In a series of experiments using atoms and molecules, upper limits have been set on the electric dipole moments of the electron and proton, as well as on possible time-reversal-violating interactions between the electron and nucleus.
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The ongoing search for electric dipole moments in neutrons, atoms, and molecules provides one of the few possibilities in high- or low-energy physics for solving the CP riddle. Neutral-Current Parity Violations in Atomic Physics A key element of the theory that has now unified the electromagnetic with the weak interaction is the prediction that the weak neutral current interactions between electrons and nucleons should produce a parity violation in atoms. The result is that the photons emitted by atoms should "prefer" one circular polarization over the other by a small amount.
In one class of experiments the parity-violating effect causes the polarization of light to rotate; the required experimental sensitivity is radian. Observation of these effects is a triumph of experimental ingenuity. Successful experiments have now been carried out with four atomic species: These experiments demonstrate neutral-current interactions by low-energy elastic interactions, an arena far distant from high-energy physics where such effects were first observed.
The atomic and high-energy experiments are complementary, and at pre- sent they are approximately equal in accuracy. Furthermore, the atomic results can be used to put constraints on alternatives to the standard electroweak model, and they provide the opportunities to. The atomic experiments appear to provide the most sensitive test yet proposed for such a particle. A molecular-beam magnetic resonance technique, similar to the one used to search for the neutron electric dipole moment, has recently been used to study parity-violating interactions between the neutron and various nuclei.
As the neutrons passed through a metal sample a large rotation of the neutron spin due to the weak interaction was observed. The results, which disagreed with the theoretical predic- tions, have led to a better understanding of nuclear structure. The experimental neutron rotation method constitutes a new tool for examining nuclear structure. Although the principal tools for studying the electroweak and the strong interaction are those of particle physics, when one contrasts the "table-top" scale of atomic experiments with the scale of high-energy research, it is evident that atomic research is extremely cost effective.
Foundations of Quantum Theory: Is Quantum Mechanics Complete? Although quantum mechanics is widely recognized as a triumph of twentieth-century thought, persistent questions remain about the valid- ity of the underlying assumptions and the completeness of the theory. The famous debate between Bohr and Einstein attests to the depth of the problem. The fact that Bohr's interpretation is now accepted as the standard model for quantum mechanics does not, of course, preclude the possibility that quantum mechanics may not be able to tell us all that there is to know.
Quantum mechanics could be incomplete. In the mids, the debate on quantum mechanics was dramati- cally altered. Bell discovered that if the quantum-mechanical description of phenomena could be supplemented by any further information- including hidden variables that would allow a determin- istic interpretation of quantum phenomena the information could lead to observably different results. Bell showed that correlations in mea- surements on particles whose initial state was highly correlated would have to lie below a given limit if quantum mechanics were incomplete but that the limit would be somewhat larger if the description by quantum mechanics were complete.
The distinction between the two alternatives was presented as an inequality between observables: The experiments are difficult, and the results were at first ambiguous. Recently, however, Bell's inequalities have been studied in an experiment whose results are clear and decisive. By combining laser-induced fluorescence with modern optical detection methods, the two alternatives could be distinguished with an uncer- tainty that is about one tenth of the difference.
Bell's inequalities were decisively confirmed. The results offer little hope that quantum me- chanics can be supplemented by a further description: The limitations of quantum mechanics remain a serious question at the foundations of physics, for the laws of physics grow out of human observations, and there is no reason to believe that they should remain valid in realms where they have never been applied.
Nevertheless, Bell's work and the ensuing experiments show that the most obvious possible defect in quantum mechanics is not, in fact, a weakness. The debate will have to turn elsewhere. Studies of Time and Space Among the most dramatic research in the general area of high- precision measurement are the studies on phenomena underlying our assumptions about the nature of time and space. Of particular interest are recent experiments on the gravitational red shift and the isotropy of space. The gravitational red shift refers to the change in the rate of time, or of the frequencies of atomic transitions, due to a gravitational field.
The shift has been measured accurately by comparing the rate of a rocketborne hydrogen maser atomic clock with one on the Earth's surface. The red shift was measured with an accuracy of about 2 parts in In addition to confirming the predictions of general relativity, the experiment provided a signif- icant advance in the practical development of atomic clocks and in the art of comparing clocks at large distances.
Fundamental to the theory of special relativity is the assumption that the speed of light in space is a universal constant. In particular, the speed is assumed to be the same in all directions. This has been studied by laser interferometry, and the isotropy of space with respect to the speed of light has been confirmed to within 1 part in In addition, experimental methods developed in AMO physics are being applied in astrophysics and cosmology. For example, hydro- gen maser clocks play vital roles in very-long-baseline radio interferometry, while laser interferometry is at the heart of an impor- tant class of gravity-wave detectors.
Future Directions Measurements of the electron-magnetic-moment anomaly using sin- gle trapped electrons are not yet at the fundamental limit. A new version of the experiment has been proposed that may lead to a hundredfold improvement. Trapped-ion methods are steadily advancing and may lead to a large increase in precision of atomic clocks. Such clocks could provide new tests of general and special relativity. The new trap technology is also expected to provide improved values for the ratio of the electron mass to the proton mass and to provide techniques for comparing the masses of nuclei to unprecedented precision.
Precision spectroscopy of positronium is coming of age. During the next decade physicists can look forward to detailed measurements of the Lamb shift and relativistic effects in positronium. These advances will put increasing pressure on QED theory. The Lamb shift of high-, hydrogenlike ions has been observed with tunable lasers, and first results have been obtained from potentially more-accurate measure- ments on this shift in the innermost level.
These techniques can be expected to advance to the point where they provide definitive tests of the Z dependence of the Lamb shift, testing essentially different QED contributions. Muonium has recently been obtained in vacuum, and the Lamb shift has been observed. Intense sources of muons and pions are now available, opening the possibility of developing intense pulsed sources of muonium and pionium that are matched to the duty factor of pulsed lasers. A large and important new field is thus developing laser spectroscopy of exotic atoms.
The enterprise has been so successful, however, that atomic structure is sometimes regarded essentially as a closed book. This is hardly the case. Trouble with Hydrogen The nonrelativistic Schrodinger equa- tion for hydrogen is solved in just about every elementary text on quantum mechanics; it seems unlikely that a serious challenge could remain.
Nevertheless, the problem of hydrogen in an applied magnetic field of arbitrary strength is unsolved. Not only are general solutions lacking, for all but the lowest states there are not even any useful approximate solutions. At present, we cannot predict qualitatively how energy levels evolve in regions where the electric and magnetic forces are comparable. The Missing Hamiltonian One view of physics is that once the Hamiltonian is known the problem is essentially solved all that remains is to work out details.
