33:
804:), 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.
2332:
819:
2321:
1290:
51:
1595:
1622:
2046:
than hydrogen, and so singly-ionized carbon atoms, and the corresponding recombining
Rydberg states, exist further from the ionizing stars, in so-called C II regions which form thick shells around H II regions. The larger volume partially compensates for the low abundance of C compared to
2311:
publicly discussed efforts to develop a super wideband radio receiver using
Rydberg atoms. In March 2020, the laboratory announced that its scientists analysed the Rydberg sensor's sensitivity to oscillating electric fields over an enormous range of frequenciesâfrom 0 to 10 Hertz (the spectrum to
2303:
was used in combination with strong interactions between two atoms excited in
Rydberg state to provide medium that exhibits strongly nonlinear behaviour at the level of individual optical photons. The tuneable interaction between Rydberg states, enabled also first quantum simulation experiments.
2239:
from neutral hydrogen. This allows radio astronomers to study both the neutral and the ionized interstellar medium from the same set of observations. Since RRLs are numerous and weak, common practice is to average the velocity spectra of several neighbouring lines, to improve sensitivity.
1931:, 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.
1279:
If the outer electron penetrates the inner electron shells, it will âseeâ 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
2022:
lower than the best laboratory vacuums attainable on Earth, it had been expected that such highly-excited atoms would be frequently destroyed by collisions, rendering the lines unobservable. Improved theoretical analysis showed that this effect had been overestimated, although
979:
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. For an atom in a multiple
Rydberg state, the additional term,
1127:
1720:
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
733:
is absorbed by the target atom, resulting in a precise 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,
2499:
2312:
0.3mm wavelength). The
Rydberg sensor can reliably detect signals over the entire spectrum and compare favourably with other established electric field sensor technologies, such as electro-optic crystals and dipole antenna-coupled passive electronics.
1634:=15. 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
1253:
2549:
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
2234:
with relatively small intervals in wavelength between them, so they frequently occur in radio spectral observations primarily targeted at other spectral lines. For instance, H166α, H167α, and H168α are very close in wavelength to the
252:
5594:
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; MacrÏ, Tommaso; Lahaye, Thierry; Browaeys, Antoine (2016). "Tunable two-dimensional arrays of single
Rydberg atoms for realizing quantum Ising models".
1819:
2031:.. The record wavelength for hydrogen is λ = 73 cm for H253α, implying atomic diameters of a few microns, and for carbon, λ = 18 metres, from C732α, from atoms with a diameter of 57 micron.
1505:
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
951:
1488:
825:. 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/
5224:
Sedlacek, Jonathon A.; Schwettmann, Arne; KĂŒbler, Harald; Löw, Robert; Pfau, Tilman; Shaffer, James P. (2012-09-16). "Microwave electrometry with
Rydberg atoms in a vapour cell using bright atomic resonances".
2259:
show that this results in strong interactions between two close
Rydberg atoms. Coherent control of these interactions combined with their relatively long lifetime makes them a suitable candidate to realize a
2135:
1715:
2543:
1375:
2816:
998:
406:
712:
632:
1924:
Rydberg states. Rydberg atomsâ large sizes and susceptibility to perturbation and ionisation by electric and magnetic fields, are an important factor determining the properties of plasmas.
2204:
of the valence electron for each element. This gives helium and carbon lines apparent Doppler shifts of â100 and â140 km/s, respectively, relative to the corresponding hydrogen line.
777:
1916:
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
2215:, which blocks photons from the more familiar optical transitions. They are also used to measure the temperature of the ionized gas, via the ratio of line intensity to the continuum
2404:
2223:. Since the temperature of H II regions is regulated by line emission from heavier elements such as C, N, and O, recombination lines also indirectly measure their abundance (
5380:
Pritchard, J. D.; Maxwell, D.; Gauguet, A.; Weatherill, K. J.; Jones, M. P. A.; Adams, C. S. (2010-11-05). "Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble".
5276:
Wade, C. G.; Ć ibaliÄ, N.; de Melo, N. R.; Kondo, J. M.; Adams, C. S.; Weatherill, K. J. (2016-11-07). "Real-time near-field terahertz imaging with atomic optical fluorescence".
2583:), 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.
1498:
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
717:
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.
2162:
3674:
Wenger, Trey V.; Dawson, J. R.; Dickey, John M.; Jordan, C. H.; McClureâGriffiths, N. M.; Anderson, L. D.; Armentrout, W. P.; Balser, Dana S.; Bania, T. M. (2021-06-01).
1861:
The radiative decay lifetimes of atoms in metastable states to the ground state are important to understanding astrophysics observations and tests of the standard model.
1155:
317:
2072:
5450:
2192:
can be used to estimate the position of the H II region on the line of sight and so its 3D position in the Galaxy. Because all astrophysical Rydberg atoms are
1891:
1729:
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
637:
Because the electron can retain any arbitrary amount of its initial kinetic energy, this process results in a population with a broad spread of different energies.
3449:
5525:
SchauĂ, P.; Zeiher, J.; Fukuhara, T.; Hild, S.; Cheneau, M.; MacrĂŹ, T.; Pohl, T.; Bloch, I.; Gross, C. (2015-03-27). "Crystallization in Ising quantum magnets".
167:
2190:
2172:
can have radial velocities up to ±150 km/s, due to their motion relative to Earth as both orbit the centre of the Galaxy. These motions are regular enough that
1502:
state (high angular momentum, âcircular orbitâ) has very little overlap with the wavefunctions of the inner electrons and hence remains relatively unperturbed.
2327:. 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.
3861:
Alves, Marta I. R.; Calabretta, Mark; Davies, Rodney D.; Dickinson, Clive; Staveley-Smith, Lister; Davis, Richard J.; Chen, Tianyue; Barr, Adam (2015-06-21).
3743:
Anderson, L. D.; Luisi, Matteo; Liu, Bin; Wenger, Trey V.; Balser, Dana. S.; Bania, T. M.; Haffner, L. M.; Linville, Dylan J.; Mascoop, J. L. (2021-06-01).
964:. In other words, the electron's orbit resembles the orbit of planets inside a solar system, similar to what was seen in the obsolete but visually useful
1395:
Additional terms in the potential energy expression for a Rydberg state, on top of the hydrogenic Coulomb potential energy require the introduction of a
1739:
2781:
2300:
2256:
521:
values of angular momentum lead to the observed discrete energy levels. A full quantitative derivation of the observed spectrum was derived by
5687:
5667:
2308:
1904:
Rydberg atoms exhibit strong electric-dipole coupling of the atoms to electromagnetic fields and has been used to detect radio communications.
1611:
Coulomb potential (there is no quantum defect) which does not couple the different Stark states. Consequently the energy levels from adjacent
3619:
2650:
2390:
field) changes the geometry of the potential, dramatically changing the behaviour of the electron. A Coulombic potential does not apply any
883:
94:
5329:
Nogues, G.; Rauschenbeutel, A.; Osnaghi, S.; Brune, M.; Raimond, J. M.; Haroche, S. (1999). "Seeing a single photon without destroying it".
1982:= 90 state. Today, Rydberg atoms of hydrogen, helium and carbon in space are routinely observed via RRLs, the brightest of which are the H
1414:
3862:
1580:
states pass closer to the nucleus potentially penetrating the ion core. A core penetration term must be added to the atomic Hamiltonian.
3301:
Nicholas D. Guise; et al. (Apr 24, 2014). "Measurement of the Kr xviii 3d 2D5/2 lifetime at low energy in a unitary Penning trap".
1901:), effects impossible to detect in ground state atoms become obvious in Rydberg atoms, which demonstrate very large diamagnetic shifts.
561:
Much early experimental work on Rydberg atoms relied on the use of collimated beams of fast electrons incident on ground-state atoms.
2855:
2694:
2296:
2077:
4838:"Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits"
2991:
T. P. Hezel, et al. (1992). "Classical view of the properties of Rydberg atoms: Application of the correspondence principle".
1671:
956:
The similarity of the effective potential "seen" by the outer electron to the hydrogen potential is a defining characteristic of
2508:
2359:
1507:
569:
to increase the atoms' internal energy exciting to a broad range of different states including many high-lying Rydberg states,
549:= 1. The study of Rydberg states requires a reliable technique for exciting ground state atoms to states with a large value of
1322:
1122:{\displaystyle U_{ee}={\dfrac {e^{2}}{4\pi \varepsilon _{0}}}\sum _{i<j}{\dfrac {1}{|\mathbf {r} _{i}-\mathbf {r} _{j}|}}.}
1951:
state, and then gradually dropping through the energy levels to the ground state, giving rise to a sequence of recombination
1840:. The presence of additional terms in the potential energy can lead to coupling resulting in avoided crossings as shown for
2711:
729:
in the 1970s allowed a much greater level of control over populations of excited atoms. In optical excitation, the incident
5449:
Firstenberg, Ofer; Peyronel, Thibault; Liang, Qi-Yu; Gorshkov, Alexey V.; Lukin, Mikhail D.; VuletiÄ, Vladan (2013-09-25).
1561:
effect due to a non-spherically symmetric potential. A core polarization term must be included in the atomic Hamiltonian.
32:
341:
1947:
with electrons, which at these very low densities usually proceeds via the electron re-joining the atom in a very high
1542:
and leads to a condition where the size of the two electronâs orbits are related; a condition sometimes referred to as
5755:
5700:
Meyer, David H.; Kunz, Paul D.; Cox, Kevin C. (2021). "Waveguide-Coupled Rydberg Spectrum Analyzer from 0 to 20 GHz".
2993:
2956:
2742:
3033:
1730:
1568:, is periodically localised within the shells of inner electrons and interacts with the full charge of the nucleus.
655:
575:
649:
and a population of neutral atoms of another species, resulting in the formation of a beam of highly excited atoms,
3213:
M. Courtney, et al. (1995). "Classical, semiclassical, and quantum dynamics of lithium in an electric field".
2642:
1134:
975:
There are three notable exceptions that can be characterized by the additional term added to the potential energy:
262:
158:
1300:=5 with all allowed values of orbital angular momentum. The black spot denotes the position of the atomic nucleus.
2291:
and quantum matters. High electric dipole moments between Rydberg atomic states are used for radio frequency and
740:
4349:
Gorshkov, Alexey V.; Otterbach, Johannes; Fleischhauer, Michael; Pohl, Thomas; Lukin, Mikhail D. (2011-09-22).
1956:
961:
463:
328:
82:
43:
1893:. As diamagnetic effects scale with the area of the orbit and the area is proportional to the radius squared (
2494:{\displaystyle |\mathbf {\tau } |=|\mathbf {r} \times \mathbf {F} |=|\mathbf {r} ||\mathbf {F} |\sin \theta }
143:
of the atom is useful in explaining these properties. Classically, an electron in a circular orbit of radius
5679:
4962:"Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction"
4158:
4095:
4032:
3969:
3515:
1870:
1726:
277:
3914:
1645:
The large separation between the electron and ion-core in a Rydberg atom makes possible an extremely large
4625:
Lukin, M. D.; Fleischhauer, M.; Cote, R.; Duan, L. M.; Jaksch, D.; Cirac, J. I.; Zoller, P. (2001-06-26).
