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Atoms and molecules in highly excited electronic states ('Rydberg atoms') have been the object of broad scientific research for almost a century. Despite this long history, the field of research has never lost its buoyancy, and recent years in particular have seen a tremendous revival of interest in the physics of Rydberg atoms and molecules from many different perspectives. Rydberg systems touch a wide range of research areas including, among others, ultralong-range molecules, artificial ('designer') atoms, quantum chaos, quantum information, ultracold Rydberg gases and plasmas, and anti-hydrogen formation. Due to the many fields involved, the physical insight and technical know-how are scattered over different communities. The goal of this special issue is to provide an integral overview of the latest developments in this highly innovative research field and to make the physical knowledge available to a wide audience. Groups from various fields of atomic, molecular and optical physics as well as condensed matter and plasma physics have contributed to this issue, which therefore spans a wide range of areas connected through the common theme: 'Rydberg physics'.

This name was given to a four-week International Workshop and Seminar which was held from 19 April to 14 May 2004 at the Max-Planck-Institut für Physik Komplexer Systeme in Dresden, Germany, and organized by the three of us. The workshop and seminar programme was a very successful mixture of topics bringing together colleagues working in different but related areas of research centred about the physics of highly excited Rydberg atoms and molecules. We would like to take this opportunity to express our gratitude to the organization team of the MPI-PKS Dresden, especially the Director, Jan-Michael Rost, and the Visitors' Programme coordinator, Mandy Lochar. The generous support of the Max Planck Society, which made this successful workshop and seminar possible, is also gratefully acknowledged. Inspired by the great response to the 'Rydberg physics' conference we thought that it would be timely and appropriate to recognize the importance of Rydberg physics with a special issue of a scientific journal. The 'unbureaucratic' and highly efficient editorial and publishing team of Journal of Physics B: Atomic, Molecular and Optical Physics (J. Phys. B) allowed this to become a reality; it was a real pleasure for us to serve as guest editors. Unlike a conventional conference proceedings, this special issue has not been restricted to participants of the 'Rydberg physics' conference, and all the original papers contained in it have been peer-reviewed to the usual high standards of J. Phys. B.

The variety and integrated discussion on the physics of Rydberg systems during the 'Rydberg physics' conference is reflected in the papers presented here. We have tried to group the papers according to the subject areas which are addressed. The first part of this special issue is devoted to high-resolution spectroscopy revealing deeper insights into the structure of Rydberg atoms and molecules as well as electronic interaction processes. The second part contains experimental and theoretical investigations on the influence of external static and oscillatory fields on Rydberg atoms. The third part takes account of the newly established field of ultracold Rydberg gases and plasmas with special emphasis on the appearance of ultralong-range interactions in these systems. Finally, the issue is concluded by articles on new developments including 'exotic' Rydberg systems.

We would like to thank all of the participants of the 'Rydberg physics' workshop and seminar, and, in particular, the contributors to this special collection of papers, for their involvement. We are deeply indebted to the J. Phys. B editorial and publishing team both for making its realization possible in an extremely efficient way, and for the journal's commitment to the physics of Rydberg systems. We are impressed by the continuing progress in this fascinating and rapidly growing field of research and we look forward to many more thrilling and surprising achievements.

The 8snl double Rydberg states of barium with l = 5 and n = 12–15 are populated by employing an isolated core excitation (ICE) scheme in conjunction with the Stark switching technique. The recorded spectra show strong configuration interaction with three adjacent 5f_jn'l' series. One of the latter series is converging to the 5f_5/2 ionization limit and the other two to the higher lying 5f_7/2 one. A multichannel quantum defect theory (MQDT) analysis reveals the presence of low-lying members of double Rydberg series converging to higher ionization thresholds and determining the configuration mixing. At least two perturbers, affecting energy level positions, are identified while a comparison between experimental and fitted excitation profiles points towards the presence of a third one. Finally, theoretical calculations of the 8snl(l = 5) series members quantum defects demonstrate the onset of mutual penetration between the two excited electrons. Nevertheless, the most important quantum defect contributions stem from exchange and polarization effects and thus long-range interactions alone are insufficient for a proper description of the double Rydberg states involved.