Without arguing the pros or cons of this view, we simply mention that the many-body relativistic Hamiltonian is not known. The problem of treating many-body systems within the framework of QED poses an important challenge to atomic physics.
Even for H- and He, the simplest two-electron systems, there are no systematic ways to identify the relevant Feynman diagrams. Retarda- tion effects between three or more particles lie at the heart of the difficulty. The problem is more than academic it is of increasing urgency to astrophysical and plasma problems. These instances suggest that problems of atomic structure continue to lie in the mainstream of physics. The field is moving forward vigorously, propelled by new spectroscopic techniques and other experimental innovations, and by new theoretical approaches re- flecting fresh points of view and increasing computational skill and power.
Loosely Bound Atomic States The advent of the laser and the development of better sources of negative ions have made it practical to study systems in which one electron is bound loosely. These systems are interesting because it is only near the atomic core that the motion is complex. Over the rest of space the motion of the loosely bound electron is understood precisely. The binding energy can be vanishingly small, and the atoms can be huge.
Rydberg atoms with dimensions in the micrometer range have been produced. Energies of Rydberg states can be measured to an accuracy of 1 part in In many cases the energy of the states is given by a simple quantum defect formula. The quantum defect is essentially the phase shift in the atomic wave functions due to scattering of the Rydberg electron off the atomic core.
The phase shift, which is commonly used in scattering theory, can be measured with spectro- scopic precision. This high precision permits the accurate study of spin-orbit, correlation, and relativistic terms that would be far too small to see in conventional scattering experiments. Negative ions represent a second type of loosely bound system. Because the electron moves in an essentially force-free region, most of the properties of these atomic species were presumed known.
When the electrons that are ejected from H- in stripping reactions were observed, however, there were surprises. If the intensity of ejected electrons is plotted versus energy and angle, forming a two- dimensional surface, only one prominent feature is expected theoreti- cally, a ridge corresponding to a two-body encounter between the loosely bound electron and the target atom or molecule.
The experi- ment revealed a valley that cut across the expected ridge, producing a much more complex electron spectrum. Indeed, observations showed two peaks where only one was expected. It is now known that the double-peaked structure is sensitive to correlations in the ground state of negative ions. This sensitivity to correlation is a new and unexpected feature of the structure of negative-ion continuum states.
Negative molecular ions have also been exploited to investigate rotational and vibrational structure by photodetachment of the loosely bound electron. This structure is rich near the energy thresholds for processes for which the residual molecule is left in an excited state. Recently, systems with two loosely bound electrons have been ob- served.
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The motion in such systems is highly correlated and is not amenable to exact treatment. Some features suggest the existence of molecule-like modes in which the two electrons vibrate and rotate about equilibrium positions. This represents a complete breakdown of the conventional independent particle model and signals the onset of collective electron motion. Lasers have dramatically broadened the scope of atomic physics by allowing the creation and study of new classes of atomic states. This apparatus is used to create highly excited or Rydberg atoms. A beam of alkali metal atoms absorbs light from two or three pulsed dye lasers; the atoms are detected by applying a strong electric field that ionizes them.
The data show the spectra of Rydberg states of lithium in a series of increasing electric fields. As the energy of the lasers is scanned, the ionization signals are recorded. They appear as horizontal peaks. Many different atomic and molecular species have been produced and studied in Rydberg states, as well as species such as planetary atoms in which two electrons are excited. The experiments have stimulated interest in the structure of atoms in strong electric and magnetic fields, a subject that bears on problems in astrophysics, in general dynamics, and in the transition from ordered to chaotic motion.
The techniques have also been applied to study collisions, photoionization, superradiance, and electrodynamics. Cour- tesy of Massachusetts Institute of Technology. Exhibiting exotic behavior and gov- erned by bizarre scaling laws, these new species are providing unex- pected insights into problems such as the nature of the continuum, the effect of symmetry on the structure and dynamics of two- and three-body systems, and the relation between regular and chaotic motion.
The experiment that launched the subfield was a study of the optical absorption spectrum of high-lying levels of barium in a strong magnetic field. It came as a surprise to discover that the energy levels display periodic structure near the ionization limit and that this structure actually extends into the positive energy region where the electron is free to escape from the nucleus. The levels display the familiar simple structure of a free electron in a magnetic field, except that the level spacing is anomalous. The significance of the anomaly is now appre- ciated; it is the signal of a new mode of electronic motion, a mode that is characteristic neither of the nuclear electric field nor of the magnetic field alone, but of the joint action of both fields.
In contrast to magnetic fields, which tend to compress electrons close to the nuclei, electric fields tend to tear the electrons out of atoms. One expects that a strong electric field will ionize an atom, but not that it will produce any sort of periodic structure. The discovery of positive-energy periodic structure in an electric field thus came as an additional surprise. In principle, hydrogen has no bound states in an electric field.
In practice this difficulty is often overlooked, and the states are treated as if they were stationary. For high-lying states this point of view breaks down, signifying the onset of ionization by tunneling of the electron through the barrier between the potentials of the nucleus and the applied field. The problem has led to new insights into the general relation between discrete states and continuum states.
Most experimental studies with strong electric fields have actually employed alkali metal atoms rather than atomic hydrogen. It seemed reasonable to expect that such an atom will behave like hydrogen if its single valence electron is promoted to a high-lying level, but once again the observations were unexpected. In many cases the energy-level structure is fundamentally different from hydrogen; the field ionization rates may not even remotely resemble the rates calculated by the hydrogenic theory.
What was not recognized is the critical role of a special symmetry of hydrogen, a dynamical symmetry, which is. The situation has an analog in planetary motion: Our understanding of the role of the dynamical symmetry is now much deeper, including an apprecia- tion of the dramatic consequences of its breakdown.
Double-Well Atomic Potentials Inner-shell electrons in most atoms are localized radially, confined by an effective potential that has a minimum at each shell's radius. The inner-shell potential is relatively insensitive to the state of the outer electrons, particularly the valence electrons. Consequently, the spec- trum for absorption by inner-shell electrons does not vary significantly if one or two of the outer electrons are missing.
For some atoms, however, the potential for inner-shell electrons can have two radial minima separated by a potential barrier. Usually the electrons are confined in one of the minima, but in some cases they can suddenly switch to the other when the system is perturbed. One way to perturb the environment of inner electrons is to remove the outer electrons by progressively ionizing the system.
Recent measurements of the inner-shell absorption of barium provide a good example of the switching effect. Two recent technical advances were crucial to seeing the effect. The second was a continuously tunable source of ultraviolet light. This was provided by a synchrotron light source. Because an electron in a double-well potential is delicately balanced in one of the two competing states, effects of perturbations are strongly enhanced.