2789:
2715:
2379:
2272:
2252:
2024:
1646:
1145:
845:
electron in a large orbit far from the ion core; in such an orbit, the outermost electron feels an almost
518:
272:
3264:
4219:
Tiarks, Daniel; Schmidt-Eberle, Steffen; Stolz, Thomas; Rempe, Gerhard; DĂŒrr, Stephan (February 2019).
3031:
I. K. Dmitrieva; et al. (1993). "Energies of Doubly Excited States. The Double Rydberg Formula".
1528:, then its wavefunction becomes almost as large as the first (a double Rydberg state). This occurs as
411:
It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as
5764:
5719:
5614:
5544:
5465:
5399:
5338:
5234:
5174:
5107:
5042:
4983:
4918:
4859:
4794:
4721:
4648:
4575:
4510:
4445:
4372:
4299:
4177:
4114:
4051:
3988:
3933:
3825:
3766:
3697:
3656:
3645:"Observations of carbon recombination lines at decametric wavelengths in the direction of Cassiopeia"
3571:
3524:
3487:
3478:
3414:
3369:
3320:
3273:
3224:
3176:
3167:
3139:
3087:
3042:
3002:
2965:
2912:
2825:
2751:
2674:
2592:
2395:
1944:
1921:
562:
428:
4895:
Weimer, Hendrik; MĂŒller, Markus; Lesanovsky, Igor; Zoller, Peter; BĂŒchler, Hans Peter (2010-03-14).
4030:
T. Wilk, et al. (2010). "Entanglement of Two Individual Neutral Atoms Using Rydberg Blockade".
3476:
G. Vitrant, et al. (1982). "Rydberg to plasma evolution in a dense gas of very excited atoms".
2398:
to the position vector (always pointing along a line running between the electron and the nucleus):
2331:
2243:
There are a variety of other potential applications of Rydberg atoms in cosmology and astrophysics.
1248:{\displaystyle U_{\text{pol}}=-{\frac {e^{2}\alpha _{\text{d}}}{(4\pi \varepsilon _{0})^{2}r^{4}}},}
498:
presented a generalized and more intuitive version of Balmer's formula that came to be known as the
5021:"Rydberg-atom quantum simulation and Chern-number characterization of a topological Mott insulator"
2292:
2039:
2019:
2018: > 100 was surprising, as even in the very low densities of interstellar space, many
502:. This formula indicated the existence of an infinite series of ever more closely spaced discrete
4156:
H. Weimer, et al. (2008). "Quantum Critical Behavior in Strongly Interacting Rydberg Gases".
2140:
5735:
5709:
5646:
5604:
5576:
5534:
5507:
5431:
5389:
5362:
5311:
5285:
5258:
5206:
5164:
5133:
5097:
5066:
5032:
5001:
4973:
4942:
4908:
4849:
4818:
4784:
4753:
4711:
4680:
4638:
4607:
4565:
4534:
4500:
4469:
4435:
4404:
4362:
4331:
4289:
4258:
4232:
4201:
4167:
4138:
4104:
4093:
L. Isenhower, et al. (2010). "Demonstration of a Neutral Atom Controlled-NOT Quantum Gate".
4075:
4041:
4012:
3978:
3949:
3923:
3874:
3815:
3756:
3687:
3644:
3559:
3540:
3430:
3404:
3336:
3310:
3192:
3058:
2928:
2903:
2597:
1967:
emitted in transitions between such states have low frequencies and long wavelengths, even up to
1573:
1308:
refers to an atom in which the valence electron(s) have been excited into a formerly unpopulated
846:
542:
287:
129:
3395:
Anderson, David A.; et al. (2021). "An Atomic Receiver for AM and FM Radio Communication".
960:
and explains why the electron wavefunctions approximate to classical orbits in the limit of the
877:-1 electrons. An electron in the spherically symmetric Coulomb potential has potential energy:
5086:"Rydberg noisy dressing and applications in making soliton molecules and droplet quasicrystals"
3513:
E. A. Manykin, et al. (2006). Samartsev VV (ed.). "Rydberg matter: Properties and decay".
2579:
The time period of the oscillation in angular momentum (the time to complete the trajectory in
1133:
If the valence electron has very low angular momentum (interpreted classically as an extremely
645:
Another mainstay of early Rydberg atom experiments relied on charge exchange between a beam of
5638:
5630:
5568:
5560:
5499:
5491:
5423:
5415:
5354:
5303:
5250:
5198:
5190:
5125:
5058:
4934:
4877:
4810:
4745:
4737:
4672:
4664:
4599:
4591:
4526:
4461:
4396:
4388:
4323:
4315:
4250:
4193:
4130:
4067:
4004:
3894:
3843:
3784:
3725:
3625:
3615:
3360:
3240:
3215:
3130:
3103:
3078:
2936:
2877:
2690:
2646:
2288:
2057:
2043:
1137:
elliptical orbit), then it may pass close enough to polarise the ion core, giving rise to a 1/
801:
530:
526:
451:
153:
117:
1148:
and the charge that produces it is always attractive so this contribution is always negative,
5772:
5727:
5622:
5552:
5481:
5473:
5407:
5346:
5295:
5242:
5182:
5115:
5050:
4991:
4926:
4867:
4802:
4729:
4656:
4583:
4518:
4453:
4380:
4307:
4242:
4185:
4122:
4059:
3996:
3941:
3884:
3833:
3774:
3715:
3705:
3607:
3532:
3495:
3422:
3377:
3328:
3281:
3232:
3184:
3147:
3095:
3050:
3010:
2973:
2920:
2833:
2785:
2759:
2740:
J. Murray-Krezan (2008). "The classical dynamics of Rydberg Stark atoms in momentum space".
2682:
2607:
2261:
2220:
2197:
1913:
1635:
1385:
969:
794:
495:
419:= 137 state of hydrogen has an atomic radius ~1 ÎŒm) and the geometric cross-section as
125:
62:
4698:
Jaksch, D.; Cirac, J. I.; Zoller, P.; Rolston, S. L.; CÎté, R.; Lukin, M. D. (2000-09-04).
2320:
2050:
In the absence of collisional broadening, the wavelengths of RRLs are modified only by the
1876:
818:
247:{\displaystyle \mathbf {F} =m\mathbf {a} \Rightarrow {ke^{2} \over r^{2}}={mv^{2} \over r}}
4277:
2851:
2612:
2371:
2358:
shows the particular orbits associated with quantum mechanically allowed values. See the
1975:
1940:
499:
5753:
T. P. Hezel, et al. (1992). "Classical view of the Stark effect in hydrogen atoms".
4487:
Friedler, Inbal; Petrosyan, David; Fleischhauer, Michael; Kurizki, Gershon (2005-10-05).
5768:
5723:
5618:
5548:
5469:
5403:
5342:
5238:
5178:
5111:
5046:
4987:
4922:
4863:
4798:
4725:
4652:
4579:
4514:
4449:
4376:
4303:
4181:
4118:
4055:
3992:
3937:
3829:
3770:
3701:
3660:
3575:
3528:
3491:
3418:
3373:
3324:
3277:
3228:
3180:
3143:
3091:
3046:
3006:
2969:
2916:
2829:
2755:
2678:
1576:
interpretation of angular momentum states in an electron orbital, illustrating that low-
5796:
4961:
2375:
2347:
2284:
2231:
2216:
2175:
2051:
1968:
1928:
1917:
1654:
1396:
1313:
1309:
1267:
1142:
957:
861:
850:
838:
797:
787:
566:
522:
435:
148:
121:
106:
102:
39:
5120:
5085:
3188:
5790:
5739:
5731:
5315:
5262:
5137:
5005:
4473:
4335:
3953:
3499:
3434:
3354:
J. Neukammer, et al. (1984). "Diamagnetic shift and singlet-triplet mixing of 6s
3196:
2602:
2343:
1952:
1825:
1607:=15. The potential energy found in the electronic Hamiltonian for hydrogen is the 1/
1558:
1381:
865:
842:
813:
483:
479:
424:
133:
74:
5580:
5435:
5152:
5070:
4946:
4822:
4757:
4684:
4611:
4553:
4538:
4408:
4350:
4262:
4205:
4079:
4016:
3745:"The GBT Diffuse Ionized Gas Survey (GDIGS): Survey Overview and First Data Release"
3544:
3340:
3062:
2954:
M. Haugh, et al. (1966). "Electronic excitation accompanying charge exchange".
782:
This form of direct optical excitation is generally limited to experiments with the
5650:
5511:
5411:
5366:
5210:
5186:
4627:"Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles"
4626:
4587:
4424:"Photon-photon gate via the interaction between two collective Rydberg excitations"
4384:
4311:
4220:
4189:
4142:
4126:
4063:
3454:
2387:
2268:
2201:
2006: = 2 and 3 are also observed. Corresponding lines for helium and carbon are He
1972:
1662:
1564:
The wavefunction of the outer electron in states with low orbital angular momentum
1289:
783:
503:
113:
4660:
3560:"Detection of a Radio Line Due to Excited Hydrogen in the Nebula NGC 6618 (Omega)"
2386:
shows how application of an external electric field (known in atomic physics as a
2283:
Since 2000's Rydberg atoms research encompasses broadly five directions: sensing,
2207:
RRLs are used to detect ionized gas in distant regions of our Galaxy, and also in
1546:. An electron-electron repulsion term must be included in the atomic Hamiltonian.
4699:
2719:
1814:{\displaystyle F_{\text{IT}}={\dfrac {e}{12\pi \varepsilon _{0}a_{0}^{2}n^{5}}}.}
1557:
between the motions of the two outermost electrons. This can be thought of as a
790:
in other species is generally too high to be accessible with most laser systems.
5020:
4772:
4733:
4488:
4423:
4000:
3945:
3165:
T. A. Heim; et al. (1995). "Excitation of high-lying pair-Rydberg states".
2224:
2212:
2035:
454:. These closely spaced Rydberg states form what is commonly referred to as the
17:
5054:
4872:
4837:
4806:
4522:
4457:
3838:
3804:"Metallicity Structure in the Milky Way Disk Revealed by Galactic H ii Regions"
3803:
3779:
3744:
3710:
3675:
3332:
2901:
J. Olmsted (1967). "Excitation of nitrogen triplet states by electron impact".
2837:
2354:-direction. Note that classically all values of angular momentum are allowed;
1653:. There is an energy associated with the presence of an electric dipole in an
4996:
4246:
3802:
Wenger, Trey V.; Balser, Dana S.; Anderson, L. D.; Bania, T. M. (2019-12-16).
3611:
2686:
2271:
were achieved experimentally. Strongly interacting Rydberg atoms also feature
2236:
2165:
1550:
965:
514:
510:
487:
324:
140:
5634:
5564:
5495:
5419:
5358:
5307:
5299:
5254:
5194:
5129:
5062:
4938:
4881:
4814:
4741:
4668:
4595:
4530:
4465:
4392:
4319:
4254:
3898:
3847:
3788:
3729:
3629:
3426:
3381:
3236:
3151:
3099:
5680:
Scientists create quantum sensor that covers entire radio frequency spectrum
5556:
3595:
2169:
1959:. The very small differences in energy between Rydberg states differing in
1274:
shows how the polarization term modifies the potential close to the nucleus.
726:
50:
5642:
5572:
5503:
5427:
5202:
4749:
4676:
4603:
4400:
4327:
4197:
4134:
4071:
4008:
3889:
3244:
3107:
2940:
101:
have a number of peculiar properties including an exaggerated response to
5683:
5153:"Supersolid Vortex Crystals in Rydberg-Dressed Bose-Einstein Condensates"
4716:
4643:
4505:
4422:
Khazali, Mohammadsadegh; Heshami, Khabat; Simon, Christoph (2015-03-17).