Collisional and thermal ionization of sodium nS and nD Rydberg atoms with n = 8–20 has been studied. The experiments were performed using a two-step pulsed laser excitation in an effusive atomic beam at atom density of about 2 × 10¹⁰ cm⁻³. Molecular and atomic ions from associative, Penning and thermal ionization processes were detected. It was found that the atomic ions were created mainly due to photoionization of Rydberg atoms by photons of blackbody radiation at the ambient temperature of 300 K. Blackbody ionization rates and effective lifetimes of Rydberg states of interest were determined. The molecular ions were found to be from associative ionization in Na(nL) + Na(3S) collisions. Rate constants of associative ionization have been measured using an original method based on relative measurements of Na⁺₂ and Na⁺ ion signals.

The production of Rydberg atoms via collisions in a resonantly laser excited dense In vapour is reported. When a dense In vapour confined in a quartz cell, whose temperature is raised above 820 °C, is excited by 100 kW cm⁻² laser pulses at 410.3 nm, resonant with the fundamental transition 5 ²P_1/2 → 6 ²S_1/2, the fluorescence spectrum shows radiative emissions from Rydberg states, namely those corresponding to the n²P → 6 ²S_1/2 series with 9 ⩽ n ⩽ 23. Fluorescences corresponding to the 5 ²D → 5 ²P_1/2,3/2 transitions are also observed. Analysis of these signals' intensity as a function of several different experimental parameters, such as the atomic density and the laser power density, indicates that the population in the Rydberg levels is produced mainly by energy pooling collisions (EPC). The EPC cross section for the population of the Rydberg levels is also given. The influence on these effects of the presence of a fine structure in the In ground state (5 ²P_1/2,3/2) is also discussed, as well as the presence of a buffer gas inside the quartz cell.

Using experimental set-ups involving single photon excitation of metastable rare gas atoms Rg(mp⁵(m + 1)s, J = 2, 0) by a pulsed frequency-doubled dye laser in conjunction with time-of-flight ion detection, we have investigated several even Rg(mp⁵_1/2np') autoionizing resonances of the heavier rare gas atoms Rg = Ne − Xe (m = 2–5) at experimental bandwidths of 0.06 cm⁻¹ (Ne) and about 0.25 cm⁻¹ (Ar, Kr, Xe). New level energies (quantum defects) and widths for these resonances have been derived by a Fano-type lineshape analysis, thus yielding reduced resonance widths. The experimental spectra and the resonance parameters are compared with theoretical calculations which are based on the configuration interaction Pauli–Fock approach, including core polarization. For Rg = Ne, good agreement between the measured and the calculated results is observed. For the heavier rare gases, significant deviations between some of the existing experimental data and the theoretical results are found, indicating the need for further studies.

We present new measurements of the even parity autoionizing resonances built on the 5p⁵7p and 5p⁵4f configurations in xenon using the laser optogalvanic detection technique in conjunction with a dc discharge cell. The autoionizing resonances 5p⁵7p[1/2]₁ and 5p⁵7p[3/2]₁ excited from the 5p⁵6s[1/2]₀ metastable level and the 5p⁵7p[3/2]₂ resonance excited from the 5p⁵6s[1/2]₁ resonance level have been studied. In addition, the 5p⁵(²P_1/2)nf (n = 4 and 5) autoionizing resonances excited from the collisionally populated levels of the 5p⁵5d configuration have been investigated. The J-value assignments are established in the light of the selection rules in the jK-coupling scheme. We have determined the resonance energies, quantum defects, line-shape parameters and resonance widths by fitting the observed resonance profiles using Fano's formula for the photoionization cross section.

New experimental data on the highly excited Rydberg states of lithium have been acquired, using a two-step laser excitation technique in combination with a thermionic diode ion detector. The atoms are prepared in the 3s ²S_1/2 intermediate level by two-photon excitation from the ground state, whereas the np ²P_1/2,3/2 levels have been approached via single photon absorption. The new observations include much extended np ²P_1/2,3/2 Rydberg series (15 ⩽ n ⩽ 60). The Rydberg relation fit to the new data yields the quantum defect for the np ²P_1/2,3/2 series as 0.051(4) and the binding energy of the 3s ²S_1/2 level as 16 281.19(2) cm⁻¹. Adding the energy of the 3s ²S_1/2 level and its binding energy reveals the first ionization potential of lithium as 43 487.26(3) cm⁻¹.