Thus, double-well potentials can serve as a "magnifying glass" for studying effects of angular momentum coupling, electron correlations, and relaxation effects. Collective Atomic States Our understanding of atomic structure has been dominated by single-particle pictures in which each electron moves independently in an effective potential that is due to the rest of the system. Departures from this idealization are described in terms of correlations, that is,.
This picture continues to serve well for those aspects of atomic structure and dynamics that deal with single-particle excitations. The opening of new spectral ranges by synchrotron light sources and multiphoton absorption of laser light, however, has revealed excited states in which two or more electrons share the excitation energy.
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These states display a surprisingly wide variation of spectral properties such as decay widths, absorption coefficients, and quantum defects. Attempts to systematize these data have led to the introduction of collective coordinates to describe the highly correlated electron wave functions. It is now realized that for these highly correlated states the independent particle model is not even an adequate zeroth approximation: Among the insights derived from the framework of correlated motion, perhaps the most significant is the prediction of new atomic states, which are entirely collective in nature but which involve only two electrons.
Such a state was predicted to occur in the negative hydrogen ion. The ion has only one true bound state but is now known to have infinitely many resonant states that live for 0. One of these resonances occurs in a region where conventional independent particle approximations predict no structure. This state was observed spectroscopically in an ingenious and ambitious experi- ment. The light was shifted from the visible to the ultraviolet by the Doppler effect. Doppler tuning made it possible to probe the absorption of H- with great precision.
The experiment constituted a major advance in our understanding of highly correlated systems. A great deal of progress has been made in extending the collective mode description to other systems with two electrons outside of an atomic core. Efforts to describe collective states with three excited electrons are under way. One implication of the collective motion of electrons is that narrow, long-lived states can appear even when the atom has absorbed enough energy to eject two, or even three, electrons. Such states present a new challenge for theory and have prompted searches for new models of atomic structure unrelated to the independent particle picture.
Relativistic and Quantum Electrodynamic Effects in Atoms In heavy atoms, relativistic effects and effects produced by the interaction between electrons are strongly intertwined. Nevertheless, ap- proximate Hamiltonians based on a many-body Dirac equation, with suitably modified instantaneous Coulomb interactions, have been extremely useful in elucidating the interplay of relativity and electron correlation.
The most successful approach to these problems has been the Dirac-Hartree-Fock self-consistent scheme. This treats relativity and electron correlation on an equal footing: Such an even-handed approach is imperative because of the interplay of the effects. For example, relativistic contraction of energetic inner-shell orbitals changes the potential in which less-energetic, outer-shell electrons move.
As a consequence, even though outer-shell electrons are generally nonrelativistic, their energies are greatly affected by relativistic effects. Experimental searches for certain specific features of atomic pro- cesses can aid in understanding the interplay of relativistic and correlation effects. The angular distribution of atomic photoelectrons is one such probe.
Without relativistic corrections, the ratios of intensi- ties at different angles is predicted to have a simple form: The relativistic random-phase approximation was created to study simultaneously relativistic and correlation effects in problems such as this. This method has been used quite successfully for studies of photoionization in xenon and barium. A serious challenge for atomic theorists lies in the calculation of QED effects in many-electron atoms. Experimentalists will soon be able to measure inner-shell energies of atoms and energies of highly stripped ions with such precision that quantities such as Lamb shifts in many-electron systems can be systematically determined.
At present, calculation of these QED effects presents immense difficulties and can only be carried out for simple systems. In addition, even in one- electron systems, calculation of the Lamb shift for very-high-, ele- ments presents a major challenge. Work is under way, mainly in Europe, to extend the Dirac-Hartree- Fock theory to molecules.
This is needed if one is to treat molecules in which one of the constituent atoms belongs to the sixth or seventh row of the periodic table. Here relativistic effects cannot be ignored, particularly if quantities such as bond lengths are desired that are sensitive to orbital size. The experiments are an essential complement to spectroscopy, for spec- troscopy generally explores only bound states of systems.
Collisions govern the transport of energy in gases and plasmas in environments ranging from high-current switching devices to the magnetically con- trolled plasma in a tokamak and the atmospheres of hot stars. The applications of atomic collisions research are numerous. The variety of collision processes is enormous. Fortunately, a number of elementary concepts help to unify atomic-collision phenom- ena. The long-range nature of the Coulomb field results in a rich and orderly structure of the continuum, manifesting itself as resonances in scattering cross sections. The mechanisms for energy transfer and other state changes during a collision can often be deciphered by comparing the time for the collision the resonance lifetime with the characteristic response times of the internal modes: The origin of the large spin-polarization and spin-exchange effects in electronic and atomic collisions can be traced to elementary consider- ations of the Pauli exclusion principle.
Unifying themes such as this provide intellectual coherence to a field that might otherwise seem bewildering. In this section, we select a few examples to illustrate advances in the field, and we discuss some of the remaining mysteries and new opportunities. Structure of the Electron Continuum For electronic energies above the threshold for ionization, or for electron detachment in the case of a negative ion, a continuum of states exists.
A continuum state is the quantum state that describes a free particle. Unlike a bound state, the energy of a continuum state can vary arbitrarily it is continuous. The intensity of the continuum states usually varies smoothly with energy, but for these systems the continuum is punctuated by a variety of resonance states in which the electron escapes slowly, as if it were reluctant to depart. These delicate resonant complexes are among the simplest atomic systems involving several simultaneous interactions. Understanding them is a fundamental problem for many-body theory. During the last decade there have been major advances in experimental techniques.
Photoionization the process by which an atom or molecule absorbs a photon and ejects an electron is important whenever a plasma interacts with radiation, as in the interior of stars or in the interstellar medium. The process is important to atmospheric physics, for the Earth's ionosphere is created by Photoionization that is due to sunlight. Photoionization is of considerable theoretical interest in atomic and molecular physics because the calculations provide sensitive tests of our understanding of atomic and molecular structure.
The upper drawing shows the Photoionization cross section of xenon as a function of wavelength. Comparison of the experimental results upper curve and theoretical calculations lower curve illustrates the excellent agreement between experiment and theory for rare-gas systems. The overall decrease in the height of the data at short wavelength is due to limited instrumental resolution and is not important. The lower drawing shows the pattern of photoelectrons that is, the number of electrons emitted in each direction from the Photoionization of atoms highly excited by laser light.
The different shapes of the patterns give precise information about the structure of these atoms. Our understanding of resonance structures and of the role they play in collision processes has advanced enormously. Until recently, resonance states were classified using a description implicitly based on the independent particle model: The simplest of these, the "potential" resonance, is due to the temporary trapping of the scattered electron in a barrier in the potential.