3983:
3450:"A new antenna using single atoms could usher in the age of atomic radio"
2339:
1978:
in 1964; the line, designated H90α, was emitted by hydrogen atoms in the
1869:
The large sizes and low binding energies of Rydberg atoms lead to a high
829:
potential of the hydrogen atom while the dashed red curve includes the 1/
491:
110:
78:
5626:
5486:
5477:
478:
The existence of the Rydberg series was first demonstrated in 1885 when
4896:
4489:"Long-range interactions and entanglement of slow single-photon pulses"
4276:
Khazali, Mohammadsadegh; Murray, Callum R.; Pohl, Thomas (2019-09-13).
3967:
D. Jaksch, et al. (2000). "Fast Quantum Gates for Neutral Atoms".
3720:
3054:
2932:
1841:
946:{\displaystyle U_{\text{C}}=-{\dfrac {e^{2}}{4\pi \varepsilon _{0}r}}.}
467:
128:
from the electric field of the nucleus such that, from a distance, the
58:
5663:
5246:
4930:
3863:"The HIPASS survey of the Galactic plane in radio recombination lines"
3536:
2977:
2811:
2763:
2034:
RRLs from hydrogen and helium are produced in highly ionized regions (
1603:. Computed energy level spectra of hydrogen in an electric field near
1483:{\displaystyle E_{\text{B}}=-{\frac {\rm {Ry}}{(n-\delta _{l})^{2}}}.}
5151:
Henkel, N.; Cinti, F.; Jain, P.; Pupillo, G.; Pohl, T. (2012-06-26).
2391:
2208:
1964:
1630:. Computed energy level spectra of lithium in an electric field near
1141:
core polarization term in the potential. The interaction between an
870:
730:
5776:
3124:
C. E. Theodosiou (1983). "Evaluation of penetration effects in high-
3014:
2924:
1971:
The first detection of such a radio recombination line (RRL) was by
1939:
Rydberg atoms occur in space due to the dynamic equilibrium between
5714:
5609:
5290:
5102:
4978:
4854:
4294:
4237:
3912:
Y. N. Gnedin, et al. (2009). "Rydberg atoms in astrophysics".
3820:
3761:
3692:
3409:
3286:
3259:
2196:, the frequencies of transitions for H, He, and C are given by the
1621:
1594:
450:
leading to ever more closely spaced levels converging on the first
27:
Excited atomic quantum state with high principal quantum number (n)
5539:
5394:
5350:
5169:
5037:
4913:
4789:
4570:
4440:
4367:
4278:"Polariton Exchange Interactions in Multichannel Optical Networks"
4172:
4109:
4046:
3928:
3879:
3315:
2330:
2319:
2265:
1288:
817:
49:
46:=12. Colors show the quantum phase of the highly excited electron.
31:
3676:"The Southern H II Region Discovery Survey. II. The Full Catalog"
2382:
making them extremely susceptible to perturbation by the field.
4554:"All-Optical Quantum Information Processing Using Rydberg Gates"
98:
3076:
L. Neale; et al. (1995). "Core Polarization in Kr VIII".
2275:
behavior, which makes them interesting to study on their own.
2251:
Due to their large size, Rydberg atoms can exhibit very large
2130:{\displaystyle v\approx c(\lambda -\lambda _{0})/\lambda _{0}}
2027:
does eventually limit detectability of the lines at very high
646:
462:
shows some of the energy levels of the lowest three values of
423:. Thus, Rydberg atoms are extremely large, with loosely bound
5019:
Dauphin, A.; MĂŒller, M.; Martin-Delgado, M. A. (2012-11-20).
2817:
Nuclear Instruments and Methods in Physics Research Section B
1832:
Coulomb potential does not couple Stark states from adjacent
1725:-levels in the Rydberg series means that states can approach
1710:{\displaystyle E_{\text{S}}=-\mathbf {d} \cdot \mathbf {F} .}
4221:"A photonâphoton quantum gate based on Rydberg interactions"
2565: = 0, to the initial orbit in the opposite sense
3649:
Pisma V Astronomicheskii Zhurnal (Soviet Astronomy Letters)
3260:"Ionic Depression of Series Limits in One-Electron Spectra"
1392:
explains why Rydberg states are susceptible to ionization.
2538:{\displaystyle \theta =\pi \Rightarrow \mathbf {\tau } =0}
1521:, energetically close to the state of the outer electron
132:
looks identical to that experienced by the electron in a
1370:{\displaystyle E_{\text{B}}=-{\frac {\rm {Ry}}{n^{2}}},}
4836:
Khazali, Mohammadsadegh; MĂžlmer, Klaus (2020-06-11).
4771:
Saffman, M.; Walker, T. G.; MĂžlmer, K. (2010-08-18).
2511:
2407:
2178:
2143:
2080:
2060:
1879:
1757:
1742:
1674:
1417:
1325:
1158:
1069:
1019:
1001:
904:
886:
743:
658:
578:
344:
327:'s expression for the orbital radius in terms of the
290:
170:
61:
showing the Rydberg series of the lowest 3 values of
5664:
Army researchers make giant leap in quantum sensing
3119:
3117:
1836:-manifolds resulting in real crossings as shown in
1304:Quantum-mechanically, a state with abnormally high
509:This series was qualitatively explained in 1913 by
5451:"Attractive photons in a quantum nonlinear medium"
2537:
2493:
2184:
2156:
2129:
2066:
1885:
1813:
1709:
1482:
1369:
1247:
1121:
945:
771:
706:
626:
401:{\displaystyle r={n^{2}\hbar ^{2} \over ke^{2}m}.}
400:
311:
246:
4351:"Photon-Photon Interactions via Rydberg Blockade"
3867:Monthly Notices of the Royal Astronomical Society
2211:, because the radio photons are not absorbed by
93:, the farther the electron is from the nucleus,
4552:Paredes-Barato, D.; Adams, C. S. (2014-01-28).
3358:p Yb Rydberg states with large radial extent".
1857:Precision measurements of trapped Rydberg atoms
1316:. In hydrogen the binding energy is given by:
707:{\displaystyle A^{+}+B\rightarrow A^{*}+B^{+}.}
627:{\displaystyle e^{-}+A\rightarrow A^{*}+e^{-}.}
490:of light associated with transitions in atomic
1408:, into the expression for the binding energy:
3397:IEEE Transactions on Antennas and Propagation
1514:If a second electron is excited into a state
8:
3558:Sorochenko, R. L.; Borodzich, Ă. V. (1965).
1615:-manifolds cross at the InglisâTeller limit.
1388:. The low binding energy at high values of
494:. Three years later, the Swedish physicist
446:, the energy level spacing falls off like 1/
3749:The Astrophysical Journal Supplement Series
3680:The Astrophysical Journal Supplement Series
3208:
3206:
2632:
2630:
2628:
2074:, is usually converted to radial velocity,
1935:In astrophysics (Radio recombination lines)
772:{\displaystyle A+\gamma \rightarrow A^{*}.}
438:of a Rydberg electron is proportional to 1/
2669:Ć ibaliÄ, Nikola; S Adams, Charles (2018).
2014:α, and so on. The discovery of lines with
1986:α lines corresponding to transitions from
873:and the lower electron shells filled with
860:, from a compact ion core consisting of a
65:converging on the first ionization energy.
5713:
5608:
5538:
5485:
5393:
5289:
5168:
5119:
5101:
5036:
4995:
4977:
4912:
4871:
4853:
4788:
4715:
4642:
4569:
4504:
4439:
4366:
4293:
4236:
4171:
4108:
4045:
3982:
3927:
3888:
3878:
3837:
3819:
3778:
3760:
3719:
3709:
3691:
3408:
3314:
3285:
3026:
3024:
2524:
2510:
2477:
2472:
2467:
2462:
2457:
2452:
2444:
2439:
2431:
2426:
2418:
2413:
2408:
2406:
2193:
2177:
2148:
2142:
2121:
2112:
2103:
2079:
2059:
1878:
1798:
1788:
1783:
1773:
1756:
1747:
1741:
1699:
1691:
1679:
1673:
1549:Polarization of the ion core produces an
1468:
1458:
1436:
1434:
1422:
1416:
1356:
1344:
1342:
1330:
1324:
1233:
1223:
1213:
1192:
1182:
1175:
1163:
1157:
1107:
1101:
1096:
1086:
1081:
1075:
1068:
1056:
1042:
1025:
1018:
1006:
1000:
927:
910:
903:
891:
885:
833:term due to polarization of the ion core.
760:
742:
695:
682:
663:
657:
615:
602:
583:
577:
383:
368:
358:
351:
343:
289:
232:
222:
211:
200:
190:
182:
171:
169:
116:that approximate, under some conditions,
4773:"Quantum information with Rydberg atoms"
3448:Oullette, Jennifer (19 September 2018).
2301:Electromagnetically induced transparency
3594:Gordon, M.A.; Sorochenko, R.L. (2009).
2775:
2773:
2624:
2047:H, making the carbon RRLs detectable.
365:
323:Combining these two equations leads to
306:
5688:United States Army Research Laboratory
5668:United States Army Research Laboratory
5084:Khazali, Mohammadsadegh (2021-08-05).
4960:Khazali, Mohammadsadegh (2022-03-03).
4700:"Fast Quantum Gates for Neutral Atoms"
3600:Astrophysics and Space Science Library
2782:"Rydberg Atoms and the Quantum Defect"
2309:United States Army Research Laboratory
2168:wavelength. H II regions in our
3589:
3587:
3585:
2710:Metcalf Research Group (2004-11-08).
7:
2664:
2662:
2378:Rydberg atoms can obtain very large
2200:, except for the slightly different
1927:Condensation of Rydberg atoms forms
2812:"Janne Rydberg â his life and work"
2856:University of Tennessee, Knoxville
2810:I. Martinson; et al. (2005).
2374:. In the presence of an external
1440:
1437:
1348:
1345:
431:by collisions or external fields.
139:In spite of its shortcomings, the
25:
5121:10.1103/PhysRevResearch.3.L032033
3258:D.R. Inglis; et al. (1939).
2299:of individual microwave photons.
1865:Investigating diamagnetic effects
1852:Applications and further research
541:The only truly stable state of a
525:in 1926 following development of
124:. The core electrons shield the
5732:10.1103/PhysRevApplied.15.014053
2473:
2458:
2440:
2432:
1700:
1692:
1620:
1593:
1097:
1082:
183:
172:
3034:Journal of Applied Spectroscopy
2295:sensing and imaging, including
1912:Rydberg atoms form commonly in
1661:, known in atomic physics as a
987:, includes a summation of each
565:processes can use the electron
427:electrons, easily perturbed or
5412:10.1103/physrevlett.105.193603
5187:10.1103/physrevlett.108.265301
4588:10.1103/physrevlett.112.040501
4385:10.1103/physrevlett.107.133602
4312:10.1103/PhysRevLett.123.113605
4190:10.1103/PhysRevLett.101.250601
4127:10.1103/PhysRevLett.104.010503
4064:10.1103/PhysRevLett.104.010502
2521:
2478:
2468:
2463:
2453:
2445:
2427:
2419:
2409:
2370:potential results in a closed
2109:
2090:
2054:, so the measured wavelength,
1465:
1445:
1220:
1200:
1108:
1076:
753:
675:
595:
517:of the hydrogen atom in which
506:converging on a finite limit.