Fine structure intervals connecting n = 19 Rydberg levels of Si⁺ with L between 9 and 16 were measured precisely using the RESIS/microwave technique. The fine structure pattern conforms closely with that predicted by an effective potential model, and indicates a value of 11.666(4)a³₀ for the adiabatic dipole polarizability of the Mg-like ion, Si²⁺.

We investigate relativistic and quantum electrodynamic effects for highly-excited bound states in hydrogen-like systems (Rydberg states). In particular, hydrogenic one-loop Bethe logarithms are calculated for all circular states (l = n − 1) in the range 20 ⩽ n ⩽ 60 and successfully compared to an existing asymptotic expansion for large principal quantum number n. We provide accurate expansions of the Bethe logarithm for large values of n, for S, P and circular Rydberg states. These three expansions are expected to give any Bethe logarithm for principal quantum number n > 20 to an accuracy of five to seven decimal digits, within the specified manifolds of atomic states. Within the numerical accuracy, the results constitute unified, general formulae for quantum electrodynamic corrections whose validity is not restricted to a single atomic state. The results are relevant for accurate predictions of radiative shifts of Rydberg states and for the description of the recently investigated laser-dressed Lamb shift, which is observable in a strong coherent-wave light field.

The use of cylindrical polar coordinates instead of the conventional spherical polar coordinates enables us to derive compact expressions of the first Born amplitude for some selected sets of transitions from an arbitrary initial circular state to a final state of large (l_f, m_f). The formulae for and transitions are expressed in terms of the Jacobi polynomials which serve as suitable starting points for constructing complete solutions over the bound energy levels of hydrogen-like atoms. The formulae for and transitions are in simple algebraic forms and are directly applicable to all possible values of n_i and n_f. It emerges that the method can be extended to evaluate the first Born amplitude for many other transitions involving states of large (l, m).

We report on field induced inelasticity effects in state-to-state transitions caused by collisions of helium with Rydberg atoms in the presence of parallel static electric and magnetic fields. Due to the phases accumulated by the wavefunctions of the states involved into the collision events, the transition cross sections plotted as a function of the external fields exhibit modulations. When the relative velocity of the colliding atoms is high enough, these modulations are wiped out, while sizable modifications of the cross sections may take place due to the alteration of the wavefunctions' spatial localization. The possibility of using the field-assisted collisions as a probe giving information on localization of the Rydberg states is discussed.

We report recent progress in our experimental investigation of high-lying Rydberg states of barium in crossed electric and magnetic fields. Through analysis of the nearest-neighbour level spacing statistics, we investigate the evolution of the electron dynamics as the electric field strength is increased.

We study electronically excited atoms exposed to a magnetic quadrupole field. In order to describe the electron dynamics, a one-body approach is employed. Due to the inhomogeneity of the field, the spatial and spin degrees of freedom become coupled in a unique way. The underlying unitary and anti-unitary symmetries are discussed in detail leading to remarkable features such as a two-fold degeneracy of any energy level. We analyse the energy level structure throughout a wide range of field gradients. An investigation of the electronic spin properties is performed by studying the spatially dependent spin-polarization which exhibits a rich nodal structure. We compute wavelengths and strengths for electromagnetic transitions and provide the selection rules. A discussion of the so-called ellipsoidal states which exhibit unique properties such as large mean orbital angular momenta and spatial compactness is provided. The property of magnetic field-induced permanent electric dipole moments is analysed in detail. Wherever reasonable, the results obtained for the quadrupole field are compared to the homogeneous field case.

We analyse a resonant-enhanced multiphoton ionization (REMPI) spectrum of the high n (35–50) members of the Rydberg series of NO molecules recorded in a 1 T external magnetic field. In this range the quadratic Zeeman interaction takes over the Coulomb interaction and gradually scrambles the Coulomb structure of the Rydberg series. A perturbative quantum treatment of the diamagnetic interaction, giving rise to the so-called l-mixing and n-mixing, shows that the apparent complexity of the higher range of the experimental spectra results essentially from the interplay of two Rydberg series associated with different rotational core states. This perturbative treatment is expected to gradually break down and a semiclassical approach is proposed to understand the underlying physical pattern governing this higher spectral range.