A second type, the "core-excited" resonance, occurs when an electron virtually excites a target atom and becomes temporarily attached. Shortcomings of these traditional classifications have become appar- ent, and the classifications have now been overturned. For example, the concept of core-excited resonances completely fails to account for structures that were recently observed near the excited states of helium and the alkali metals. The measurements were achieved with new high-resolution electron scattering and negative-ion photodetachment techniques that have revolutionized our ability to study narrow reso- nance structures.
These results have forced us to think in terms of a whole new class of electron-atom resonance states. The resonances correspond to unstable multiply excited states of an atomic negative ion. They can occur even if a bound state of the ion is nonexistent, as in the case of He-. The discovery of these resonances has prompted new approaches to the mathematical physics of excited complexes, for instance the use of hyperspherical coordinates in which two-electron correlations are explicitly built into the representation of the system. The independent particle model also breaks down under the domi- nance of correlation effects in the recently discovered Wannier-ridge resonances in He-.
These states were discovered in high-resolution electron scattering. The measured energies suggest two electrons moving in opposition, equidistant from the ion core. The failure of these resonances to fit within the framework of a single-electron Rydberg series clearly indicates an essential three-body structure: Understand- ing the dynamics of this primary three-body system is an urgent goal for atomic theory: To an ion moving at relativistic speeds, the light from a near-ultraviolet laser can look like it is in the far ultraviolet.
This makes it possible to carry out laser spectroscopy in a spectral region where laser light is not available. This principle has been applied to study the H- ion a proton surrounded by two electrons with much higher resolution than previously possible. The method combines techniques of particle physics and atomic physics. An MeV H- beam, moving at 85 percent of the speed of light, crosses a beam of laser light. Because of the Doppler effect, the apparent wavelength of the laser light is shortened. As the turntable is rotated, the wavelength "seen" by the H- changes, allowing the ultraviolet spectrum of H- to be scanned.
Although H- possesses no excited electronic states, it has many quasi-bound states in which one of the electrons is temporarily trapped by the remaining hydrogen atom. These quasi-bound states, or resonances, are detected by measuring the intensity of emitted electrons. H- is interesting theoretically because it is one of the simplest systems in which the electrons are always highly correlated. Dielectronic Recombination Electron-ion systems display large resonances that are distinctively core excited. These resonances result in a process known as dielectronic recombination.
Dielectronic recombination can occur when an electron hits an ion with slightly less energy than needed to excite the ion. The electron is attracted to the ion until it gets enough kinetic energy to excite one of the valence electrons; at this point the electron becomes trapped in a large highly excited state a Rydberg level of the doubly excited neutral atom. If the two excited electrons collide the Rydberg electron can be ejected while the valence electron returns to the ground state of the ion, but if the valence electron radiates its excess energy be- fore such a collision occurs the capture is stabilized and dielectronic.
The process occurs much more readily than originally expected. It is so rapid that often it is the leading recombination process in a plasma, governing the equilibrium charge density and dominating the plasma's operating conditions. Conse- quently, the process is of fundamental interest to the understanding of laboratory, astrophysical, and fusion plasmas. Until recently dielectronic recombination rates had to be determined indirectly from studying plasma behavior. The situation was unsatis- factory, for the process is so important that precise measurements were essential for verifying the theoretical values.
Recently the situa- tion changed dramatically, for within a short period of time three separate groups observed dielectronic recombination using different techniques. Direct measurements have now been made for five ion species by using colliding beams of electrons and ions.
For four of the five, the experimental cross sections are substantially larger than predicted by theory. Because of the many systems that are affected by dielectronic recombination, including plasma fusion, there is high interest in understanding the source of the discrepancy. Ultraslow Collisions When the relative speed of colliding species is small compared with the characteristic speeds of internal motions, the energy levels are slowly perturbed, but the system does not jump discontinuously between states: In such a situation the motions of the particles are usually strongly correlated.
Adiabatic motion is not normally observed. For instance, when an electron is knocked out of an atom by electron impact, the process is generally nonadiabatic. At an energy just above threshold, however, the two electrons escaping from the ion share a small amount of energy and their motion is essentially adiabatic. This process, near-threshold ionization, provides an ideal system for studying strongly correlated motions.
An early theoretical study of near-threshold ionization of atoms by electrons, using a classical approach, predicted that the cross section would be proportional to the electron energy measured from the ionization threshold raised to a rather unlikely power, 1. The problem has so far eluded a rigorous quantum solution though an approximate theory predicts that the variation with energy should be close to linear. Results of a careful experiment with ionization in helium agreed with the classical theory. A highly accelerated beam of H- ions.
The results can be fit by both the classical and the approximate quantum threshold laws. The adiabatic motion of two electrons near an ion remains an enigma. Adiabatic motion can also be observed in photodetachment, the process in which a negative ion absorbs a photon and ejects a single electron, leaving a neutral atom. By employing intense high-resolution tunable lasers, threshold phenomena can be studied with a resolution that exceeds that of conventional electron-scattering studies by a factor of The number of applications of the technique is large.
Photodetachment studies of OH- at threshold have already opened the way to observing the adiabatic response of a molecule to an electron. Experiments on two-electron photoejection should soon be feasible, providing an important experimental advance on the elusive three- body Coulomb problem. Collisions with Rydberg Atoms The experimental art of creating and detecting highly excited atoms Rydberg atoms has rapidly developed to the point where a wide range of precisely controlled conditions are realizable, including orbital shapes and matches between energy levels and level spacings.
The techniques have opened the way to the study of large classes of collision phenomena and have led to a number of dramatic discoveries. For example, the cross sections for resonant transfer of rotational and vibrational energy of a polar molecule to the electronic excitation of Rydberg atoms has been found to be enormous, up to a thousand times larger than typical molecular collision cross sections. Another discov- ery occurred in the study of collisions between Rydberg atoms. The energy levels can be shifted or tuned by applying an electric field. When the excited Rydberg level is tuned to be exactly midway between two adjacent levels, an enormous enhancement in the cross section for energy-level-changing collision was found close to one million times the area of a typical ground-state atom.
This enhancement provides another example of the unusual properties of adiabatic motion. If the principal quantum number n of a Rydberg atom is large enough, the electron's orbit can be so big that the electron and the ion core essentially interact independently with a neutral target particle. This vastly simplifies the problem. Because the kinetic energy of the Rydberg electron is only a few millielectron volts, Rydberg atoms provide a way to study low-energy electron scattering in a regime virtually inaccessible by conventional scattering techniques.