187:
120:orbits of electrons about the
1:
4897:"A Rydberg quantum simulator"
4661:10.1103/physrevlett.87.037901
2637:Gallagher, Thomas F. (1994).
1312:with higher energy and lower
800:(equivalent to a large first
2247:Strongly interacting systems
2157:{\displaystyle \lambda _{0}}
991:of highly excited electrons:
5756:American Journal of Physics
4734:10.1103/physrevlett.85.2208
4001:10.1103/PhysRevLett.85.2208
3946:10.1016/j.newar.2009.07.003
3643:Konovalenko, A. A. (1984).
3596:"Radio Recombination Lines"
3189:10.1088/0953-4075/28/24/015
2994:American Journal of Physics
2957:Journal of Chemical Physics
2878:"The Structure of the Atom"
2780:Nolan, James (2005-05-31).
2743:American Journal of Physics
2297:non-demolition measurements
2279:Current research directions
2230:RRLs are spread across the
1963:by one or a few means that
1296:. Semiclassical orbits for
786:, because the ground state
442:and hence falls off like 1/
312:{\displaystyle mvr=n\hbar }
5813:
5055:10.1103/physreva.86.053618
4873:10.1103/physrevx.10.021054
4807:10.1103/revmodphys.82.2313
4523:10.1103/physreva.72.043803
4458:10.1103/physreva.91.030301
3500:10.1088/0022-3700/15/2/004
3333:10.1103/PhysRevA.89.040502
2838:10.1016/j.nimb.2005.03.137
2643:Cambridge University Press
2372:Keplerian elliptical orbit
1285:Quantum-mechanical details
811:
641:Charge exchange excitation
557:Electron impact excitation
89:. The higher the value of
4997:10.22331/q-2022-03-03-664
4777:Reviews of Modern Physics
4247:10.1038/s41567-018-0313-7
3808:The Astrophysical Journal
3612:10.1007/978-0-387-09691-9
2876:Niels Bohr (1922-12-11).
2687:10.1088/978-0-7503-1635-4
1553:potential that causes an
545:is the ground state with
109:, long decay periods and
5300:10.1038/nphoton.2016.214
5090:Physical Review Research
3839:10.3847/1538-4357/ab53d3
3780:10.3847/1538-4365/abef65
3711:10.3847/1538-4365/abf4d4
3427:10.1109/TAP.2020.2987112
3382:10.1103/PhysRevA.30.1142
3237:10.1103/PhysRevA.51.3604
3152:10.1103/PhysRevA.28.3098
3100:10.1103/PhysRevA.51.4272
2067:{\displaystyle \lambda }
1957:electromagnetic spectrum
962:correspondence principle
484:simple empirical formula
464:orbital angular momentum
329:principal quantum number
83:principal quantum number
63:orbital angular momentum
57:Energy levels in atomic
5702:Physical Review Applied
5557:10.1126/science.1258351
5382:Physical Review Letters
5157:Physical Review Letters
4704:Physical Review Letters
4631:Physical Review Letters
4558:Physical Review Letters
4355:Physical Review Letters
4282:Physical Review Letters
4159:Physical Review Letters
4096:Physical Review Letters
4033:Physical Review Letters
3970:Physical Review Letters
3516:Proceedings of the SPIE
2394:as the force is always
2380:electric dipole moments
2350:E = -3 x 10 V/m in the
2287:, quantum computation,
2253:electric dipole moments
1871:magnetic susceptibility
793:For atoms with a large
725:The arrival of tunable
42:of a Rydberg atom with
3564:Soviet Physics Doklady
3523:(5): 618105â618105â9.
2716:Stony Brook University
2539:
2495:
2363:
2328:
2186:
2158:
2131:
2068:
2042:). Carbon has a lower
2025:collisional broadening
1887:
1815:
1711:
1647:electric dipole moment
1494:Electron wavefunctions
1484:
1371:
1301:
1249:
1123:
947:
834:
773:
708:
628:
402:
313:
248:
81:that have a very high
66:
47:
3915:New Astronomy Reviews
3265:Astrophysical Journal
2712:"Rydberg Atom Optics"
2561:, to a straight line
2540:
2496:
2334:
2323:
2307:In October 2018, the
2255:. Calculations using
2187:
2159:
2132:
2069:
1888:
1886:{\displaystyle \chi }
1816:
1712:
1638:of the energy levels.
1485:
1372:
1292:
1250:
1124:
948:
821:
774:
709:
629:
537:Methods of production
403:
314:
249:
53:
35:
3890:10.1093/mnras/stv751
3519:. SPIE Proceedings.
3479:Journal of Physics B
3168:Journal of Physics B
2593:Heavy Rydberg system
2509:
2405:
2338:. Trajectory of the
2316:Classical simulation
2176:
2141:
2078:
2058:
1877:
1740:
1672:
1415:
1323:
1156:
999:
972:models of the atom.
884:
808:Hydrogenic potential
741:
656:
576:
563:Inelastic scattering
342:
288:
271:Orbital momentum is
168:
5769:1992AmJPh..60..324H
5724:2021PhRvP..15a4053M
5627:10.1038/nature18274
5619:2016Natur.534..667L
5549:2015Sci...347.1455S
5533:(6229): 1455â1458.
5478:10.1038/nature12512
5470:2013Natur.502...71F
5404:2010PhRvL.105s3603P
5343:1999Natur.400..239N
5239:2012NatPh...8..819S
5179:2012PhRvL.108z5301H
5112:2021PhRvR...3c2033K
5047:2012PhRvA..86e3618D
4988:2022Quant...6..664K
4923:2010NatPh...6..382W
4864:2020PhRvX..10b1054K
4799:2010RvMP...82.2313S
4726:2000PhRvL..85.2208J
4653:2001PhRvL..87c7901L
4580:2014PhRvL.112d0501P
4515:2005PhRvA..72d3803F
4450:2015PhRvA..91c0301K
4377:2011PhRvL.107m3602G
4304:2019PhRvL.123k3605K
4182:2008PhRvL.101y0601W
4119:2010PhRvL.104a0503I
4056:2010PhRvL.104a0502W
3993:2000PhRvL..85.2208J
3938:2009NewAR..53..259G
3830:2019ApJ...887..114W
3771:2021ApJS..254...28A
3702:2021ApJS..254...36W
3661:1984PAZh...10..846K
3576:1966SPhD...10..588S
3529:2006SPIE.6181E..05M
3492:1982JPhB...15L..49V
3419:2021ITAP...69.2455A
3374:1984PhRvA..30.1142N
3325:2014PhRvA..89d0502G
3278:1939ApJ....90..439I
3229:1995PhRvA..51.3604C
3181:1995JPhB...28.5309H
3144:1983PhRvA..28.3098T
3092:1995PhRvA..51.4272N
3047:1993JApSp..59..466D
3007:1992AmJPh..60..329H
2970:1966JChPh..44..837H
2917:1967RadR...31..191O
2830:2005NIMPB.235...17M
2756:2008AmJPh..76.1007M
2679:2018ryph.book.....S
2257:perturbation theory
2040:Warm Ionised Medium
2020:orders of magnitude
1793:
1731:InglisâTeller limit
1555:angular correlation
515:semiclassical model
159:Newton's second law
147:, about a hydrogen
3055:10.1007/BF00663353
2904:Radiation Research
2722:on August 26, 2005
2673:. IOP Publishing.
2598:Old quantum theory
2535:
2491:
2364:
2329:
2289:quantum simulation
2219:emission from the
2182:
2154:
2127:
2064:
1955:spread across the
1883:
1811:
1806:
1779:
1707:
1585:In external fields
1544:radial correlation
1480:
1367:
1302:
1245:
1119:
1114:
1067:
1050:
943:
938:
835:
769:
721:Optical excitation
704:
624:
543:hydrogen-like atom
398:
309:
244:
130:electric potential
67:
48:
5603:(7609): 667â670.
5337:(6741): 239â242.
5247:10.1038/nphys2423
5025:Physical Review A
4931:10.1038/nphys1614
4842:Physical Review X
4710:(10): 2208â2211.
4493:Physical Review A
4428:Physical Review A
3922:(7â10): 259â265.
3621:978-0-387-09604-9
3537:10.1117/12.675004
3361:Physical Review A
3303:Physical Review A
3216:Physical Review A
3175:(24): 5309â5315.
3131:Physical Review A
3128:Rydberg states".
3079:Physical Review A
2978:10.1063/1.1726773
2764:10.1119/1.2961081
2750:(11): 1007â1011.
2652:978-0-521-02166-1
2213:interstellar dust
2209:external galaxies
2185:{\displaystyle v}
2044:ionization energy
2036:H II regions
1976:radio astronomers
1943:by hot stars and
1805:
1750:
1682:
1636:avoided crossings
1475:
1425:
1362:
1333:
1240:
1195:
1166:
1113:
1052:
1049:
937:
894:
802:ionization energy
531:Werner Heisenberg
527:quantum mechanics
452:ionization energy
393:
242:
217:
77:with one or more
16:(Redirected from
5804:
5781:
5780:
5750:
5744:
5743:
5717:
5697:
5691:
5677:
5671:
5661:
5655:
5654:
5612:
5591:
5585:
5584:
5542:
5522:
5516:
5515:
5489:
5455:
5446:
5440:
5439:
5397:
5377:
5371:
5370:
5326:
5320:
5319:
5293:
5278:Nature Photonics
5273:
5267:
5266:
5221:
5215:
5214:
5172:
5148:
5142:
5141:
5123:
5105:
5081:
5075:
5074:
5040:
5016:
5010:
5009:
4999:
4981:
4957:
4951:
4950:
4916:
4892:
4886:
4885:
4875:
4857:
4833:
4827:
4826:
4792:
4783:(3): 2313â2363.
4768:
4762:
4761:
4719:
4717:quant-ph/0004038
4695:
4689:
4688:
4646:
4644:quant-ph/0011028
4622:
4616:
4615:
4573:
4549:
4543:
4542:
4508:
4506:quant-ph/0503071
4484:
4478:
4477:
4443:
4419:
4413:
4412:
4370:
4346:
4340:
4339:
4297:
4273:
4267:
4266:
4240:
4216:
4210:
4209:
4175:
4153:
4147:
4146:
4112:
4090:
4084:
4083:
4049:
4027:
4021:
4020:
3986:
3984:quant-ph/0004038
3964:
3958:
3957:
3931:
3909:
3903:
3902:
3892:
3882:
3873:(2): 2025â2042.
3858:
3852:
3851:
3841:
3823:
3799:
3793:
3792:
3782:
3764:
3740:
3734:
3733:
3723:
3713:
3695:
3671:
3665:
3664:
3640:
3634:
3633:
3591:
3580:
3579:
3555:
3549:
3548:
3510:
3504:
3503:
3473:
3467:
3466:
3464:
3462:
3445:
3439:
3438:
3412:
3403:(5): 2455â2462.
3392:
3386:
3385:
3368:(2): 1142â1144.
3351:
3345:
3344:
3318:
3298:
3292:
3291:
3289:
3255:
3249:
3248:
3223:(5): 3604â3620.
3210:
3201:
3200:
3162:
3156:
3155:
3138:(5): 3098â3101.
3121:
3112:
3111:
3086:(5): 4272â4275.
