populations of Rydberg atoms thus becomes the somewhat simpler problem of precisely controlling the frequency of the laser output,
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| :<math> A + \gamma \rarr A^*</math>.
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| This form of direct optical excitation is generally limited to experiments with the [[alkali metal]]s because the ground state [[binding energy]] in other species is generally too high to be accessible with most laser systems.
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| For atoms with a large [[valence electron]] [[binding energy]] (equivalent to a large first [[ionization energy]]) the excited states of the Rydberg series are inaccessible with conventional laser systems. Initial collisional excitation can make up the energy shortfall allowing optical excitation to be used to select the final state. Although the initial step excites to a broad range of intermediate states, the precision inherent in the optical excitation process means that the laser light only interacts with a specific subset of atoms in a particular state, exciting to the chosen final state.
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| == Hydrogenic potential ==
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| {{main|Hydrogen atom}}
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| [[File:CorePolarizationPotential.svg|thumb|right|'''Figure 2'''. A comparison of the potential in a hydrogen atom with that in a Rydberg state of a different atom. A large core polarizability has been used in order to make the effect clear. The black curve is the Coulombic 1/''r'' potential of the hydrogen atom while the dashed red curve includes the 1/''r''<sup>4</sup> term due to polarization of the ion core.]]
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| An atom in a [[Rydberg states|Rydberg state]] has a [[Valence shell|valence]] electron in a large orbit far from the ion core; in such an orbit the outermost electron feels an almost [[Hydrogen-like atom|hydrogenic]], Coulomb [[potential well|potential]], ''U''<sub>C</sub> from a compact ion core consisting of a [[Atomic nucleus|nucleus]] with [[Atomic number|''Z'']] [[proton]]s and the lower electron shells filled with ''Z''-1 electrons. An electron in the spherically symmetric Coulomb potential has potential energy:
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| :<math>U_\text{C} = -\dfrac{e^2}{4\pi\varepsilon_0r}</math>.
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| The similarity of the effective potential ‘seen’ by the outer electron to the hydrogen potential is a defining characteristic of [[Rydberg states]] and explains why the electron wavefunctions approximate to classical orbits in the limit of the [[correspondence principle]].<ref name="Classical">{{cite journal |author=T. P. Hezel |title=Classical view of the properties of Rydberg atoms: Application of the correspondence principle |journal=[[American Journal of Physics]] |volume=60 |issue=4 |pages=329–335 |year=1992 |doi=10.1119/1.16876|bibcode = 1992AmJPh..60..329H |author-separator=, |display-authors=1 |author2=<Please add first missing authors to populate metadata.> }}</ref> In other words, the electron's orbit resembles the orbit of planets inside a solar system, much like the obsolete but visually useful [[Bohr model|Bohr]] and [[Rutherford model|Rutherford]] models of the atom used to show.
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| There are three notable exceptions that can be characterized by the additional term added to the potential energy:
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| *An atom may have two (or more) electrons in highly excited states with comparable orbital radii. In this case the electron-electron interaction gives rise to a significant deviation from the hydrogen potential.<ref name="Double">{{cite journal |author=I. K. Dmitrieva and G. I. Plindov |title=Energies of Doubly Excited Sates. The Double Rydberg Formula |journal=[[Journal of Applied Spectroscopy]] |volume=59 |issue=1–2 |pages=466–470 |year=1993 |doi=10.1007/BF00663353 |bibcode=1993JApSp..59..466D}}</ref> For an atom in a multiple Rydberg state, the additional term, ''U<sub>ee</sub>'', includes a summation of each ''pair'' of highly excited electrons:
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| :<math>U_{ee} = \dfrac{e^2}{4\pi\varepsilon_0}\sum_{i < j}\dfrac{1}{|\mathbf{r}_i - \mathbf{r}_j|}</math>.
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| *If the valence electron has very low angular momentum (interpreted classically as an extremely [[Eccentricity (mathematics)|eccentric]] elliptical orbit) then it may pass close enough to polarise the ion core, giving rise to a 1/''r''<sup>4</sup> core polarization term in the potential.<ref name="Polarization">{{cite journal |author=L. Neale and M. Wilson |title=Core Polarization in Kr VIII |year=1995 |journal=[[Physical Review A]] |volume=51 |issue=5 |pages=4272–4275 |doi=10.1103/PhysRevA.51.4272|pmid=9912104|bibcode = 1995PhRvA..51.4272N }}</ref> The interaction between an [[Polarizability|induced]] [[Electric dipole moment|dipole]] and the charge that produces it is always attractive so this contribution is always negative,
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| :<math>U_\text{pol} = -\dfrac{e^2\alpha_\text{d}}{(4\pi\varepsilon_0)^2r^4}</math>, | |
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| :where α<sub>d</sub> is the dipole [[polarizability]]. '''Figure 2''' shows how the polarization term modifies the potential close to the nucleus.
