THE 1989 Ion Traps, an Isolated Electron and Atomic Clocks W. Schleich and H. Walther Max-Planck-Institut für Quantenoptik, Garching, FRG

It has traditionally been the main The importance of these discoveries of the electron from the value 2. The endeavour of atomic spectroscopists to has been acknowledged by the decision first quantum electrodynamical cor­ develop measurement techniques yield­ of the Royal Swedish Academy of rection was calculated by Julian ing ever higher resolutions, and to fi­ Sciences to award one half of the 1989 Schwinger in 1949. Today, higher order nally achieve the ultimate limit — the Nobel Prize in to Professor corrections have been included giving natural linewidth set by the sponta­ Norman F. Ramsey, Harvard University, g/2 = 1.001 159 652 133 (29). This neous decay of energy levels. When Cambridge, USA, for the invention of deviation from Dirac's original theory long lifetimes are involved, as e.g. for the separated oscillatory fields method triggered in the 1950's much work to hyperfine splittings of atomic ground and its use in the hydrogen maser and test the QED prediction. A group at the states or of forbidden transitions, it is other atomic clocks; and one half jointly University of Michigan led by H.C. Crane mostly the finite interaction time of the to Professor Hans G. Dehmelt, Univer­ and A. Rich stored a beam of electrons atom with the probing field which deter­ sity of Washington, Seattle, USA, and in a magnetic bottle. An applied magne­ mines the linewidth. An extension of Professor Wolfgang Paul, University of tic field causes the electron's spin axis the interaction region is sometimes not , FRG, for the development of the to precess, forcing the electrons them­ a way out since additional problems technique. selves to describe circular orbits. If g may arise owing to field imperfections The present article illustrates the dis­ were exactly 2, the frequency of the which usually become more significant coveries of the Nobel laureates by con­ spin precession and the orbit frequency as the interaction zone becomes larger. centrating on a few highlights, but reco­ would be the same. The experiment [1] There have been two developments gnizing that they have contributed ex­ therefore detects the difference bet­ which overcame this problem and ex­ tensively to various branches of physics ween the two frequencies, i.e., g-2. Un­ tended resolution limits. The first is the in ways that will not be discussed. fortunately, the accuracy of this method invention of traps for charged particles is limited by the presence of many inter­ together with new cooling techniques. The g-factor of the Electron acting, high speed electrons. These allow one to store a single char­ In the late 1920's P.A.M. Dirac disco­ To isolate an electron from all extra­ ged particle for days and even months, vered a matter wave equation which, in neous influences and hold it still for exa­ and to cool it to temperatures in the contrast to the Schrödinger equation, mination — that is the ultimate goal. milli-Kelvin regime. Together they elimi­ satisfies the laws of special relativity. Hans Dehmelt once said that he reco­ nate transit time broadening as well as The equation predicts a g-factor for the gnized this experimentalist's dream the quadratic Doppler effect which be­ electron of value 2. recogni­ “the day I saw my teacher, Richard comes important at resolutions in the zed in the 1940's that the vacuum of Becker, in his electricity and magnetism range of 1012. The other approach uses the microscopic world is by no means lecture draw a dot on the blackboard two separated, phase coupled, measu­ empty: the creation and annihilation of saying, "Here is an electron..."". It was ring fields leading to an effective inter­ electron and positron pairs and fluctua­ trap technology developed by groups action time determined by the atom's tions of electric and magnetic fields led by Wolfgang Paul and Hans Dehmelt time of flight between the two regions. cause a slight departure of the g-factor which made this dream come true.