3073:
3067:
3066:
3041:(1â2): 466â470.
3028:
3019:
3018:
2988:
2982:
2981:
2951:
2945:
2944:
2898:
2892:
2891:
2889:
2888:
2882:
2873:
2867:
2866:
2864:
2863:
2852:"The Bohr Model"
2848:
2842:
2841:
2807:
2801:
2800:
2798:
2797:
2788:. Archived from
2786:Davidson College
2777:
2768:
2767:
2737:
2731:
2730:
2728:
2727:
2718:. Archived from
2707:
2701:
2700:
2666:
2657:
2656:
2634:
2608:Rydberg molecule
2544:
2542:
2541:
2536:
2528:
2500:
2498:
2497:
2492:
2481:
2476:
2471:
2466:
2461:
2456:
2448:
2443:
2435:
2430:
2422:
2417:
2412:
2273:quantum critical
2262:quantum computer
2191:
2189:
2188:
2183:
2163:
2161:
2160:
2155:
2153:
2152:
2136:
2134:
2133:
2128:
2126:
2125:
2116:
2108:
2107:
2073:
2071:
2070:
2065:
1892:
1890:
1889:
1884:
1820:
1818:
1817:
1812:
1807:
1804:
1803:
1802:
1792:
1787:
1778:
1777:
1758:
1752:
1751:
1748:
1716:
1714:
1713:
1708:
1703:
1695:
1684:
1683:
1680:
1624:
1597:
1489:
1487:
1486:
1481:
1476:
1474:
1473:
1472:
1463:
1462:
1443:
1435:
1427:
1426:
1423:
1386:Rydberg constant
1380:where Ry = 13.6
1376:
1374:
1373:
1368:
1363:
1361:
1360:
1351:
1343:
1335:
1334:
1331:
1310:electron orbital
1254:
1252:
1251:
1246:
1241:
1239:
1238:
1237:
1228:
1227:
1218:
1217:
1198:
1197:
1196:
1193:
1187:
1186:
1176:
1168:
1167:
1164:
1128:
1126:
1125:
1120:
1115:
1112:
1111:
1106:
1105:
1100:
1091:
1090:
1085:
1079:
1070:
1066:
1051:
1048:
1047:
1046:
1030:
1029:
1020:
1014:
1013:
952:
950:
949:
944:
939:
936:
932:
931:
915:
914:
905:
896:
895:
892:
795:valence electron
778:
776:
775:
770:
765:
764:
713:
711:
710:
705:
700:
699:
687:
686:
668:
667:
633:
631:
630:
625:
620:
619:
607:
606:
588:
587:
496:Johannes Rydberg
407:
405:
404:
399:
394:
392:
388:
387:
374:
373:
372:
363:
362:
352:
318:
316:
315:
310:
253:
251:
250:
245:
243:
238:
237:
236:
223:
218:
216:
215:
206:
205:
204:
191:
186:
175:
40:Electron orbital
21:
18:Rydberg blockade
5812:
5811:
5807:
5806:
5805:
5803:
5802:
5801:
5787:
5786:
5785:
5784:
5777:10.1119/1.16875
5752:
5751:
5747:
5699:
5698:
5694:
5678:
5674:
5662:
5658:
5593:
5592:
5588:
5524:
5523:
5519:
5464:(7469): 71â75.
5453:
5448:
5447:
5443:
5379:
5378:
5374:
5328:
5327:
5323:
5275:
5274:
5270:
5233:(11): 819â824.
5223:
5222:
5218:
5150:
5149:
5145:
5083:
5082:
5078:
5018:
5017:
5013:
4959:
4958:
4954:
4894:
4893:
4889:
4835:
4834:
4830:
4770:
4769:
4765:
4697:
4696:
4692:
4624:
4623:
4619:
4551:
4550:
4546:
4486:
4485:
4481:
4421:
4420:
4416:
4348:
4347:
4343:
4275:
4274:
4270:
4218:
4217:
4213:
4155:
4154:
4150:
4092:
4091:
4087:
4029:
4028:
4024:
3977:(10): 2208â11.
3966:
3965:
3961:
3911:
3910:
3906:
3860:
3859:
3855:
3801:
3800:
3796:
3742:
3741:
3737:
3673:
3672:
3668:
3642:
3641:
3637:
3622:
3593:
3592:
3583:
3557:
3556:
3552:
3512:
3511:
3507:
3475:
3474:
3470:
3460:
3458:
3447:
3446:
3442:
3394:
3393:
3389:
3353:
3352:
3348:
3300:
3299:
3295:
3257:
3256:
3252:
3212:
3211:
3204:
3164:
3163:
3159:
3123:
3122:
3115:
3075:
3074:
3070:
3030:
3029:
3022:
3015:10.1119/1.16876
2990:
2989:
2985:
2953:
2952:
2948:
2925:10.2307/3572319
2900:
2899:
2895:
2886:
2884:
2883:. Nobel Lecture
2880:
2875:
2874:
2870:
2861:
2859:
2850:
2849:
2845:
2809:
2808:
2804:
2795:
2793:
2779:
2778:
2771:
2739:
2738:
2734:
2725:
2723:
2709:
2708:
2704:
2697:
2671:Rydberg Physics
2668:
2667:
2660:
2653:
2636:
2635:
2626:
2621:
2613:Rydberg polaron
2589:
2575:
2560:
2507:
2506:
2403:
2402:
2318:
2281:
2249:
2174:
2173:
2144:
2139:
2138:
2117:
2099:
2076:
2075:
2056:
2055:
1994:Weaker lines, H
1941:photoionization
1937:
1910:
1875:
1874:
1867:
1859:
1854:
1794:
1769:
1762:
1743:
1738:
1737:
1675:
1670:
1669:
1643:
1642:
1641:
1640:
1639:
1625:
1617:
1616:
1598:
1587:
1540:
1533:
1526:
1519:
1496:
1464:
1454:
1444:
1418:
1413:
1412:
1407:
1352:
1326:
1321:
1320:
1287:
1265:
1229:
1219:
1209:
1199:
1188:
1178:
1177:
1159:
1154:
1153:
1095:
1080:
1074:
1038:
1031:
1021:
1002:
997:
996:
985:
923:
916:
906:
887:
882:
881:
859:
816:
810:
756:
739:
738:
723:
691:
678:
659:
654:
653:
643:
611:
598:
579:
574:
573:
559:
539:
500:Rydberg formula
476:
379:
375:
364:
354:
353:
340:
339:
286:
285:
266:
228:
224:
207:
196:
192:
166:
165:
107:magnetic fields
28:
23:
22:
15:
12:
11:
5:
5810:
5808:
5800:
5799:
5789:
5788:
5783:
5782:
5763:(4): 324â328.
5745:
5692:
5672:
5656:
5586:
5517:
5441:
5388:(19): 193603.
5372:
5321:
5268:
5227:Nature Physics
5216:
5163:(26): 265301.
5143:
5096:(3): L032033.
5076:
5011:
4952:
4907:(5): 382â388.
4901:Nature Physics
4887:
4828:
4763:
4690:
4617:
4544:
4479:
4414:
4361:(13): 133602.
4341:
4288:(11): 113605.
4268:
4231:(2): 124â126.
4225:Nature Physics
4211:
4166:(25): 250601.
4148:
4085:
4022:
3959:
3904:
3853:
3794:
3735:
3666:
3635:
3620:
3581:
3550:
3505:
3486:(2): L49âL55.
3468:
3440:
3387:
3346:
3293:
3287:10.1086/144118
3250:
3202:
3157:
3113:
3068:
3020:
3001:(4): 329â335.
2983:
2964:(2): 837â839.
2946:
2911:(2): 191â200.
2893:
2868:
2843:
2824:(1â4): 17â22.
2802:
2769:
2732:
2702:
2695:
2658:
2651:
2623:
2622:
2620:
2617:
2616:
2615:
2610:
2605:
2600:
2595:
2588:
2585:
2573:
2558:
2547:
2546:
2534:
2531:
2527:
2523:
2520:
2517:
2514:
2503:
2502:
2490:
2487:
2484:
2480:
2475:
2470:
2465:
2460:
2455:
2451:
2447:
2442:
2438:
2434:
2429:
2425:
2421:
2416:
2411:
2376:electric field
2348:electric field
2317:
2314:
2285:quantum optics
2280:
2277:
2264:. In 2010 two-
2248:
2245:
2232:radio spectrum
2217:bremsstrahlung
2181:
2151:
2147:
2124:
2120:
2115:
2111:
2106:
2102:
2098:
2095:
2092:
2089:
2086:
2083:
2063:
2052:Doppler effect
1953:spectral lines
1936:
1933:
1929:Rydberg matter
1918:kinetic energy
1909:
1906:
1882:
1866:
1863:
1858:
1855:
1853:
1850:
1822:
1821:
1810:
1801:
1797:
1791:
1786:
1782:
1776:
1772:
1768:
1765:
1761:
1755:
1746:
1718:
1717:
1706:
1702:
1698:
1694:
1690:
1687:
1678:
1655:electric field
1626:
1619:
1618:
1599:
1592:
1591:
1590:
1589:
1588:
1586:
1583:
1582:
1581:
1574:semi-classical
1562:
1547:
1538:
1531:
1524:
1517:
1495:
1492:
1491:
1490:
1479:
1471:
1467:
1461:
1457:
1453:
1450:
1447:
1442:
1439:
1433:
1430:
1421:
1403:
1397:quantum defect
1378:
1377:
1366:
1359:
1355:
1350:
1347:
1341:
1338:
1329:
1314:binding energy
1286:
1283:
1282:
1281:
1276:
1275:
1268:polarizability
1266:is the dipole
1263:
1256:
1255:
1244:
1236:
1232:
1226:
1222:
1216:
1212:
1208:
1205:
1202:
1191:
1185:
1181:
1174:
1171:
1162:
1150:
1149:
1130:
1129:
1118:
1110:
1104:
1099:
1094:
1089:
1084:
1078:
1073:
1065:
1062:
1059:
1055:
1045:
1041:
1037:
1034:
1028:
1024:
1017:
1012:
1009:
1005:
993:
992:
983:
958:Rydberg states
954:
953:
942:
935:
930:
926:
922:
919:
913:
909:
902:
899:
890:
857:
812:Main article:
809:
806:
798:binding energy
788:binding energy
780:
779:
768:
763:
759:
755:
752:
749:
746:
722:
719:
715:
714:
703:
698:
694:
690:
685:
681:
677:
674:
671:
666:
662:
642:
639:
635:
634:
623:
618:
614:
610:
605:
601:
597:
594:
591:
586:
582:
567:kinetic energy
558:
555:
538:
535:
523:Wolfgang Pauli
475:
472:
456:Rydberg series
436:binding energy
409:
408:
397:
391:
386:
382:
378:
371:
367:
361:
357:
350:
347:
321:
320:
308:
305:
302:
299:
296:
293:
264:
255:
254:
241:
235:
231:
227:
221:
214:
210:
203:
199:
195:
189:
185:
181:
178:
174:
126:outer electron
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5809:
5798:
5795:
5794:
5792:
5778:
5774:
5770:
5766:
5762:
5758:
5757:
5749:
5746:
5741:
5737:
5733:
5729:
5725:
5721:
5716:
5711:
5708:(1): 014053.