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| *If the outer electron penetrates the inner electron shells, it will 'see' more of the charge of the nucleus and hence experience a greater force. In general the modification to the potential energy is not simple to calculate and must be based on knowledge of the geometry of the ion core.<ref name="Core penetration">{{cite journal |author=C. E. Theodosiou |title=Evaluation of penetration effects in high-''l'' Rydberg states |year=1983 |journal=[[Physical Review A]] |volume=28 |issue=5 |pages=3098–3101 |doi=10.1103/PhysRevA.28.3098|bibcode = 1983PhRvA..28.3098T }}</ref>
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| == Quantum-mechanical details ==
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| [[File:Sommerfeld ellipses.svg|thumb|right|'''Figure 3'''. Semiclassical orbits for ''n''=5 with all allowed values of orbital angular momentum. The black spot denotes the position of the atomic nucleus.]]
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| Quantum mechanically a state with abnormally high ''n'' refers to an atom in which the valence electron(s) have been excited into a formerly unpopulated [[Atomic orbital|electron orbital]] with higher energy and lower [[binding energy]]. In hydrogen the binding energy is given by:
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| :<math> E_\text{B} = -\dfrac{Ry}{n^2}</math>,
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| where ''Ry'' = 13.6 [[electron volt|eV]] is the [[Rydberg constant]]. The low binding energy at high values of ''n'' explains why Rydberg states are susceptible to ionization.
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| Additional terms in the potential energy expression for a Rydberg state, on top of the hydrogenic Coulomb potential energy require the introduction of a [[quantum defect]],<ref name="Nolan"/> δ<sub>''l''</sub>, into the expression for the binding energy:
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| :<math>E_\text{B} = -\dfrac{Ry}{(n-\delta_l)^2}</math>.
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| === Electron wavefunctions ===
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| The long lifetimes of Rydberg states with high orbital angular momentum can be explained in terms of the overlapping of wavefunctions. The wavefunction of an electron in a high ''l'' state (high angular momentum, 'circular orbit') has very little overlap with the wavefunctions of the inner electrons and hence remains relatively unperturbed.
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| The three exceptions to the definition of a Rydberg atom as an atom with a hydrogenic potential, have an alternative, quantum mechanical description that can be characterized by the additional term(s) in the atomic [[Hamiltonian (quantum mechanics)|Hamiltonian]]:
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| *If a second electron is excited into a state ''n<sub>i</sub>'', energetically close to the state of the outer electron ''n<sub>o</sub>'', then its wavefunction becomes almost as large as the first (a double Rydberg state). This occurs as ''n<sub>i</sub>'' approaches ''n<sub>o</sub>'' and leads to a condition where the size of the two electron’s orbits are related;<ref name="Double"/> a condition sometimes referred to as ''radial correlation''.<ref name="Gallagher"/> An electron-electron repulsion term must be included in the atomic Hamiltonian.
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| *Polarization of the ion core produces an [[Anisotropy|anisotropic]] potential that causes an ''angular correlation'' between the motions of the two outermost electrons.<ref name="Gallagher"/><ref name="Angular correlation">{{cite journal |author=T. A. Heim and A. R. P. Rau
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| |title=Excitation of high-lying pair-Rydberg states |journal=[[Journal of Physics B]] |volume=28 |issue= 24|pages=5309–5315 |year=1995 |doi=10.1088/0953-4075/28/24/015|bibcode = 1995JPhB...28.5309H }}</ref> This can be thought of as a [[tidal locking]] effect due to a non-spherically symmetric potential. A core polarization term must be included in the atomic Hamiltonian.
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| *The wavefunction of the outer electron in states with low orbital angular momentum ''l'', is periodically localised within the shells of inner electrons and interacts with the full charge of the nucleus.<ref name="Core penetration"/> '''Figure 3''' shows a [[Old quantum theory|semi-classical]] interpretation of angular momentum states in an electron orbital, illustrating that low-''l'' states pass closer to the nucleus potentially penetrating the ion core. A core penetration term must be added to the atomic Hamiltonian.
