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In this work, we have experimentally and theoretically investigated the high-lying Rydberg state excitation for noble gas atoms subject to an intense near-infrared laser field. To obtain the signal of these high-lying Rydberg atoms which are further ionized by a constant electric field $({F}_{c})$, coincident detection of the photoelectrons and photoions with well-chosen arrival times is performed. Based on a fitting to the time dependence of the coincidently measured photofragment yields with a semiempirical formula, we can extract a principal quantum number distribution (PQND) of the population of the excited states in a range closely related to the strength of ${F}_{c}$. The extracted valid PQND is in qualitative agreement with a semiclassical model calculation. Our work thus provides a method to extract the PQND and study the ultrafast high-lying Rydberg state excitation.

Molecular cationic states with two valence holes and one $n$-Rydberg electron can be created after spectator Auger decay. Unraveling these states' dissociation is often very challenging due to the frequent occurrence of conical intersections between cationic potential energy curves. Here, based on an advanced analysis of the experimental multicoincidence data obtained after $\mathrm{O}1s$ core excitation in ${\mathrm{O}}_{2}$, we achieved an energy-resolution better than we recently exploited in Phys. Rev. A 99, 022511 (2019). We therefore revealed a group of weak channels in the two-dimensional energy-correlation map between the coincident resonant Auger electron and ion in addition to the previously reported strong ones. The fragments in the identified weak channels contain only outmost electrons in valence orbitals; in contrast, the fragments in the strong channels contain an outmost electron in a ${n}^{\ensuremath{'}}$-Rydberg orbital. Compared with the strong channels, the weak channels preferentially occur at smaller principal quantum number $n$. It indicates that the electron orbital size tends to be conserved during the dissociation process. These weak features are suggested to be created by the Rydberg-valence mixing between the molecular spectator Auger final state and the very dissociative molecular cationic states without the Rydberg electron. A tendency to orbital selection is also suggested in the Rydberg-valence mixing.

We use the adiabatic-nuclei molecular convergent close-coupling method to perform calculations of 0.01--1000 eV electrons scattering on the $c^{3}\mathrm{\ensuremath{\Pi}}_{u}$, $a^{3}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$, $B^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$, $C^{1}\mathrm{\ensuremath{\Pi}}_{u}$, and $EF^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ states of ${\mathrm{H}}_{2}$ in the $v=0$ vibrational level. Elastic, superelastic, ionization, and grand-total cross sections are presented, as well as cross sections for excitation of the $n=2$--3 singlet and triplet states of ${\mathrm{H}}_{2}$ (where $n$ is the atomic-limit principle quantum number). Comparison with available theoretical results is made. Good agreement is found with the recent $R$-matrix results [J. Phys. B 53, 245203 (2020)] for most of the exchange and dipole-forbidden transitions, but not for the dipole-allowed transitions. The sources of disagreement were found to be an unconverged partial-wave expansion and the utilization of the fixed-nuclei approximation (as opposed to adiabatic-nuclei) in the $R$-matrix calculations.

We present a precise measurement of the rubidium ionic core polarizability. The results can be useful for interpreting experiments such as parity violation or black-body radiation shifts in atomic clocks since the ionic core electrons contribute significantly to the total electrical polarizability of rubidium. We report a dipole polarizability ${\ensuremath{\alpha}}_{d}$ = $9.116(9)\phantom{\rule{0.16em}{0ex}}{a}_{0}^{3}$ and quadrupole polarizability ${\ensuremath{\alpha}}_{q}$ = $38.4(6)\phantom{\rule{4pt}{0ex}}{a}_{0}^{5}$ derived from microwave and radio-frequency spectroscopy measurements of Rydberg states with large angular momentum. By using a relatively low principal quantum number ($17\ensuremath{\le}n\ensuremath{\le}19$) and high angular momentum ($4\ensuremath{\le}\ensuremath{\ell}\ensuremath{\le}6$), systematic effects are reduced compared to previous experiments. We develop an empirical approach to account for nonadiabatic corrections to the polarizability model. The corrections have less than a 1% effect on ${\ensuremath{\alpha}}_{d}$ but almost double ${\ensuremath{\alpha}}_{q}$ from its adiabatic value, bringing it into much better agreement with theoretical values.

Measurements of the loss rates for strontium $n^{3}S_{1}$ Rydberg atoms excited in a dense Bose-Einstein condensate are presented for values of principal quantum number $n$ in the range $49\ensuremath{\lesssim}n\ensuremath{\lesssim}150$ and local atom densities of $\ensuremath{\sim}1$ to $3\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. Two main processes contribute to loss, associative ionization, and state changing. The relative importance of these two loss channels is investigated, and their $n$ and density dependences are discussed using a model in which the Rydberg atom loss is presumed to involve a close collision between the Rydberg core ion and ground-state atoms. The present measurements are compared to earlier results obtained using rubidium Rydberg atoms. For both species the observed loss rates are sizable, $\ensuremath{\sim}{10}^{5}\ensuremath{-}{10}^{6}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, and limit the timescales over which measurements involving Rydberg atoms immersed in quantum degenerate gases can be conducted.