5707:
5703:
5696:
5693:
5689:
5685:
5681:
5676:
5673:
5669:
5665:
5660:
5657:
5652:
5648:
5644:
5640:
5636:
5632:
5628:
5624:
5620:
5616:
5611:
5606:
5602:
5598:
5590:
5587:
5582:
5578:
5574:
5570:
5566:
5562:
5558:
5554:
5550:
5546:
5541:
5536:
5532:
5528:
5521:
5518:
5513:
5509:
5505:
5501:
5497:
5493:
5488:
5483:
5479:
5475:
5471:
5467:
5463:
5459:
5452:
5445:
5442:
5437:
5433:
5429:
5425:
5421:
5417:
5413:
5409:
5405:
5401:
5396:
5391:
5387:
5383:
5376:
5373:
5368:
5364:
5360:
5356:
5352:
5351:10.1038/22275
5348:
5344:
5340:
5336:
5332:
5325:
5322:
5317:
5313:
5309:
5305:
5301:
5297:
5292:
5287:
5283:
5279:
5272:
5269:
5264:
5260:
5256:
5252:
5248:
5244:
5240:
5236:
5232:
5228:
5220:
5217:
5212:
5208:
5204:
5200:
5196:
5192:
5188:
5184:
5180:
5176:
5171:
5166:
5162:
5158:
5154:
5147:
5144:
5139:
5135:
5131:
5127:
5122:
5117:
5113:
5109:
5104:
5099:
5095:
5091:
5087:
5080:
5077:
5072:
5068:
5064:
5060:
5056:
5052:
5048:
5044:
5039:
5034:
5031:(5): 053618.
5030:
5026:
5022:
5015:
5012:
5007:
5003:
4998:
4993:
4989:
4985:
4980:
4975:
4971:
4967:
4963:
4956:
4953:
4948:
4944:
4940:
4936:
4932:
4928:
4924:
4920:
4915:
4910:
4906:
4902:
4898:
4891:
4888:
4883:
4879:
4874:
4869:
4865:
4861:
4856:
4851:
4848:(2): 021054.
4847:
4843:
4839:
4832:
4829:
4824:
4820:
4816:
4812:
4808:
4804:
4800:
4796:
4791:
4786:
4782:
4778:
4774:
4767:
4764:
4759:
4755:
4751:
4747:
4743:
4739:
4735:
4731:
4727:
4723:
4718:
4713:
4709:
4705:
4701:
4694:
4691:
4686:
4682:
4678:
4674:
4670:
4666:
4662:
4658:
4654:
4650:
4645:
4640:
4637:(3): 037901.
4636:
4632:
4628:
4621:
4618:
4613:
4609:
4605:
4601:
4597:
4593:
4589:
4585:
4581:
4577:
4572:
4567:
4564:(4): 040501.
4563:
4559:
4555:
4548:
4545:
4540:
4536:
4532:
4528:
4524:
4520:
4516:
4512:
4507:
4502:
4499:(4): 043803.
4498:
4494:
4490:
4483:
4480:
4475:
4471:
4467:
4463:
4459:
4455:
4451:
4447:
4442:
4437:
4434:(3): 030301.
4433:
4429:
4425:
4418:
4415:
4410:
4406:
4402:
4398:
4394:
4390:
4386:
4382:
4378:
4374:
4369:
4364:
4360:
4356:
4352:
4345:
4342:
4337:
4333:
4329:
4325:
4321:
4317:
4313:
4309:
4305:
4301:
4296:
4291:
4287:
4283:
4279:
4272:
4269:
4264:
4260:
4256:
4252:
4248:
4244:
4239:
4234:
4230:
4226:
4222:
4215:
4212:
4207:
4203:
4199:
4195:
4191:
4187:
4183:
4179:
4174:
4169:
4165:
4161:
4160:
4152:
4149:
4144:
4140:
4136:
4132:
4128:
4124:
4120:
4116:
4111:
4106:
4103:(1): 010503.
4102:
4098:
4097:
4089:
4086:
4081:
4077:
4073:
4069:
4065:
4061:
4057:
4053:
4048:
4043:
4040:(1): 010502.
4039:
4035:
4034:
4026:
4023:
4018:
4014:
4010:
4006:
4002:
3998:
3994:
3990:
3985:
3980:
3976:
3972:
3971:
3963:
3960:
3955:
3951:
3947:
3943:
3939:
3935:
3930:
3925:
3921:
3917:
3916:
3908:
3905:
3900:
3896:
3891:
3886:
3881:
3876:
3872:
3868:
3864:
3857:
3854:
3849:
3845:
3840:
3835:
3831:
3827:
3822:
3817:
3813:
3809:
3805:
3798:
3795:
3790:
3786:
3781:
3776:
3772:
3768:
3763:
3758:
3754:
3750:
3746:
3739:
3736:
3731:
3727:
3722:
3717:
3712:
3707:
3703:
3699:
3694:
3689:
3685:
3681:
3677:
3670:
3667:
3662:
3658:
3654:
3650:
3646:
3639:
3636:
3631:
3627:
3623:
3617:
3613:
3609:
3605:
3601:
3597:
3590:
3588:
3586:
3582:
3577:
3573:
3569:
3565:
3561:
3554:
3551:
3546:
3542:
3538:
3534:
3530:
3526:
3522:
3518:
3517:
3509:
3506:
3501:
3497:
3493:
3489:
3485:
3481:
3480:
3472:
3469:
3457:
3456:
3451:
3444:
3441:
3436:
3432:
3428:
3424:
3420:
3416:
3411:
3406:
3402:
3398:
3391:
3388:
3383:
3379:
3375:
3371:
3367:
3363:
3362:
3357:
3350:
3347:
3342:
3338:
3334:
3330:
3326:
3322:
3317:
3312:
3309:(4): 040502.
3308:
3304:
3297:
3294:
3288:
3283:
3279:
3275:
3271:
3267:
3266:
3261:
3254:
3251:
3246:
3242:
3238:
3234:
3230:
3226:
3222:
3218:
3217:
3209:
3207:
3203:
3198:
3194:
3190:
3186:
3182:
3178:
3174:
3170:
3169:
3161:
3158:
3153:
3149:
3145:
3141:
3137:
3133:
3132:
3127:
3120:
3118:
3114:
3109:
3105:
3101:
3097:
3093:
3089:
3085:
3081:
3080:
3072:
3069:
3064:
3060:
3056:
3052:
3048:
3044:
3040:
3036:
3035:
3027:
3025:
3021:
3016:
3012:
3008:
3004:
3000:
2996:
2995:
2987:
2984:
2979:
2975:
2971:
2967:
2963:
2959:
2958:
2950:
2947:
2942:
2938:
2934:
2930:
2926:
2922:
2918:
2914:
2910:
2906:
2905:
2897:
2894:
2879:
2872:
2869:
2857:
2853:
2847:
2844:
2839:
2835:
2831:
2827:
2823:
2819:
2818:
2813:
2806:
2803:
2792:on 2015-12-06
2791:
2787:
2783:
2776:
2774:
2770:
2765:
2761:
2757:
2753:
2749:
2745:
2744:
2736:
2733:
2721:
2717:
2713:
2706:
2703:
2698:
2696:9780750316354
2692:
2688:
2684:
2680:
2676:
2672:
2665:
2663:
2659:
2654:
2648:
2644:
2640:
2639:Rydberg Atoms
2633:
2631:
2629:
2625:
2618:
2614:
2611:
2609:
2606:
2604:
2603:Quantum chaos
2601:
2599:
2596:
2594:
2591:
2590:
2586:
2584:
2582:
2577:
2572:
2568:
2564:
2557:
2553:
2532:
2529:
2525:
2518:
2515:
2512:
2505:
2504:
2488:
2485:
2482:
2449:
2436:
2423:
2414:
2401:
2400:
2399:
2397:
2393:
2389:
2385:
2381:
2377:
2373:
2369:
2361:
2357:
2353:
2349:
2345:
2344:hydrogen atom
2341:
2337:
2333:
2326:
2322:
2315:
2313:
2310:
2305:
2302:
2298:
2294:
2290:
2286:
2278:
2276:
2274:
2270:
2267:
2263:
2258:
2254:
2246:
2244:
2241:
2238:
2233:
2228:
2226:
2222:
2218:
2214:
2210:
2205:
2203:
2199:
2195:
2179:
2171:
2167:
2149:
2145:
2122:
2118:
2113:
2104:
2100:
2096:
2093:
2087:
2084:
2081:
2061:
2053:
2048:
2045:
2041:
2037:
2032:
2030:
2026:
2021:
2017:
2013:
2009:
2005:
2001:
1997:
1993:
1989:
1985:
1981:
1977:
1974:
1970:
1966:
1962:
1958:
1954:
1950:
1946:
1945:recombination
1942:
1934:
1932:
1930:
1925:
1923:
1919:
1915:
1907:
1905:
1902:
1900:
1896:
1880:
1872:
1864:
1862:
1856:
1851:
1849:
1847:
1843:
1839:
1835:
1831:
1828:, the pure 1/
1827:
1826:hydrogen atom
1808:
1799:
1795:
1789:
1784:
1780:
1774:
1770:
1766:
1763:
1759:
1753:
1744:
1736:
1735:
1734:
1732:
1728:
1724:
1704:
1696:
1688:
1685:
1676:
1668:
1667:
1666:
1664:
1660:
1656:
1652:
1648:
1637:
1633:
1629:
1623:
1614:
1610:
1606:
1602:
1596:
1584:
1579:
1575:
1571:
1567:
1563:
1560:
1559:tidal locking
1556:
1552:
1548:
1545:
1541:
1534:
1527:
1520:
1513:
1512:
1511:
1509:
1503:
1501:
1493:
1477:
1469:
1459:
1455:
1451:
1448:
1431:
1428:
1419:
1411:
1410:
1409:
1406:
1402:
1398:
1393:
1391:
1387:
1383:
1364:
1357:
1353:
1339:
1336:
1327:
1319:
1318:
1317:
1315:
1311:
1307:
1299:
1295:
1291:
1284:
1278:
1277:
1273:
1269:
1262:
1258:
1257:
1242:
1234:
1230:
1224:
1214:
1210:
1206:
1203:
1189:
1183:
1179:
1172:
1169:
1160:
1152:
1151:
1147:
1144:
1140:
1136:
1132:
1131:
1116:
1102:
1092:
1087:
1071:
1063:
1060:
1057:
1053:
1043:
1039:
1035:
1032:
1026:
1022:
1015:
1010:
1007:
1003:
995:
994:
990:
986:
978:
977:
976:
973:
971:
967:
963:
959:
940:
933:
928:
924:
920:
917:
911:
907:
900:
897:
888:
880:
879:
878:
876:
872:
869:
868:
863:
856:
852:
848:
844:
840:
839:Rydberg state
837:An atom in a
832:
828:
824:
820:
815:
814:Hydrogen atom
807:
805:
803:
799:
796:
791:
789:
785:
784:alkali metals
766:
761:
757:
750:
747:
744:
737:
736:
735:
732:
728:
720:
718:
701:
696:
692:
688:
683:
679:
672:
669:
664:
660:
652:
651:
650:
648:
640:
638:
621:
616:
612:
608:
603:
599:
592:
589:
584:
580:
572:
571:
570:
568:
564:
556:
554:
552:
548:
544:
536:
534:
532:
528:
524:
520:
516:
512:
507:
505:
504:energy levels
501:
497:
493:
489:
485:
482:discovered a
481:
480:Johann Balmer
473:
471:
469:
465:
461:
457:
453:
449:
445:
441:
437:
432:
430:
426:
422:
418:
414:
395:
389:
384:
380:
376:
369:
359:
355:
348:
345:
338:
337:
336:
334:
330:
326:
303:
300:
297:
294:
291:
284:
283:
282:
280:
279:
274:
269:
267:
260:
239:
233:
229:
225:
219:
212:
208:
201:
197:
193:
179:
176:
164:
163:
162:
160:
156:
155:
150:
146:
142:
137:
135:
134:hydrogen atom
131:
127:
123:
119:
115:
114:wavefunctions
112:
108:
104:
100:
96:
92:
88:
84:
80:
76:
72:
64:
60:
56:
52:
45:
41:
38:
34:
30:
19:
5760:
5754:
5748:
5705:
5701:
5695:
5690:, 2020-03-19
5675:
5670:, 2018-10-25
5659:
5600:
5596:
5589:
5530:
5526:
5520:
5487:1721.1/91605
5461:
5457:
5444:
5385:
5381:
5375:
5334:
5330:
5324:
5284:(1): 40â43.