Even the largest computer cannot accurately model a simple helium-helium collision. Broad organizing principles are essential in order to understand such collisions. One of the most fruitful principles to emerge in the past decade is the electron promo- tion model. Here is one example of this point of view. The surprising feature is that such quantum numbers can be approximately conserved in energetic collisions of many-electron atoms and ions. The conservation rules are central to our understanding of ion-atom collisions. As ionic projectiles approach atomic targets, the electrons of the system move into superpositions of states of the diatomic molecule.
This results in a nonstationary state in which the electron distribution oscillates with frequencies characteris- tic of the transient diatomic molecule. By measuring the angle- and velocity-dependent electron-capture probabilities, the oscillation fre- quency can be determined. It is unexpectedly high. This high fre- quency has been shown to imply a new conservation rule based on the symmetry of the simplest molecular ion.
In essence, only states allowed by these new rules can be populated. In many-electron systems these correspond to states with many electrons excited. At a large detuning from the first dressing field, , we find that the resonance points are approximately given by. In this limit, the first coupling given in equation 20 above is the expected Rabi frequency seen with the solid coloured arrows in figures 10 a and b being either red, or blue, depending on whether , or , respectively.
However, for the second coupling in equation 20 we see that, because we are in the limit , this second coupling is much reduced. This agrees with the picture given in figure 10 a , where the second resonance is not visible. In fact, though, as approaches , the two couplings become less unequal and also approach each other, in agreement with figure 10 b [ 9 ]. The last condition for resonance in equation 19 is suggestive of the multiphoton interpretation of resonances, illustrated in figure 10 c. Looking first at the right-hand side of figure 10 c , there is a set of three resonances indicated in the bare basis i.
Left of the main resonance is a process involving the absorption of two RF 'dressing photons' and the emission of an photon. This higher order process seen in figure 10 c corresponds to the location of the blue dashed line in figure 10 b and is, of course, in addition to the first order processes seen in figure 10 a. A similar argument applies to the red-dashed resonance which can be decomposed as the third order process, involving the emission of two RF 'photons' and the absorption of an photon for the case , seen at the far right of figure 10 c.
Finally, we draw the reader's attention to the short black arrows indicated on the left side of figures 10 b and c. These arrows indicate the locations of a low frequency resonance at where transitions are directly stimulated between adiabatic states in the same manifold figure 10 b.
The low frequency resonance can also be viewed in the bare basis as occurring via multiphoton processes figure 10 c i. The low frequency resonance has been experimentally observed with dressed atoms [ 8 , 10 ]; see the next section. In practice, the 3D situation makes the simple picture given above incomplete. We will explore this with figure 11 for the case of a dressed quadrupole trap shown in 2D cross-section. In figure 11 a we see two resonant surfaces either side of the main trapping surface marked with a dashed line.
Only very energetic atoms will reach these two surfaces because of the tight trapping transverse to the trapping surface. For , the dominant surface with stronger coupling is the outer inner surface. In off-resonant spectroscopic probing we start to pick up a tail of the distribution of the atoms, see figure 11 e.
We could also perform evaporative cooling in this regime. As the frequency approaches , the surfaces eventually meet at the bottom of the dressed trap in figure 11 b. This is because the Rabi frequency is stronger at the bottom of the trap in a quadrupole trap with linear and horizontal RF polarisation in the y -direction.
For figure 11 b the condition is met at the trap bottom. At this point, in a spectroscopy measurement, the trap will be quickly emptied, indicating that the bottom of the trap has been located. This method can be used to determine accurately the local Rabi frequency in the trap. The Rabi frequency is slightly reduced as one climbs the sides of the atom trap and, for this reason, the surfaces meet on the sides of the trap, figure 11 c , only when the RF frequency is closer to than the value of at the trap bottom, to match the Rabi frequency at those locations.
In a spectroscopic measurement there is still some atom loss i. However, this is typically a narrow regime in , as seen in figure 11 e. Figure showing resonances, or evaporation surfaces for a dressed quadrupole atom trap, with a linear RF polarisation along the y -axis. In a — c the dashed line indicates the location of the first dressing field resonance in this 2D section through the magnetic trap. The solid lines indicate the location of the second RF resonance in three situations: In all cases a — c , both surfaces contribute to the spectroscopy signal.
The two peaks appear around. The minima occur at resonance at the trap bottom. The low high frequency wing of the lowest highest frequency spectrum correspond to the case a , the central wing corresponds to the case c. For evaporative cooling it is generally desirable to start with a RF frequency resulting in resonances away from the location of the atoms, as in figure 11 a or c , and then adjust the frequency so that the evaporation resonance surface approaches the atoms. The second RF can then remove the most energetic atoms and cool the gas to very low temperatures: One can also directly address the gap between the dressed states with a low frequency field.
At the minimum point, this means applying a second RF field with a frequency equal to the Rabi frequency of the first RF field. In this situation, the minimum point of the trap is addressed and the atoms will empty out. However, if the low RF frequency is somewhat above the Rabi frequency, evaporative cooling can be performed, as demonstrated in [ 10 ] and reported in [ 8 , 74 ]. Evaporation can be maintained by reducing the RF frequency to approach the Rabi frequency.
The low frequency resonance can be used for spectroscopy, as outlined in section 3. However, for evaporative cooling, rather than spectroscopy, it can be desirable to use a fairly strong second field to ensure the hot atoms are out-coupled adiabatically. Non-adiabatic transitions lead to the population of different states which either are not trapped or lead to collisional losses [ 36 , 43 ]. For the direct transition, where , the Rabi frequency is modified by an approximate factor [ 10 ]: Finally, we note that it is possible to perform evaporative cooling without a second RF field [ 75 ].
In this case we can use the fact that for a quadrupole field, and for RF linearly polarised in a horizontal direction, the Rabi frequency varies hugely around the resonant ellipsoid: These locations are places where the dressed trap 'leaks', i. But since these 'holes' are located high up on the sides of the ellipsoid, at the equator for a horizontal linear polarisation, only the most excited atoms can reach the hole and escape. Thus, we can implement evaporative cooling using this feature, as was reported in [ 75 ], although this evaporation through two holes is expected to be less efficient than an evaporation through a whole resonant surface [ 76 ].
To adjust the cooling and reduce temperature the holes can be lowered by controlling the RF polarisation using elliptically polarised RF. We note briefly that the holes could also be closed by using a rotating circular polarisation [ 77 ] which is a variant of a TAAP, a time-averaged adiabatic potential, see section 4. This same kind of evaporation was used in a double well TAAP in [ 78 ]. Ring traps for atoms have considerable interest, for example, as a geometry for excitations and solitons in quantum gases [ 79 ], as a way of pinning a vortex [ 80 ], and as an instrument for Sagnac interferometry [ 81 ].