The influence of a superposed offset field on the response of very-high-n Rydberg atoms to a sequence of impulsive perturbations provided by a train of (N ⪅ 40) short unidirectional electric field pulses is investigated. Each pulse, termed a half-cycle pulse (HCP), has a duration T_p ≪ T_n, where T_n is the classical electron orbital period. The presence of the offset field leads to dramatic changes in the survival probability, this peaking when the net average field experienced by the atom is zero. The physical mechanisms responsible for this are discussed with the aid of classical trajectory Monte Carlo simulations. Good agreement between theory and experiment is observed.

The ionization probability for a one-dimensional (1D) Rydberg atom interacting with two short half-cycle pulses is calculated as a function of the time delay between them. The impulse and semiclassical approximations are used. The ionization probability oscillates with a Kepler period around some constant value evaluated analytically too. The oscillations exhibit the quantum-mechanical revival and depend on the orientation of the momentum transfer and the principal quantum number of the initial state.

We present protocols for steering a Rydberg wave packet towards a preferred region in phase space using a train of half-cycle pulses. Developing such protocols is aided by classical phase space portraits. The classical phase space changes its structure as the frequency and the strength of a train of pulses are modulated. The quantum wave packet can be made to follow such a change. The movement of the wave packet can thus be controlled by a proper modulation of the perturbation. In addition, this technique can be used to create a focused wave packet or to transfer it from one island to another associated with a different quasi-periodic motion.

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.

Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected level of intricacy even on this most elementary level of the dynamics. We describe the dynamics of tunnelling ionization through the barriers semiclassically and use our results to shed new light on the success of a recent theory of molecular tunnelling ionization as well as earlier theories that restrict the electric field to be aligned with the molecular axis.

The transition state is fundamental to modern theories of reaction dynamics. While transition state theory (TST) has been used mainly in chemical physics, it can be applied to any problem that involves some form of transformation, including half-scattering events such as ionization of Rydberg atoms. In this paper, we construct the ionization transition states of H⁺₂ in an external electric field. In the process, we encounter and eliminate small divisors in our perturbation expansion and monitor its convergence using a new error criterion. The procedure is readily applicable to multiple Coulomb centres at large separations characteristic of Rydberg plasmas.

The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Q_j of each polar atom. Analytical expressions are obtained for all Q_j associated with principal quantum number n of H(n) and permit the long-range expansion for the H(n)–H(n') first-order interaction to be explicitly expressed analytically in terms of n, n' and internuclear distance R. Possible quasi-molecular formation is investigated. Direct calculations show that the H(n = 2)–H(n' = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.

We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C-coefficients are determined for all symmetries of molecular states that correlate to the ns–ns, np–np and nd–nd asymptotes. Fitted parameters are given for the scaling of the C-coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.

Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg–Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C₃/R³ interactions. We show in this paper that even under resonant conditions C₃ often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples.

We report on experiments on Rydberg–Rydberg interaction-induced effects in a gas of ⁸⁷Rb Rydberg atoms. A compact setup for two-photon continuous-wave excitation of high-lying Rydberg states out of an ultracold atomic gas is presented. The performance of the apparatus is characterized by high-resolution spectroscopy of Rydberg states. Signatures of interaction-induced effects are identified by qualitatively analysing the dependence of Rydberg excitation spectra on the intensity and the duration of the second-step laser excitation.

Using a classical trajectory Monte Carlo method, we have computed the ionization resulting from the interaction between two cold Rydberg atoms. We focus on the products resulting from close interaction between two highly excited atoms. We give information on the distribution of ejected electron energies, the distribution of internal atom energies and the velocity distribution of the atoms and ions after the ionization. If the potential for the atom is not purely Coulombic, the average interaction between two atoms can change from attractive to repulsive giving a Van de Graaff-like mechanism for accelerating atoms. In a small fraction of ionization cases, we find that the ionization leads to a positive molecular ion where all of the distances are larger than 1000 Bohr radii.