5281:
5277:
5271:
5230:
5226:
5219:
5160:
5156:
5146:
5093:
5089:
5079:
5028:
5024:
5014:
4969:
4965:
4955:
4904:
4900:
4890:
4845:
4841:
4831:
4780:
4776:
4766:
4707:
4703:
4693:
4634:
4630:
4620:
4561:
4557:
4547:
4496:
4492:
4482:
4431:
4427:
4417:
4358:
4354:
4344:
4285:
4281:
4271:
4228:
4224:
4214:
4163:
4157:
4151:
4100:
4094:
4088:
4037:
4031:
4025:
3974:
3968:
3962:
3919:
3913:
3907:
3870:
3866:
3856:
3811:
3807:
3797:
3752:
3748:
3738:
3683:
3679:
3669:
3652:
3648:
3638:
3603:
3599:
3567:
3563:
3553:
3520:
3514:
3508:
3483:
3477:
3471:
3461:19 September
3459:. Retrieved
3455:Ars Technica
3453:
3443:
3400:
3396:
3390:
3365:
3359:
3355:
3349:
3306:
3302:
3296:
3269:
3263:
3253:
3220:
3214:
3172:
3166:
3160:
3135:
3129:
3125:
3083:
3077:
3071:
3038:
3032:
2998:
2992:
2986:
2961:
2955:
2949:
2908:
2902:
2896:
2885:. Retrieved
2871:
2860:. Retrieved
2858:. 2000-08-10
2846:
2821:
2815:
2805:
2794:. Retrieved
2790:the original
2747:
2741:
2735:
2724:. Retrieved
2720:the original
2705:
2670:
2638:
2580:
2578:
2570:
2566:
2562:
2555:
2551:
2548:
2396:antiparallel
2383:
2367:
2365:
2355:
2351:
2335:
2324:
2306:
2282:
2250:
2242:
2229:
2206:
2202:reduced mass
2198:same formula
2049:
2033:
2028:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1987:
1983:
1979:
1969:radio waves.
1960:
1948:
1938:
1926:
1922:autoionising
1911:
1903:
1898:
1894:
1868:
1860:
1845:
1837:
1833:
1829:
1823:
1722:
1719:
1658:
1650:
1644:
1631:
1627:
1612:
1608:
1604:
1600:
1577:
1569:
1565:
1554:
1543:
1536:
1529:
1522:
1515:
1504:
1499:
1497:
1404:
1400:
1394:
1389:
1379:
1305:
1303:
1297:
1293:
1271:
1260:
1138:
988:
981:
974:
955:
874:
866:
854:
836:
830:
826:
822:
792:
781:
724:
716:
644:
636:
560:
550:
546:
540:
533:and others.
508:
477:
459:
455:
447:
443:
439:
434:Because the
433:
420:
416:
412:
410:
332:
322:
276:
275:in units of
270:
258:
256:
152:
144:
138:
90:
86:
75:excited atom
71:Rydberg atom
70:
68:
54:
36:
29:
3721:1885/287773
3655:: 353â356.
2366:A simple 1/
2225:metallicity
1920:often form
1663:Stark shift
1551:anisotropic
1535:approaches
1508:Hamiltonian
488:wavelengths
151:of charge +
5715:2009.14383
5610:1509.04543
5291:1603.07107
5103:2007.01039
4979:2101.11412
4855:2006.07035
4295:1903.12442
4238:1807.05795
3821:1910.14605
3814:(2): 114.
3762:2103.10466
3693:2103.12199
3410:1808.08589
2887:2018-11-16
2862:2009-11-25
2796:2008-07-30
2726:2008-07-30
2619:References
2237:21-cm line
2194:hydrogenic
2166:rest-frame
1908:In plasmas
1727:degeneracy
970:Rutherford
847:hydrogenic
727:dye lasers
511:Niels Bohr
141:Bohr model
97:. Rydberg
95:on average
5740:222067191
5635:0028-0836
5565:0036-8075
5540:1404.0980
5496:0028-0836
5420:0031-9007
5395:0911.3523
5359:0028-0836
5316:119212524
5308:1749-4885
5263:121120666
5255:1745-2473
5195:0031-9007
5170:1111.5761
5138:220301701
5130:2643-1564
5063:1050-2947
5038:1207.6373
5006:246635019
4939:1745-2473
4914:0907.1657
4882:2160-3308
4815:0034-6861
4790:0909.4777
4742:0031-9007
4669:0031-9007
4596:0031-9007
4571:1309.7933
4531:1050-2947
4474:118859994
4466:1050-2947
4441:1407.7510
4393:0031-9007
4368:1103.3700
4336:202577976
4320:0031-9007
4255:1745-2473
4173:0806.3754
4110:0907.5552
4047:0908.0454
3954:119276100
3929:1208.2516
3899:1365-2966
3880:1411.4497
3848:1538-4357
3789:0067-0049
3755:(2): 28.
3730:0067-0049
3686:(2): 36.
3630:0067-0057
3435:118828101
3316:1404.6181
3197:250862926
2526:τ
2522:⇒
2519:π
2513:θ
2489:θ
2486:
2437:×
2415:τ
2360:animation
2293:terahertz
2146:λ
2119:λ
2101:λ
2097:−
2094:λ
2085:≈
2062:λ
1881:χ
1771:ε
1767:π
1697:⋅
1689:−
1456:δ
1452:−
1432:−
1340:−
1211:ε
1207:π
1190:α
1173:−
1135:eccentric
1093:−
1054:∑
1040:ε
1036:π
925:ε
921:π
901:−
851:potential
762:∗
754:→
751:γ
684:∗
676:→
617:−
604:∗
596:→
585:−
519:quantized
513:with his
366:ℏ
307:ℏ
273:quantized
188:⇒
118:classical
79:electrons
55:Figure 2:
37:Figure 1:
5791:Category
5684:Phys.org
5643:27281203
5581:28102735
5573:25814579
5504:24067613
5436:12217031
5428:21231168
5203:23004994
5071:55200016
4947:54710282
4823:14285764
4758:16713798
4750:10970499
4685:13452668
4677:11461592
4612:19020862
4604:24580425
4539:30993913
4409:11681713
4401:22026852
4328:31573258
4263:54072181
4206:28636728
4198:19113686
4135:20366355
4080:16384272
4072:20366354
4017:16713798
4009:10970499
3545:96732651
3341:54090132
3063:96628309
2587:See also
2581:figure 8
2384:Figure 7
2356:figure 4
2340:electron
2336:Figure 8
2325:Figure 7
2137:, where
2038:and the
2002:Îł, with
1846:figure 6
1838:figure 5
1628:Figure 6
1601:Figure 5
1572:shows a
1570:Figure 4
1294:Figure 4
1272:Figure 3
849:Coulomb
823:Figure 3
492:hydrogen
486:for the
460:Figure 2
157:, obeys
111:electron
103:electric
5765:Bibcode
5720:Bibcode
5651:4461633
5615:Bibcode
5545:Bibcode
5527:Science
5512:1699899
5466:Bibcode
5400:Bibcode
5367:4367650
5339:Bibcode
5235:Bibcode
5211:1782501
5175:Bibcode
5108:Bibcode
5043:Bibcode
4984:Bibcode
4972:: 664.
4966:Quantum
4919:Bibcode
4860:Bibcode
4795:Bibcode
4722:Bibcode
4649:Bibcode
4576:Bibcode
4511:Bibcode
4446:Bibcode
4373:Bibcode
4300:Bibcode
4178:Bibcode
4143:2091127
4115:Bibcode
4052:Bibcode
3989:Bibcode
3934:Bibcode
3826:Bibcode
3767:Bibcode
3698:Bibcode
3657:Bibcode
3572:Bibcode
3570:: 588.
3525:Bibcode
3488:Bibcode
3415:Bibcode
3370:Bibcode
3321:Bibcode
3274:Bibcode
3272:: 439.
3245:9912027
3225:Bibcode
3177:Bibcode
3140:Bibcode
3108:9912104
3088:Bibcode
3043:Bibcode
3003:Bibcode
2966:Bibcode
2941:6025857
2933:3572319
2913:Bibcode
2826:Bibcode
2752:Bibcode
2675:Bibcode
2164:is the
1965:photons
1914:plasmas
1842:lithium
1824:In the
1384:is the
1143:induced
871:protons
862:nucleus
843:valence
474:History
468:lithium
429:ionized
425:valence
261:= 1/(4Ï
149:nucleus
59:lithium
5738:
5649:
5641:
5633:
5597:Nature
5579:
5571:
5563:
5510:
5502:
5494:
5458:Nature
5434:
5426:
5418:
5365:
5357:
5331:Nature
5314:
5306:
5261:
5253:
5209:
5201:
5193:
5136:
5128:
5069:
5061:
5004:
4945:
4937:
4880:
4821:
4813:
4756:
4748:
4740:
4683:
4675:
4667:
4610:
4602:
4594:
4537:
4529:
4472:
4464:
4407:
4399:
4391:
4334:
4326:
4318:
4261:
4253:
4204:
4196:
4141:
4133:
4078:
4070:
4015:
4007:
3952:
3897:
3846:
3787:
3728:
3628:
3618:
3543:
3433:
3339:
3243:
3195:
3106:
3061:
2939:
2931:
2693:
2649:
2392:torque
2346:in an
2221:plasma
2170:Galaxy
1996:nÎČ and
1990:+1 to
1973:Soviet
1259:where
1146:dipole
841:has a
731:photon
257:where
122:nuclei
73:is an
5797:Atoms
5736:S2CID
5710:arXiv
5647:S2CID
5605:arXiv
5577:S2CID
5535:arXiv
5508:S2CID
5454:(PDF)
5432:S2CID
5390:arXiv
5363:S2CID
5312:S2CID
5286:arXiv
5259:S2CID
5207:S2CID
5165:arXiv
5134:S2CID
5098:arXiv
5067:S2CID
5033:arXiv
5002:S2CID
4974:arXiv
4943:S2CID
4909:arXiv
4850:arXiv
4819:S2CID
4785:arXiv
4754:S2CID
4712:arXiv
4681:S2CID
4639:arXiv
4608:S2CID
4566:arXiv
4535:S2CID
4501:arXiv
4470:S2CID
4436:arXiv
4405:S2CID
4363:arXiv
4332:S2CID
4290:arXiv
4259:S2CID
4233:arXiv
4202:S2CID
4168:arXiv
4139:S2CID
4105:arXiv
4076:S2CID
4042:arXiv
4013:S2CID
3979:arXiv
3950:S2CID
3924:arXiv
3875:arXiv
3816:arXiv
3757:arXiv
3688:arXiv
3541:S2CID
3431:S2CID
3405:arXiv
3337:S2CID
3311:arXiv
3193:S2CID
3059:S2CID
2929:JSTOR
2881:(PDF)
2388:Stark
2342:in a
2269:gates
2266:qubit
2227:).