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| == Rydberg atoms in external fields ==
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| {{multiple image
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| | image1 = hfspec1.jpg
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| | alt1 = Stark-map for hydrogen
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| | caption1 = '''Figure 4'''. Computed energy level spectra of hydrogen in an electric field near ''n''=15.<ref name="Courtney">{{cite journal |author=M. Courtney |title=Classical, semiclassical, and quantum dynamics of lithium in an electric field |year=1995 |journal=[[Physical Review A]] |volume=51 |issue=5 |pages=3604–3620 |doi=10.1103/PhysRevA.51.3604|pmid=9912027|bibcode = 1995PhRvA..51.3604C |author-separator=, |display-authors=1 |last2=Spellmeyer |first2=Neal |last3=Jiao |first3=Hong |last4=Kleppner |first4=Daniel }}</ref> The potential energy found in the electronic Hamiltonian for hydrogen is the 1/''r'' Coulomb potential (there is no quantum defect) which does not couple the different Stark states. Consequently the energy levels from adjacent ''n''-manifolds cross at the Inglis-Teller limit.
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| | image2 = lfspec1.jpg
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| | alt2 = Stark-map for lithium
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| | caption2 = '''Figure 5'''. Computed energy level spectra of lithium in an electric field near ''n''=15.<ref name="Courtney"/> The presence of an ion-core that can be polarized and penetrated by the Rydberg electron adds additional terms to the electronic Hamiltonian (resulting in a finite quantum defect) leading to coupling of the different Stark states and hence [[avoided crossing]]s of the energy levels.
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| }}
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| The large separation between the electron and ion-core in a Rydberg atom makes possible an extremely large [[electric dipole moment]], '''d'''. There is an energy associated with the presence of an electric dipole in an [[electric field]], '''F''', known in atomic physics as a [[Stark effect|Stark shift]],
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| :<math>E_\text{S} = -\mathbf{d}\cdot\mathbf{F}.</math>
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| Depending on the sign of the projection of the dipole moment onto the local electric field vector a state may have energy that increases or decreases with field strength (low-field and high-field seeking states respectively). The narrow spacing between adjacent ''n''-levels in the Rydberg series means that states can approach [[Degenerate energy level|degeneracy]] even for relatively modest field strengths. The theoretical field strength at which a crossing would occur assuming no coupling between the states is given by the [[Inglis-Teller Equation|Inglis-Teller limit]],<ref name="Inglis-Teller">{{cite journal |author=D.R. Inglis and E. Teller |title=Ionic Depression of Series Limits in One-Electron Spectra |journal=[[Astrophysical Journal]] |volume=90 |issue= |page=439 |year=1939 |doi= 10.1086/144118 |bibcode=1939ApJ....90..439I}}</ref>
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| :<math>F_\text{IT} = \dfrac{e}{12\pi\varepsilon_0a_0^2n^5}.</math>
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| In the [[hydrogen atom]], the pure 1/''r'' Coulomb potential does not couple Stark states from adjacent ''n''-manifolds resulting in real crossings as shown in '''figure 4'''. The presence of additional terms in the potential energy can lead to coupling resulting in avoided crossings as shown for [[lithium]] in '''figure 5'''.
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| == Applications and further research ==
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| === Investigating diamagnetic effects ===
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| The large sizes and low binding energies of Rydberg atoms lead to a high [[magnetic susceptibility]], ''Χ''. As diamagnetic effects scale with the area of the orbit and the area is proportional to the radius squared (''A'' ∝ ''n''<sup>4</sup>), effects impossible to detect in ground state atoms become obvious in Rydberg atoms, which demonstrate very large diamagnetic shifts.<ref name="Diamagnetic">{{cite journal |author=J. Neukammer |title=Diamagnetic shift and singlet-triplet mixing of 6s''n''p Yb Rydberg states with large radial extent |year=1984 |journal=[[Physical Review A]] |volume=30 |issue=2 |pages=1142–1144 |doi=10.1103/PhysRevA.30.1142|bibcode = 1984PhRvA..30.1142N |author-separator=, |display-authors=1 |last2=Rinneberg |first2=H. |last3=Majewski |first3=U. }}</ref>
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| === Rydberg atoms in plasmas ===