In this context atom chips are of interest because they may lead to the creation of compact devices. However, a conventional atom chip approach would be to create a circular waveguide based on steady currents and magnetic fields such as in [ 82 ]. This is based on the idea that with current flowing down several long parallel wires on a chip surface, a magnetic 2D quadrupole field can be created away from the chip surface [ 83 ]. To trap atoms in a circular waveguide, one simply bends the parallel current carrying wires into concentric loops.
However, a weakness of the single circular magnetic waveguide is the end effects associated with how the currents are brought into and out of the waveguide loop [ 84 ]. The potential issues, where currents enter and exit a waveguide ring, include distortion of the circular symmetry and the introduction of local bumps or dips in the waveguide potential. In this section, and in section 6 , we will see a number of techniques using dressed atom traps that avoid this problem and create smooth and symmetric ring traps for ultra-cold atoms.
In Morizot et al [ 11 ] published a proposal for a ring trap for atoms based on the intersection of two types of potential for ultra-cold atoms. First, an 'egg-shell' potential from a 3D quadrupole magnetic field dressed to resonance is used. Since 3D quadrupole fields have an axis with higher gradient because of Maxwell's equations 3 , this steeper gradient is arranged to be vertical, so that in the x —y plane a circular cross-section is obtained.
Then the egg-shell system is overlaid with a blue-detuned optical potential formed from vertical standing waves of light a 1D optical lattice. The intersection of these two potentials forms a set of ring potentials, stacked above each other, with different radii, see figure 12 a. Blue-detuned light was proposed to exclude atoms from regions of light and reduce photon scattering in the trap. For practical values of parameters [ 11 ], the trapping frequency in the vertical direction optical confinement is higher than in the horizontal direction RF confinement.
Indeed, the frequencies can be sufficiently high to reach a low-dimensional regime for a 1D, or 2D, quantum gas. A simple loading scheme was proposed which involved starting with the dressed RF atoms in the egg-shell trap, applying the blue-detuned standing wave of light to trap the atoms in a plane at the bottom of the egg-shell, and then shifting the RF trap downwards in position to open out the ring [ 11 ].
This latter step can be accomplished by applying a bias field to shift the quadrupole field downwards. The scheme was realised in [ 12 ], but with the standing wave of light replaced by two sheets of light. Reference [ 12 ] also demonstrated a novel variation of the loading scheme in which a blue detuned sheet is applied first before the RF radiation. This is used to push the atoms away from the zero region of the quadrupole trap as the RF is turned on. The ring trapping scheme of [ 11 ] has also been realised with light sheets in [ 85 ]. A ring of atoms is confined by the RF egg-shell potential radially with minimum marked in green , and vertically by a blue-detuned optical standing wave shown in blue.
Figure adapted from [ 11 ]. The different cases show different vertical bias fields which have the effect of moving the eggshell potential vertically, thus changing the ring diameter. Figure 12 b reproduced from [ 12 ] under a CC-BY 3. At the start of section 4 , we mentioned that conventional atom-chip ring traps, based on purely magnetic waveguides without dressing , can have issues with their circular symmetry and local bumps or dips in the waveguide potential where currents enter and exit the waveguide structure.
One approach to resolve this is to use induction methods see section 6. Another approach uses two-phase RF currents [ 15 , 69 ] to make 2D rings or tubes in 3D. Figure 13 a shows the chip with two RF wires on the underside. By adjusting the phase difference between the currents of the wires, the character of the proposed dressed trap can be changed significantly. The underlying magnetic trap is formed from DC currents in all three wires shown in figure 13 a with appropriate bias fields in the z and vertical directions.
The bias field in the z -direction ensures a functional magnetic trap in all three directions. The bias field in the vertical direction shifts the magnetic trap to the correct vertical position. When the currents are out of phase, there is either a trap not unlike the original magnetic trap, or a ring-trap in the 2D plane shown.
In this latter case, the conventional orientation of atom chips horizontally, with the atoms underneath means that the 'ring' belongs to a vertical plane, a bit like a car tyre, i. So, for the ring to be fully populated with atoms, it should either be very small, or there should be compensation of gravity from a Rabi coupling gradient [ 16 ], or an additional potential, such as an optical gradient or a tilt of the chip. The depth of the ring in the horizontal z -direction in figure 13 a is determined by the length of the current carrying wires on the chip and the method used to confine the atoms in the z -direction.
In [ 15 ] the confinement was proposed to be formed by shaping the RF wires and the width was just a micrometre or so. In general, there are limitations to this approach because large rings will require large currents to place the magnetic linear quadrupole away from the chip surface; the part of the ring near the chip surface may be influenced by significant deviations from quadrupolar due to the proximity of the three wires and the finite width of the nearest current carrying wire, changing the local magnetic field direction.
An approximate linear quadrupole field is formed from DC currents in all three chip wires. In the case , a ring trap is produced. The cases produce double-well potentials in the x — y plane and the case produces a single potential well in the x —y plane. This scheme was realised in [ 16 ].
A 'ring' quadrupole is formed from ring-shaped permanent magnets b , left. It is not necessary to plug the centre of the quadrupole field because, under the right conditions, the dressing forms a trapping region away from the circular path of the quadrupole centre. The RF is applied from two circular coils panel b right which can have RF currents with amplitude and phase differences. Double ring traps and toroidal traps can be formed from this set-up. Figure 13 a reprinted with permission from [ 15 ], Copyright by the American Physical Society.
Figure 13 b reprinted with permission from [ 27 ], Copyright by the American Physical Society. Figure 13 b shows a different approach taken from [ 27 ]. In this case the ring potential will lie in a horizontal plane and the underlying magnetic trap is formed from two ring-shaped and concentric permanent magnets that provide a 'linear'-type quadrupole field with a zero that runs around the path of the ring trap. As a magnetic waveguide this trap would leak atoms from the centre but, by turning on the dressing field, the degeneracy at the bottom of the trap is lifted.
In the simplest case, the RF field is generated by a pair of external Helmholtz coils which are operated out of phase to generate, in general, an elliptically polarised RF field. In the plane of the trap, the field can be arranged to be circularly polarised with respect to a quantisation axis which varies around the circle at the centre of the quadrupole field so that it is tangent to the ring see figure 13 b right panel. This creates a uniform coupling around the ring. Then a dressed-RF trap minimum occurs when magnetic resonance takes place away from the centre of the ring quadrupole and around a surface following the zero field centre: By deliberately creating an imbalance in the currents in the external coils, an elliptical polarisation can be generated which results in a double-well potential around the ring: A Sagnac interferometer is proposed using this scheme in [ 86 ].
The technique of obtaining new potentials by means of fast oscillations of other potentials is well established. The Paul trap for ions [ 87 ] works by periodically inverting an unstable saddle-point potential to obtain a stable trapping potential for certain trajectories.