Professor Herbert Walther has been with the University of München since 1975. He is also the Director of the Max-Planck-Institut für Quantenoptik (MPQ), Postfach 1513, D-8046 Garching, FRG and a scientific member of the Max-Planck-Gesellschaft. A graduate of the Universities of Heidelberg and Hannover, his main interests lie in quantum electronics. He has received several important awards, the latest being the American Optical Society's Charles Hard Townes Award for 1990. Dr. Wolfgang Schleich is a graduate of the Ludwig Maximilians University, München where he received his final degree in 1989. A theoretician with MPQ, Garching since 1986, his interests include general relatively and quantum phenomena. He has worked at the Centre for Theoretical Physics, Texas, and at the Centre for Advanced Studies, New Mexico. Fig. 1 — Electrode arrangements of the Paul (left) and Penning (right) traps. Europhys. News 21 (1990) 31 Trapping Ions and Electrons quency of the electron depends on its In contrast to neutral atoms, ions can spin orientation. The spin-flip that takes easily be influenced by electromagnetic place when the transition with ωa is fields because of their charge. In a first induced causes a detectable change of attempt towards trapping one can apply the axial oscillation frequency. The im­ a constant voltage between a ring elec­ pressive result of these experiments trode and two end caps as shown in and their successors [1] is a value of Fig. 1. This arrangement, however, does g/2 = 1.001 159 652 188 (4), equiva­ not achieve three-dimensional confine­ lent to 4 parts in 1012. When we com­ ment. The potential that governs the pare it to the quantum electrodynamical ion's trajectory in the trap causes stable result we find agreement to one part in motion in the radial direction and unsta­ 1010. ble motion in the orthogonal direction, If space permitted it would be tempt­ creating a saddle point at the trap cen­ Fig. 2 — Energy levels of a trapped elec­ ing to stroll from the possibilities of per­ tre. It is tempting to think that another, tron. forming spectroscopy on an isolated ion more sophisticated arrangement of first demonstrated by Hans Dehmelt electrodes would achieve three-dimen­ and P. Toschek to the precision experi­ sional confinement but the laws of elec­ loops (the cyclotron motion); the centre ments with mHz resolution, or the ob­ trostatics, and more precisely Poisson's of these loops progresses slowly servation of quantum jumps [3] and equation, prevent this. around a larger circle (the magnetron phase transitions of a few ions caught Fortunately there are at least two motion). in a trap [4]. However, in the next sec­ techniques that offer a way out of the Hans Dehmelt and his group were tion we focus on two clocks of unprece­ problem. The first is based solely on the able to confine a single electron for dented level of precision, the hydrogen use of (time varying) electric fields. It is months in such a trap. The set up in fact maser and the cesium clock developed easily understood if we consider the represented an artificial atom of macro­ by N. Ramsey and collaborators [5]. saddle potential. As the particle starts scopic dimensions, namely an electron to roll down the unstable hillside the tied to an extraordinarily massive nu­ The Hydrogen Maser sign of the voltage at the electrodes cleus — the earth — which has led to One of the essential ingredients of must be reversed so that the particle it being called a geonium. the hydrogen maser constructed for the suddenly sees a rising rather than a first time by Norman Ramsey and D. decreasing potential, thus achieving dy­ The Geonium Experiment Kleppner is a magnetic hexapole lens namic binding. The motion of an ion in Quantum mechanics restricts the invented in 1951 by Wolfgang Paul and such a situation is described by the energy of an electron circulating in a H. Friedburg. Hydrogen atoms passing Mathieu differential equation, well- magnetic field to discrete, equally the hexapole field are selected accord­ known in classical mechanics, which, spaced levels as shown on the left-hand ing to their ground state hyperfine depending on the voltages applied to side of Fig. 2. The frequency difference states: the F = 1 atoms are focussed the trap, allows stable and unstable ωc between consecutive energy levels and the F = 0 defocussed resulting in solutions. Under appropriate conditions of the electron's cyclotron motion, that the population inversion of the two one is able to obtain dynamic, three- is, between two adjacent cyclotron hyperfine states required for maser ope­ dimensional confinement in the trap. orbits is ωc = 2µBB/ where B denotes ration. This type of "lonenkäfig" (ion cage) the magnetic field and µB is the Bohr The hydrogen maser gives remarka­ was conceived by the Nobel laureate magneton. The two possible spin orien­ bly precise values of the hyperfine split­ Wolfgang Paul in 1955 and realized ex­ tations, spin parallel and antiparallel to ting of the hydrogen ground state (in Hz perimentally by his group [2]. The so- the magnetic field, split each energy for 1H: 1 420 405 751.768 ± 0.002; called Paul trap was based on Paul's level into two energies with a frequency for 2H: 327 384 352.5222 ± 0.0024. earlier work with H. Steinwedel and separation ωs = gµBB/h. It possesses a considerably higher fre­ M. Raether demonstrating the use of a The energy difference hωa (Fig. 2) is quency stability than the cesium clock four-pole, time dependent electric field proportional to (g-2) in that hωa = for short and intermediate times (hours as a mass filter, a technique that is now h(ωs-ωc) = (g-2)µBB. The transition - days) but its absolute accuracy is in­ the standard method for mass analysis with frequency ωa is a forbidden transi­ ferior so it has been mainly employed as and is also used extensively for trace tion for the "geonium" but nevertheless a secondary standard. For example, it analysis. it can be measured. When we divide ωa has been used to measure the continen­ A different approach for obtaining by the cyclotron frequency, i.e., ωa/ωc tal drift between Europe and the USA as three-dimensional confinement con­ = (g-2)/2, the dependence on the ma­ being 17 ± 3 mm/year. This value was sists in superimposing on the electric gnetic field B and the Bohr magneton obtained by receiving signals from an field a constant, homogeneous, magne­ can be eliminated. Hence, by measuring astronomical pulsar by means of radio tic field aligned along the symmetry the frequencies ωa and ωc one can de­ telescopes placed at various locations axis (Fig. 1, right-hand side). In the termine the quantity [g-2)/2, giving the on the two continents; the relative Penning trap the vertical magnetic field quantum electrodynamical correction timing of the signals was determined forces the charged particle to perform a to the g-factor directly. The transition is using hydrogen masers [6]. circular motion in the plane orthogonal measured by observing the axial oscilla­ Another application is the verification to the magnetic field, overruling the tion frequency of the electron. Owing to of the gravitational red shift. By com­ radial instability caused by the elec­ a small inhomogeneity of the magnetic paring the frequencies of rocket-borne trostatic field. While the ion oscillates field (produced by a nickel wire in the and earth-bound hydrogen masers, the back and forth along the symmetry axis ring electrode, Fig. 1) and the continu­ prediction of general relativity has been of the trap it gyrates rapidly in small ous Stern-Gerlach effect, the axial fre­ verified to seven parts in 105. 32 Europhys. News 21 (1990) experiment at the present time gives an upper limit of 5 x 10-25 e.cm for the electric dipole moment. The Nobel laureates of 1989 have clearly set the stage for a series of preci­ sion experiments in atomic spectrosco­ py. The field is still undergoing rapid development so further interesting re­ sults and applications relating to preci­ sion measurements must be expected in the near future. FURTHER READING [1] For a review of the history of the g-2 Fig. 3 — The Ramsey technique for two probing fields (right) as compared with the experiments, see: Dehmelt H.G. in: Ad­ conventional one-field method (left). The left-hand hatched area symbolizes an atom-field vances in Laser Spectroscopy, Eds. F.T. interaction region with an interaction time At while T is the time-of-flight between two Arecchi, F. Strumia and H. Walther (Plenum regions for the two-field arrangement. The two-field frequency spectrum is analogous Press, New York) 1983; Ekstrom P. and to a two-slit interference pattern. Its envelope (dashed line) is equivalent to the one-field Wineland D., Scientific American 243 spectrum. (1980) 104. [2] For the original description of the Paul In Ramsey's two-field method, the the hydrogen maser). Transitions bet­ trap: Paul W., Osberghaus O. and Fischer atoms under investigation interact with ween the hyperfine levels are induced in E., Ein lonenkäfig (Forschungsberichte des two fields which are phase coupled (see the two-field interaction region and de­ Wirtschafts- und Verkehrsministeriums, Fig. 3). Owing to the coherent action of tected by means of a second hexapole Nordrhein-Westfalen) 1958. the two fields, the resonance curve is magnet and a detector. According to [3] On ion traps, laser cooling, quantum changed and shows an additional "in­ the adopted definition of the time stan­ jumps, etc. : Itano W.M., Bergquist J.C. and terference" structure. The width of the dard, the peak of the resonance curve Wineland D.J., Science 237 (1987) 612. central narrow peak is determined by (i.e. the hyperfine splitting), corresponds [4] On phase transitions and chaos: Quint the atom's time of flight between the to exactly 9 192 631 770 Hz. W., Schleich W. and Walther H., Physics The two-field method is the basis of World 2 (1989) 30 and La Recherche 20 two interaction regions. (1989) 1194. The cesium clock, which has been experiments aiming to determine the [5] On Ramsey's method: Ramsey N.F., used as a time standard since 1967, electric dipole moment of the neutron Physics Today (July 1980) 25. is based on this principle. Cesium-133 that are currently being undertaken by [6] On atomic clocks: Hellwig H., Evenson atoms in a beam are state selected Norman Ramsey and collaborators at K.M. and Wineland D.J., Physics Today (De­ according to their hyperfine states (as in the ILL, Grenoble. The accuracy of the cember 1978) 23.

The 1989 Nobel Laureates

The group of electronic ceramics at the Swiss Federal Institute of Technology in Lausanne has the following openings: Research associates (post-doc­ toral fellows): 1. Electrical properties of ferro- electrics and high-K dielectrics 2. Processing of ferroelectric ce­ ramics 3. Crystallographic study of elec­ tronic materials Norman Ramsey was appointed to the faculty of Harvard University in 1947 and Doctorate students: retired recently as the Higgins Professor of Physics. He remains very active in lectu­ 1. Ferroelectric materials ring and research, commuting regularly to 2. Microwave ceramics the ILL, Grenoble where he continues his collaboration using the Institute's cold Submit applications to: neutron facility. A graduate of Columbia Prof. N. Setter University, he received his Ph.D. in 1940. Département des matériaux After working at the MIT Radiation Labo­ EPFL ratory and on the Manhattan Project, he 34, chemin de Bellerive The 1989 Nobel laureates :Norman Ramsey returned to Columbia as an associate pro­ CH - 1007 Lausanne (top), Hans Dehmelt (bottom) and Wolfgang fessor. He helped found Associate Univer­ Switzerland Paul (top right). sities Inc., the group that created the Europhys. News 21 (19901 33