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| Rydberg atoms form commonly in [[Plasma (physics)|plasma]]s due to the recombination of electrons and positive ions; low energy recombination results in fairly stable Rydberg atoms, while recombination of electrons and positive ions with high [[kinetic energy]] often form [[Ionization potential|autoionising]] Rydberg states. Rydberg atoms’ large sizes and susceptibility to perturbation and ionisation by electric and magnetic fields, are an important factor determining the properties of plasmas.<ref name="Plasma">{{cite journal |author=G. Vitrant |title=Rydberg to plasma evolution in a dense gas of very excited atoms |journal=[[Journal of Physics B]] |volume=15 |issue=2 |pages=L49–L55 |year=1982 |doi= 10.1088/0022-3700/15/2/004|bibcode = 1982JPhB...15L..49V |author-separator=, |display-authors=1 |last2=Raimond |first2=J M |last3=Gross |first3=M |last4=Haroche |first4=S }}</ref>
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| Condensation of Rydberg atoms forms [[Rydberg matter]] most often observed in form of long-lived clusters. The de-excitation is significantly impeded in Rydberg matter by exchange-correlation effects in the non-uniform electron liquid formed on condensation by the collective valence electrons, which causes extended lifetime of clusters.<ref name="Matter">{{cite journal |author=E. A. Manykin |title=Rydberg matter: properties and decay |journal=[[Proceedings of the SPIE]] |volume=6181 |issue=5 |pages=1–9 |year=2006 |doi=10.1117/12.675004 |author-separator=, |display-authors=1 |author2=<Please add first missing authors to populate metadata.>}}</ref>
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| === Rydberg atoms in astrophysics ===
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| It has been suggested<ref name="Astrophysics">{{cite journal|author=Y. N. Gnedin |title=Rydberg atoms in astrophysics |journal=[[New Astronomy Reviews]] |volume=53 |issue=7–10 |pages=259–265 |year=2009 |doi=10.1016/j.newar.2009.07.003|bibcode = 2009NewAR..53..259G|author-separator=,|display-authors=1|last2=Mihajlov|first2=A.A.|last3=Ignjatović|first3=Lj.M.|last4=Sakan|first4=N.M.|last5=Srećković|first5=V.A.|last6=Zakharov|first6=M.Yu.|last7=Bezuglov|first7=N.N.|last8=Klycharev|first8=A.N. |arxiv = 1208.2516 }}</ref> that Rydberg atoms are common in interstellar space and could be observed from earth. Since the density within interstellar gas clouds is many [[orders of magnitude]] lower than the best laboratory vacuums attainable on Earth, Rydberg states could persist for long periods of time without being destroyed by collisions.
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| === Strongly interacting systems ===
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| Due to their large size, Rydberg atoms can exhibit very large [[electric dipole moment]]s. Calculations using [[Perturbation theory (quantum mechanics)|perturbation theory]] show that this results in strong interactions between two close Rydberg atoms. Coherent control of these interactions combined with the their relatively long lifetime makes them a suitable candidate to realize a [[quantum computer]].<ref name="Jaksch gate">{{cite journal|author=D. Jaksch|title=Fast Quantum Gates for Neutral Atoms|journal=[[Physical Review Letters]]|doi=10.1103/PhysRevLett.85.2208 |volume=85|issue=10|pages=2208–11|year=2000|arxiv=quant-ph/0004038|pmid=10970499|bibcode=2000PhRvL..85.2208J|author-separator=,|display-authors=1|last2=Cirac|first2=J. I.|last3=Zoller|first3=P.|last4=Côté|first4=R.|last5=Lukin|first5=M. D.|last6=Lukin|first6=MD}}</ref> {{As of|2009|March}}, a two-[[qubit]] [[Quantum gate|gate]] has not been achieved experimentally; however, observations of collective excitations or conditional dynamics have been reported, both between two individual atoms <ref name="Gaetan2009">{{cite journal|author=A. Gaëtan|title=Observation of collective excitation of two individual atoms in the Rydberg blockade regime|journal=[[Nature Physics]]|volume=5|issue=2|pages=115–118|year=2009 |doi=10.1038/nphys1183|arxiv=0810.2960|bibcode = 2009NatPh...5..115G|author-separator=,|display-authors=1|last2=Miroshnychenko|first2=Yevhen|last3=Wilk|first3=Tatjana|last4=Chotia|first4=Amodsen|last5=Viteau|first5=Matthieu|last6=Comparat|first6=Daniel|last7=Pillet|first7=Pierre|last8=Browaeys|first8=Antoine|last9=Grangier|first9=Philippe }}</ref><ref name="Urban2009">{{cite journal|author=E. Urban|title=Observation of Rydberg blockade between two atoms|journal=[[Nature Physics]]|volume=5|issue=2|pages=110–114|year=2009 |doi=10.1038/nphys1178|arxiv=0805.0758|bibcode = 2009NatPh...5..110U|author-separator=,|display-authors=1|last2=Johnson|first2=T. A.|last3=Henage|first3=T.|last4=Isenhower|first4=L.|last5=Yavuz|first5=D. D.|last6=Walker|first6=T. G.