The TOP trap [ 88 ] time-orbiting potential is a magnetic trap for neutral atoms where a lossy field-zero point which is vulnerable to spin-flips is time-averaged away to make a well-behaved atom trap. The general principle is that the time-dependent motion, or oscillation, should be much faster than the mechanical motion of the atom or particle in the time-averaged potential.
The same approach can be used with adiabatic potentials to create an even greater variety of trapping geometries [ 13 ]. The proposal to make a ring trap this way involved the time-dependent motion of an ellipsoidal surface trap or more specifically, a dressed 3D quadrupole field with the strongest field gradient to the vertical.
If a uniform vertical bias field is applied, the centre of the quadrupole field is simply shifted and, as a result, the surface potential is also shifted vertically. By applying an oscillating bias field, i. Two extrema of the motion, labelled t 1 and t 2 are depicted in figure 14 a with dashed lines indicating the ellipsoidal surface trap location.
The time-averaged potential minimum is dominated by the time spent in these extremal locations, and especially at their intersection. Thus, the time-averaged potential minimum is close to the intersection, and the full calculations show that a ring trap is formed with an isopotential surface shown in figure 14 b.
The trap is formed by time-averaging a vertically oscillating RF shell trap which is seen in a in a section across a diameter of the ring with contours showing the time-averaged potential. The atoms are viewed from above in c with an absorption image. Figures 14 a and b reprinted with permission from [ 13 ], Copyright by the American Physical Society. Figure 14 c reprinted with permission from [ 14 ], Copyright by the American Physical Society.
These time-averaged adiabatic potentials or TAAPs have considerable potential for variable geometry and one can drive the trap in several directions as a function of time [ 13 ], as well as modulating the RF amplitude and frequency [ 89 ]. One should bear in mind that the driving has to be faster than the mechanical motion of the atoms i. In addition, care has to be taken with exotic geometries to avoid any RF holes due to polarisation section 3 where atoms could be lost. The TAAP was first realised experimentally in [ 14 ] with some quite large and well defined rings see figure 14 c , and in [ 89 ], even larger, mm scale rings were formed for Sagnac interferometry.
In addition to rings, we note here that a double-well potential was experimentally formed with a TAAP in [ 78 , 90 ], and the versatility of TAAPs was demonstrated in [ 78 ] where, as well as demonstrating evaporative cooling, a vortex array was created in the TAAP. The whole vortex creation process in [ 78 ] was engineered with time-dependent adiabatic potentials. Artificial lattices have been of importance in atomic physics for some time [ 91 ].
They have allowed the investigation of previously unseen condensed matter models and play an important role in the development of atomic clocks [ 92 ]. To date the lattices investigated have been optical lattices; typically a retro-reflected beam creates standing waves with periodic light shifts of energy levels.
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RF dressed lattices offer different parameter ranges, such as the possibility for sub-optical-wavelength lattices. The first theoretical proposal is essentially an extension of the trapping concept of figure 3 to multiple RF frequencies [ 18 ], and even beyond the two frequencies considered for spectroscopy or direct evaporative cooling of an RF trap section 3. Figure 15 a shows how the lattice is built by having multiple magnetic resonances with many RF fields. In fact we can see from figure 15 a that every lattice site generated requires two unique RF frequencies.
Provided the underlying magnetic fields were linear in the one-dimensional space, the RF frequencies would approximately belong to a frequency comb if a regular lattice is desired. In that case, the lattice spacing is approximately determined by the frequency comb spacing and the magnetic field gradient. That is, for a lattice spacing d and field gradient , the frequency spacing of RF fields is.
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The result of a detailed calculation of the potential which has to account for the cumulative off-resonant shifts of the multiple RF fields on each other's resonance points , is shown in figure 15 b. One notes, however, that many RF fields are required to make a long lattice and that the lattice described is a 1D lattice. In the proposed variant of [ 93 ], a RF square wave produces the harmonics, but the decreasing amplitudes of those harmonics means that the 1D lattice is less effective as one travels out from the centre.
In [ 94 ] three 1D potential wells are proposed to be produced with six RF frequencies. The potential wells are moved in space by controlling the RF frequencies in time. In this way it was possible to modify the tunelling rates between the wells for the controlled and efficient transfer of population between them.
Detailed calculations include 'light' shifts where one RF resonance shifts the location of another. Figure 15 b taken with permission from [ 18 ]. In our second example of rf dressed lattice physics the dressing field is applied to atoms already in an optical lattice. This results in a 2D dressed lattice which has been observed experimentally [ 17 ].
The optical field is necessarily off-resonant, as shown in figure 16 a , and has a well chosen laser wavelength between the D 1 and D 2 lines of 87 Rb. Hybrid dressed optical-RF 2D lattice in the experiment of [ 17 ]. Figure 16 is taken with permission from [ 17 ]. The resultant 2D optical lattices are depicted in figure 16 b top. By mixing these optical potentials it is possible to form new structures on a sub-wavelength scale, as shown in figure 16 c bottom. These potential structures include lattices of ring traps [ 17 ].
RF dressed optical potentials have been further studied in [ 95 , 96 ] and we note a scheme for optically dressed sub-wavelength lattices was proposed in [ 97 ]. Finally, we mention the proposal for lattices to be created with arrays of wires on an atom chip. In [ 98 ] an array of current carrying wires produced a 1D diffraction grating for atoms where magnetic-field zeros were plugged with RF potentials.
However, a 2D RF dressed lattice which can trap atoms has also been proposed in [ 99 , ] see figure It is based on a double-layer atom chip with two perpendicular sets of parallel wires. A DC current is snaked backwards and forwards across one set of wires, and an AC current is similarly sent through the perpendicular set of wires. Because the currents in adjacent wires go in opposite directions, it is clear that a system of periodic magnetic fields is created with a period governed by the wire spacings on the chips.
The RF frequency is chosen to ensure that the lattice is located away from the surface of the chip. To avoid all the potential 'holes', an additional uniform RF field, with the same frequency, has to be added at an angle in the x — y plane: By tuning the field amplitudes and phases, a variety of lattices can be made, including ladder lattices and dipolar lattices; for examples, see figures 17 b — e and [ 99 ]. To create the RF dressed lattice, a DC current is sent through one set of wires, and an RF current is sent down a perpendicular set of wires.
In addition, a uniform external RF field is applied in the x —y plane. The different lattices are obtained by changing the amplitude and phase of the two RF fields: Figures taken with permission from [ 99 ]. As discussed already in section 4. For the dressed traps of section 4. However, another approach is to create circular currents in conducting loops by induction. In the original proposal, which does not use dressing, a low frequency EM field couples to a macroscopic conducting loop of metal [ ].