While ion heating by elastic electron–ion collisions may be neglected for a description of the evolution of freely expanding ultracold neutral plasmas, the situation is different in scenarios where the ions are laser-cooled during the system evolution. We show that electron–ion collisions in laser-cooled plasmas influence the ionic temperature, decreasing the degree of correlation obtainable in such systems. However, taking into account the collisions increases the ion temperature much less than what would be estimated based on static plasma clouds neglecting the plasma expansion. The latter leads to both adiabatic cooling of the ions as well as, more importantly, a rapid decrease of the collisional heating rate.

Absorption imaging and spectroscopy can probe the dynamics of an ultracold neutral plasma during the first few microseconds after its creation. Quantitative analysis of the data, however, is complicated by the inhomogeneous density distribution, expansion of the plasma and possible lack of global thermal equilibrium for the ions. In this paper, we describe methods for addressing these issues. Using simple assumptions about the underlying temperature distribution and ion motion, the Doppler-broadened absorption spectrum obtained from plasma images can be related to the average temperature in the plasma.

Double Rydberg wave packets for He electronic states are propagated in time using fully quantum mechanical calculations. The wave packets are constructed so that the two electrons are simultaneously excited up to n_Ryd ∼ 15 states and coupled to total orbital angular momentum equal to zero and to total spin equal to zero. We attempt to construct a wave packet to isolate symmetric stretch motion. Classical and quantum ideas are used to interpret several features of the time-dependent wave function. We briefly discuss some of the interesting problems that can be addressed.

The nature of the electronically excited states of He clusters and their relaxation mechanisms are investigated by spectroscopy using monochromatized synchrotron radiation. Time correlated fluorescence excitation and energy resolved luminescence spectra of the clusters are recorded in separate wavelength ranges. The size of the clusters and the isotopic constitution is also varied. The spectral features are analysed and discussed particularly with regard to the high lying states and their possible Rydberg nature. While Rydberg states seem not to exist in the interior region of large clusters there is experimental evidence that sharp lines in the spectrum are either due to He Rydberg atoms or excimer molecules in high vibrational states bound at the surface of large clusters or due to very small positively charged clusters with the Rydberg electron outside. The spectra of large ³He clusters exhibit a larger contribution of Rydberg lines than ⁴He clusters. He clusters also emit fluorescence at energies above the ionization energy of He atoms. This is attributed to the barrier for the injection of electrons into the conduction band which was found to be 1.35 eV for ⁴He and 0.95 eV for ³He clusters, respectively.

We present the results of a computational study of the recombination and cascade of antihydrogen into its ground state. We use a full time-dependent theory for recombination and compare the results with those predicted by (quasi-) time-independent theories. We introduce a stochastic interpretation of the recombination process and use it to explore the dependence of the recombination coefficient on plasma temperature and density. We use the time-dependent approach, introduced here, to explore the effect of a stimulating laser field on the recombination process.

Exotic Rydberg atom formation in collisions between low-energy antiprotons and helium atoms is studied. We present state-selective (n, l) capture cross sections for antiproton-capture from ³He and ⁴He targets as a function of impact energy. The simulation is based on the 3-body classical trajectory Monte Carlo method. We find the resulting (n, l) distributions of captured antiprotons in good agreement with recent measurements.

We propose a novel Stark decelerator for atoms or molecules excited in Rydberg states, in which the electric field continuously follows the motion of particles. Using moderate m Rydberg states (m > 2) in low-field seeker Stark levels, the evolution in the decelerator field should be hydrogen-like. Furthermore, the electric field seen by the particles is roughly constant; this greatly reduces the losses due to electric field induced transitions. We show that this decelerator fulfils the requirement of phase-space stability, since it is equivalent to a smoothly travelling well. This kind of decelerator should provide a new tool to obtain cold molecules, and is applicable to a very large range of molecules. Numerical simulation shows that within times compatible with Rydberg lifetimes, a cloud of sodium atoms can be stopped in the laboratory frame from a supersonic beam.

The applicability of Rydberg atoms to quantum computers is examined from an experimental point of view. In many recent theoretical proposals, the excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole–dipole interactions that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analysed. We also present the results of modelling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S_1/2 → 37P_1/2 and two-photon 37S_1/2 → 38S_1/2 transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The results may be applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.