|last7=Saffman|first7=M. }}</ref> and in [[mesoscopic]] samples.<ref name="Collective excitations">{{cite journal|author=R. Heidemann|title= Evidence for Coherent Collective Rydberg Excitation in the Strong Blockade Regime|journal=[[Physical Review Letters]]|volume=99|issue=16|page=163601|year=2007|doi=10.1103/PhysRevLett.99.163601|arxiv=quant-ph/0701120|pmid=17995249|bibcode=2007PhRvL..99p3601H|author-separator=,|display-authors=1|last2=Raitzsch|first2=Ulrich|last3=Bendkowsky|first3=Vera|last4=Butscher|first4=Björn|last5=Löw|first5=Robert|last6=Santos|first6=Luis|last7=Pfau|first7=Tilman}}</ref> Strongly interacting Rydberg atoms also feature [[Quantum critical point|quantum critical]] behavior, which makes them interesting to study on their own.<ref name="Quantum critical behavior">{{cite journal|author=H. Weimer|title=Quantum Critical Behavior in Strongly Interacting Rydberg Gases|journal=[[Physical Review Letters]]|doi=10.1103/PhysRevLett.101.250601|year=2008|volume=101|issue=25|page=250601|arxiv=0806.3754|pmid=19113686|bibcode=2008PhRvL.101y0601W|author-separator=,|display-authors=1|last2=Löw|first2=Robert|last3=Pfau|first3=Tilman|last4=Büchler|first4=Hans Peter}}</ref>
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| == Classical simulation ==
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| [[File:Stark - Coulomb potential.png|thumb|left|'''Figure 6'''. Stark - Coulomb potential for a Rydberg atom in a static electric field. An electron in such a potential feels a torque that can change its angular momentum.]]
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| [[File:Rydberg plot with electric field.png|right|thumb|'''Figure 7'''. Trajectory of the [[electron]] in a [[hydrogen atom]] in an [[electric field]] E = -3 x 10<sup>6</sup> V/m in the ''x''-direction. Note that classically all values of angular momentum are allowed; '''figure 3''' shows the particular orbits associated with quantum mechanically allowed values. See the [[Media:Rydberg atom animation.gif|animation]].]]
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| A simple 1/''r'' potential results in a closed [[Planetary orbit|Keplerian elliptical orbit]]. In the presence of an external [[electric field]] Rydberg atoms can obtain very large [[electric dipole moment]]s making them extremely susceptible to perturbation by the field. '''Figure 6''' shows how application of an external electric field (known in atomic physics as a [[Stark effect|Stark]] field) changes the geometry of the potential, dramatically changing the behaviour of the electron. A Coulombic potential does not apply any [[torque]] as the force is always [[antiparallel (mathematics)|antiparallel]] to the position vector (always pointing along a line running between the electron and the nucleus):
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| :<math>|\mathbf{\tau}|=|\mathbf{r} \times \mathbf{F}|=|\mathbf{r}||\mathbf{F}|\sin\theta </math>,
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| :<math>\theta=\pi \Rightarrow \mathbf{\tau}=0 </math>.
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| With the application of a static electric field, the electron feels a continuously changing torque. The resulting trajectory becomes progressively more distorted over time, eventually going through the full range of angular momentum from ''L'' = ''L''<sub>MAX</sub>, to a straight line ''L''=0, to the initial orbit in the opposite sense
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| ''L'' = -''L''<sub>MAX</sub>.<ref name="Simulation">{{cite journal |author=T. P. Hezel |title=Classical view of the Stark effect in hydrogen atoms |journal=[[American Journal of Physics]] |volume=60 |issue=4 |pages=324–328 |year=1992 |doi=10.1119/1.16875|bibcode = 1992AmJPh..60..324H |author-separator=, |display-authors=1 |author2=<Please add first missing authors to populate metadata.> }}</ref>
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| The time period of the oscillation in angular momentum (the time to complete the trajectory in '''figure 7'''), almost exactly matches the quantum mechanically predicted period for the wavefunction to return to its initial state, demonstrating the classical nature of the Rydberg atom.
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| == See also ==
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| * [[Heavy Rydberg system]]
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| * [[Old quantum theory]]
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| * [[Quantum chaos]]
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| * [[Rydberg molecule]]
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| == References ==
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| {{reflist|2}}
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| [[Category:Atoms]]
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