The induced circuital current creates its own local oscillating field, which has a phase dependent on resistance and inductance and which varies in amplitude hugely near the metal loop surface. The combined original and induced oscillating magnetic field vanishes around a circle in the plane of the ring.
This circle sweeps back and forth across the induction ring itself during a cycle of field oscillation. By adding a bias field we can obtain a situation, reminiscent of the TOP trap, where the circle of zero field travels around the location where the atoms are trapped in a time-averaged potential [ , ]. A dressed variant of the induction trap was proposed in [ 19 ], which operates at higher frequency. There are two versions involving different arrangements of coils for the static field and RF field see figures 18 a and b. In both cases the RF field is applied to the metal loop and, because of induction, it produces a spatially varying RF field which is strong near the surface of the loop.
Because of cancellation between the induced and applied field, the net RF field is reduced around an approximately circular loop close to the metallic ring. The loop is inhomogeneous because the direction of the horizontal bias field breaks the circular symmetry. However, by rotating the bias field in the horizontal plane, the inhomogeneity in the adiabatic potential is averaged out as in a TAAP , and the resulting ring trap is circular [ 19 ].
The minimum of the time-averaged ring trap is indicated by the white cross in figure 18 c. It is possible to use the induction method without time-averaging the potentials: In this case the two bias coils are in an anti-Helmholtz configuration, i. With an appropriate RF frequency, a ring trap and even a double ring trap can be produced. The RF coils are shown in orange and other coils in light and dark blue. In both cases the RF coils are arranged to get an oscillating magnetic flux through the metal ring.
In a the blue coils are used to produce a rotating bias field, while in b the blue coils produce a static quadrupolar magnetic field. The black arc indicates the locus of the weakest point of adiabaticity as the bias field is rotated [ 19 ]. Figures taken with permission from [ 19 ].
An approach to inductive dressed trapping that avoids both using a TAAP and precision alignment issues involves a switch to microwaves [ ]. This proposal uses an off-resonant inductive microwave field, as shown in figure 19 a. Off-resonant microwaves have been used to trap atoms in [ 38 , 39 , 71 ], and proposed for quantum information processing in [ ]. In [ ] the combination of applied and induced microwave fields creates a circular quadrupole structure near the inner surface of the metal ring which gives the spatial dependence of the dressed potentials. The uniform bias field in this case can be perpendicular to the metal induction loop because of the different selection rules for microwave transitions.
The field zero in the centre of the quadrupole guide does not cause atom loss from the dressed trap because the microwave field is detuned. An interesting possibility for this geometry is that different planar shapes for the conductor can be considered as in figure 19 b. This is because the waveguide structure formed does not depend on modest curvature and, with the vertical bias field, the shape can be flexibly changed in the x — y plane. There are limits to the flexibility: Atomic structure a and chip design b for a variable shape atomic waveguide for cold atoms from [ ].
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The resulting fields, with the bias field B DC , creates a waveguide for atoms red near the conductor. As a result the shape of the conductor determines the path of the waveguide. Figures taken from [ ]. Future directions in the trapping and manipulation of atoms with adiabatic potentials may involve developments in quantum technology. The ring traps offer various opportunities for Sagnac interferometry and rotation sensing. In this respect the improvement of atom chips and compact devices goes in the direction of advances in quantum technology.
Those same atom chips can also create high field gradients and quite strong magnetic fields. In that respect the nonlinear Zeeman effect can play a role, as already seen in the dressed lattice experiment of Lundblad et al [ 17 ]. Dressing in the nonlinear Zeeman regime was investigated more generally in [ ] where weaker and tighter RF trapping was theoretically predicted. Nonlinear corrections to the Zeeman effect in atom dressing have already played a role in proposed developments of improved atomic clocks [ , ] and may also be important in situations where there is breakdown of the RWA.
Two or more stacked rings of atoms can be made by many of the ring trap methods described here, for example, by sheets of light [ 11 ], by using a TAAP [ 13 ], permanent magnet rings [ 27 ], or by dressing with an induction ring [ 19 ]. These systems are promising for atom interferometry and measurements of gravity. In the absence of gravity, or rather in the presence of micro-gravity, it may be possible to observe RF egg-shells, or bubbles with atoms, or a BEC, spread around the whole shell.
This can be achieved for small bubbles with the compensation of gravity [ 5 ]. For large bubbles and short times, the experiment could be dropped in a tower [ , ]. However, for long interaction times the experiment can be placed into orbit, as should be possible with the NASA Cold Atom Laboratory, currently under construction [ , ]. Finally, the relatively new field of atomtronics [ — ] concentrates on the manipulation of atomic systems in a modular way which has some analogies with electronics.
The flexible and highly configurable nature of dressed atom potentials may have a role to play here for example, dressed potentials have already been used to make a flexible lens for atoms [ ]. Generally, adiabatic potentials are so versatile and varied in geometry that we think there may be significant applications in the future. We would also like to thank Romain Dubessy, Wolf von Klitzing and the Cretan matterwaves group, Thorsten Schumm, and German Sinuco for useful comments on the manuscript.
Introduction As the field of ultra-cold atomic physics develops, it becomes increasingly important to be able to trap and manipulate atoms in potentials that are more complex than the standard, well established harmonic potential. Magnetic traps Before looking at 'dressing' [ 20 ], we examine the individual components required: Zoom In Zoom Out Reset image size. Resonant surfaces with a second RF field To gain some insight into the features introduced by a second RF field, we start by looking at the situation with a first RF field in the bare basis, such as used in figure 3 for a linear magnetic field top figure for bare state picture or figure 5 a for a quadrupolar or IP type of field.
RF egg-shell with optical assist In Morizot et al [ 11 ] published a proposal for a ring trap for atoms based on the intersection of two types of potential for ultra-cold atoms. X 4 Crossref. A 69 Crossref. A 76 Crossref. A 74 Crossref. Lesanovsky I and von Klitzing W Phys. A 83 Crossref.
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A 73 Crossref. A 93 Crossref. Sukumar C and Brink D Phys. A 56 —4 Crossref. Brink D and Sukumar C Phys. A 75 Crossref. Landau L Phys. Zener C Proc. A — Crossref. A 56 R—80 Crossref. Hess H F Phys. B 34 Crossref. A 58 —92 Crossref. IV —52 Crossref. A 53 —51 Crossref. A 58 Crossref. D 47 —14 Crossref. A 88 Crossref. A 77 Crossref. Sewell R J et al J. D 35 —6 Crossref. D 32 —80 Crossref. Henkel C and Wilkins M Europhys. A 86 Crossref. Ammar M et al Phys.