1280:core.
864:with
415:(the
99:atoms
5639:PMID
5631:ISSN
5569:PMID
5561:ISSN
5500:PMID
5492:ISSN
5424:PMID
5416:ISSN
5355:ISSN
5304:ISSN
5251:ISSN
5199:PMID
5191:ISSN
5126:ISSN
5059:ISSN
4935:ISSN
4878:ISSN
4811:ISSN
4746:PMID
4738:ISSN
4673:PMID
4665:ISSN
4600:PMID
4592:ISSN
4527:ISSN
4462:ISSN
4397:PMID
4389:ISSN
4324:PMID
4316:ISSN
4251:ISSN
4194:PMID
4131:PMID
4068:PMID
4005:PMID
3895:ISSN
3844:ISSN
3785:ISSN
3726:ISSN
3626:ISSN
3616:ISBN
3521:6181
3463:2018
3241:PMID
3104:PMID
2937:PMID
2691:ISBN
2647:ISBN
2010:α, C
1061:<
989:pair
968:and
966:Bohr
647:ions
325:Bohr
105:and
5773:doi
5728:doi
5623:doi
5601:534
5553:doi
5531:347
5482:hdl
5474:doi
5462:502
5408:doi
5386:105
5347:doi
5335:400
5296:doi
5243:doi
5183:doi
5161:108
5116:doi
5051:doi
4992:doi
4927:doi
4868:doi
4803:doi
4730:doi
4657:doi
4584:doi
4562:112
4519:doi
4454:doi
4381:doi
4359:107
4308:doi
4286:123
4243:doi
4186:doi
4164:101
4123:doi
4101:104
4060:doi
4038:104
3997:doi
3942:doi
3885:doi
3871:450
3834:doi
3812:887
3775:doi
3753:254
3716:hdl
3706:doi
3684:254
3608:doi
3604:282
3533:doi
3496:doi
3423:doi
3378:doi
3329:doi
3282:doi
3233:doi
3185:doi
3148:doi
3096:doi
3051:doi
3011:doi
2974:doi
2921:doi
2834:doi
2822:235
2760:doi
2683:doi
2574:MAX
2569:= â
2559:MAX
2483:sin
1844:in
1270:.
1165:pol
529:by
466:in
458:.
268:).
5793::
5771:.
5761:60
5759:.
5734:.
5726:.
5718:.
5706:15
5704:.
5682:,
5666:,
5645:.
5637:.
5629:.
5621:.
5613:.
5599:.
5575:.
5567:.
5559:.
5551:.
5543:.
5529:.
5506:.
5498:.
5490:.
5480:.
5472:.
5460:.
5456:.
5430:.
5422:.
5414:.
5406:.
5398:.
5384:.
5361:.
5353:.
5345:.
5333:.
5310:.
5302:.
5294:.
5282:11
5280:.
5257:.
5249:.
5241:.
5229:.
5205:.
5197:.
5189:.
5181:.
5173:.
5159:.
5155:.
5132:.
5124:.
5114:.
5106:.
5092:.
5088:.
5065:.
5057:.
5049:.
5041:.
5029:86
5027:.
5023:.
5000:.
4990:.
4982:.
4968:.
4964:.
4941:.
4933:.
4925:.
4917:.
4903:.
4899:.
4876:.
4866:.
4858:.
4846:10
4844:.
4840:.
4817:.
4809:.
4801:.
4793:.
4781:82
4779:.
4775:.
4752:.
4744:.
4736:.
4728:.
4720:.
4708:85
4706:.
4702:.
4679:.
4671:.
4663:.
4655:.
4647:.
4635:87
4633:.
4629:.
4606:.
4598:.
4590:.
4582:.
4574:.
4560:.
4556:.
4533:.
4525:.
4517:.
4509:.
4497:72
4495:.
4491:.
4468:.
4460:.
4452:.
4444:.
4432:91
4430:.
4426:.
4403:.
4395:.
4387:.
4379:.
4371:.
4357:.
4353:.
4330:.
4322:.
4314:.
4306:.
4298:.
4284:.
4280:.
4257:.
4249:.
4241:.
4229:15
4227:.
4223:.
4200:.
4192:.
4184:.
4176:.
4162:.
4137:.
4129:.
4121:.
4113:.
4099:.
4074:.
4066:.
4058:.
4050:.
4036:.
4011:.
4003:.
3995:.
3987:.
3975:85
3973:.
3948:.
3940:.
3932:.
3920:53
3918:.
3893:.
3883:.
3869:.
3865:.
3842:.
3832:.
3824:.
3810:.
3806:.
3783:.
3773:.
3765:.
3751:.
3747:.
3724:.
3714:.
3704:.
3696:.
3682:.
3678:.
3653:10
3651:.
3647:.
3624:.
3614:.
3606:.
3602:.
3598:.
3584:^
3568:10
3566:.
3562:.
3539:.
3531:.
3494:.
3484:15
3482:.
3452:.
3429:.
3421:.
3413:.
3401:69
3399:.
3376:.
3366:30
3364:.
3335:.
3327:.
3319:.
3307:89
3305:.
3280:.
3270:90
3268:.
3262:.
3239:.
3231:.
3221:51
3219:.
3205:^
3191:.
3183:.
3173:28
3171:.
3146:.
3136:28
3134:.
3116:^
3102:.
3094:.
3084:51
3082:.
3057:.
3049:.
3039:59
3037:.
3023:^
3009:.
2999:60
2997:.
2972:.
2962:44
2960:.
2935:.
2927:.
2919:.
2909:31
2907:.
2854:.
2832:.
2820:.
2814:.
2784:.
2772:^
2758:.
2748:76
2746:.
2714:.
2689:.
2681:.
2661:^
2645:.
2641:.
2627:^
2576:.
2554:=
2004:În
1992:n.
1897:â
1873:,
1848:.
1764:12
1749:IT
1733:,
1665:,
1657:,
1649:,
1510::
1399:,
1382:eV
984:ee
853:,
553:.
470:.
335::
331:,
281::
161::
136:.
85:,
69:A
5779:.
5775::
5767::
5742:.
5730::
5722::
5712::
5686:/
5653:.
5625::
5617::
5607::
5583:.
5555::
5547::
5537::
5514:.
5484::
5476::
5468::
5438:.
5410::
5402::
5392::
5369:.
5349::
5341::
5318:.
5298::
5288::
5265:.
5245::
5237::
5231:8
5213:.
5185::
5177::
5167::
5140:.
5118::
5110::
5100::
5094:3
5073:.
5053::
5045::
5035::
5008:.
4994::
4986::
4976::
4970:6
4949:.
4929::
4921::
4911::
4905:6
4884:.
4870::
4862::
4852::
4825:.
4805::
4797::
4787::
4760:.
4732::
4724::
4714::
4687:.
4659::
4651::
4641::
4614:.
4586::
4578::
4568::
4541:.
4521::
4513::
4503::
4476:.
4456::
4448::
4438::
4411:.
4383::
4375::
4365::
4338:.
4310::
4302::
4292::
4265:.
4245::
4235::
4208:.
4188::
4180::
4170::
4145:.
4125::
4117::
4107::
4082:.
4062::
4054::
4044::
4019:.
3999::
3991::
3981::
3956:.
3944::
3936::
3926::
3901:.
3887::
3877::
3850:.
3836::
3828::
3818::
3791:.
3777::
3769::
3759::
3732:.
3718::
3708::
3700::
3690::
3663:.
3659::
3632:.
3610::
3578:.
3574::
3547:.
3535::
3527::
3502:.
3498::
3490::
3465:.
3437:.
3425::
3417::
3407::
3384:.
3380::
3372::
3356:n
3343:.
3331::
3323::
3313::
3290:.
3284::
3276::
3247:.
3235::
3227::
3199:.
3187::
3179::
3154:.
3150::
3142::
3126:â
3110:.
3098::
3090::
3065:.
3053::
3045::
3017:.
3013::
3005::
2980:.
2976::
2968::
2943:.
2923::
2915::
2890:.
2865:.
2840:.
2836::
2828::
2799:.
2766:.
2762::
2754::
2729:.
2699:.
2685::
2677::
2655:.
2571:L
2567:L
2563:L
2556:L
2552:L
2545:.
2533:0
2530:=
2516:=
2501:,
2479:|
2474:F
2469:|
2464:|
2459:r
2454:|
2450:=
2446:|
2441:F
2433:r
2428:|
2424:=
2420:|
2410:|
2368:r
2362:.
2352:x
2180:v
2150:0
2123:0
2114:/
2110:)
2105:0
2091:(
2088:c
2082:v
2029:n
2016:n
2012:n
2008:n
2000:n
1998:H
1988:n
1984:n
1980:n
1961:n
1949:n
1899:n
1895:A
1834:n
1830:r
1809:.
1800:5
1796:n
1790:2
1785:0
1781:a
1775:0
1760:e
1754:=
1745:F
1723:n
1705:.
1701:F
1693:d
1686:=
1681:S
1677:E
1659:F
1651:d
1632:n
1613:n
1609:r
1605:n
1578:â
1566:â
1539:o
1537:n
1532:i
1530:n
1525:o
1523:n
1518:i
1516:n
1500:â
1478:.
1470:2
1466:)
1460:l
1449:n
1446:(
1441:y
1438:R
1429:=
1424:B
1420:E
1405:â
1401:ÎŽ
1390:n
1365:,
1358:2
1354:n
1349:y
1346:R
1337:=
1332:B
1328:E
1306:n
1298:n
1264:d
1261:α
1243:,
1235:4
1231:r
1225:2
1221:)
1215:0
1204:4
1201:(
1194:d
1184:2
1180:e
1170:=
1161:U
1139:r
1117:.
1109:|
1103:j
1098:r
1088:i
1083:r
1077:|
1072:1
1064:j
1058:i
1044:0
1033:4
1027:2
1023:e
1016:=
1011:e
1008:e
1004:U
982:U
941:.
934:r
929:0
918:4
912:2
908:e
898:=
893:C
889:U
875:Z
867:Z
858:C
855:U
831:r
827:r
767:.
758:A
748:+
745:A
702:.
697:+
693:B
689:+
680:A
673:B
670:+
665:+
661:A
622:.
613:e
609:+
600:A
593:A
590:+
581:e
551:n
547:n
448:n
444:n
440:r
421:n
417:n
413:n
396:.
390:m
385:2
381:e
377:k
370:2
360:2
356:n
349:=
346:r
333:n
319:.
304:n
301:=
298:r
295:v
292:m
278:ħ
265:0
263:Δ
259:k
240:r
234:2
230:v
226:m
220:=
213:2
209:r
202:2
198:e
194:k
184:a
180:m
177:=
173:F
154:e
145:r
91:n
87:n
44:n
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