We resonantly excite the $K$ series of O$^{5+}$ and O$^{6+}$ up to principal quantum number $n=11$ with monochromatic x rays, producing $K$-shell holes, and observe their relaxation by soft-x-ray emission. Some photoabsorption resonances of O$^{5+}$ reveal strong two-electron--one-photon (TEOP) transitions. We find that for the $[(1s\,2s)_1\,5p_{3/2}]_{3/2;1/2}$ states, TEOP relaxation is by far stronger than the radiative decay and competes with the usually much faster Auger decay path. This enhanced TEOP decay arises from a strong correlation with the near-degenerate upper states $[(1s\,2p_{3/2})_1\,4s]_{3/2;1/2}$ of a Li-like satellite blend of the He-like $K\alpha$ transition. Even in three-electron systems, TEOP transitions can play a dominant role, and the present results should guide further research on the ubiquitous and abundant many-electron ions where electronic energy degeneracies are far more common and configuration mixing is stronger., Comment: Published in PRA

We characterized the pulsed Rydberg-positronium production inside the Antimatter Experiment: Gravity, Interferometry, Spectroscopy (AE$\overline{\textrm{g}}$IS) apparatus in view of antihydrogen formation by means of a charge exchange reaction between cold antiprotons and slow Rydberg-positronium atoms. Velocity measurements on the positronium along two axes in a cryogenic environment (≈10K) and in 1T magnetic field were performed. The velocimetry was done by microchannel-plate (MCP) imaging of a photoionized positronium previously excited to the $n$=3 state. One direction of velocity was measured via Doppler scan of this $n$=3 line, another direction perpendicular to the former by delaying the exciting laser pulses in a time-of-flight measurement. Self-ionization in the magnetic field due to the motional Stark effect was also quantified by using the same MCP-imaging technique for Rydberg positronium with an effective principal quantum number $n_\textrm{eff}$ ranging between 14 and 22. We conclude with a discussion about the optimization of our experimental parameters for creating Rydberg positronium in preparation for an efficient pulsed production of antihydrogen. We characterized the pulsed Rydberg-positronium production inside the AEgIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) apparatus in view of antihydrogen formation by means of a charge exchange reaction between cold antiprotons and slow Rydberg-positronium atoms. Velocity measurements on positronium along two axes in a cryogenic environment (10K) and in 1T magnetic field were performed. The velocimetry was done by MCP-imaging of photoionized positronium previously excited to the $n=3$ state. One direction of velocity was measured via Doppler-scan of this $n=3$-line, another direction perpendicular to the former by delaying the exciting laser pulses in a time-of-flight measurement. Self-ionization in the magnetic field due to motional Stark effect was also quantified by using the same MCP-imaging technique for Rydberg positronium with an effective principal quantum number $n_{eff}$ ranging between 14 and 22. We conclude with a discussion about the optimization of our experimental parameters for creating Rydberg-positronium in preparation for an efficient pulsed production of antihydrogen.

The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number $n=105$ in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the $1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}\ensuremath{\rightarrow}1s105p\phantom{\rule{0.16em}{0ex}}^{3}P$ transition, were identified from Autler-Townes splittings of the $1s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1s105s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.

We report the results of experiments in which positronium (Ps) atoms, optically excited to Rydberg-Stark states with principal quantum numbers ranging from $n=13$ to 19, were transported along the axis of a multiring electrode structure. By applying alternate positive and negative potentials to the ring electrodes, inhomogeneous electric fields suitable for guiding low-field-seeking atoms along the guide axis were generated. The multiring configuration used has the advantage that once the atoms are confined within it appropriate time-varying fields can be generated for deceleration and trapping. However, in this type of structure the possibility of nonadiabatic transitions of the fast (100 km/s) Ps atoms to unconfined high-field-seeking states exists. We show that for typical guiding fields this is not a significant loss mechanism and that efficient Ps transport can be achieved. Our data are in accordance with a Landau-Zener analysis of adiabatic transport through the field minima and Monte Carlo simulations that take into account Ps velocity distributions, electric dipole moments, and lifetimes, as well as the electric-field distributions in the guide.

The strong-field ionization behavior when a Rydberg atom is exposed to a terahertz single-cycle pulse is studied. Fully three-dimensional time-dependent Schr\"odinger equations and classical trajectory Monte Carlo calculations are performed. Results from stationary eigenstates and Rydberg wave packets are presented, and it is found that the ionization properties can be different for the two cases. All of the pulse parameters and physical quantities are scaled versus the principal quantum number $n$. The ionized electron's scaled radial, energy, and angular distributions are investigated for different $n$, and the quantum results are interpreted using a semiclassical method. The scaling relations of quantum interference amplitudes are discussed.

We present an experimental and theoretical study of the structure and autoionization dynamics of the ${(3{p}_{{j}_{\text{c}}}n{d}_{j})}_{J=1,3}$ core-excited Rydberg states of Mg. Spectra were recorded experimentally for principal quantum numbers $n$ in the range from 30 to 100 using the isolated-core-excitation technique. Large-scale configuration-interaction calculations combined with the exterior-complex-scaling method were also carried out, which do not rely on the assumptions used in the usual $R$-matrix multichannel-quantum-defect-theory treatment of core-excited Rydberg states. Agreement between theory and experiment is excellent over the entire range of principal quantum numbers studied and allows us to elucidate in detail the structure of the core-excitation spectra. The dominant autoionization mechanisms are identified, and in particular the very fast spin-orbit autoionization of some ${(3{p}_{3/2}n{d}_{j})}_{J}$ states above the $3{p}_{1/2}$ ionization threshold. We discuss the influence of the principal and total-angular-momentum quantum numbers $n$ and $j$ of the Rydberg electron and the total-angular-momentum quantum number $J$ of the atom on the autoionization dynamics. We also identify previously unobserved resonances attributed to members of the ${(3{p}_{{j}_{\text{c}}}n{g}_{j})}_{J}$ series.

We report experiments in which positronium (Ps) atoms, optically excited to Rydberg states with principal quantum numbers $n$ in the range 18--25, were selectively ionized by both static and pulsed electric fields. The experiments were modeled using Monte Carlo simulations that include tunnel ionization rates calculated for hydrogen and scaled by the Ps reduced mass. Our measurements exhibit a small disagreement with the calculated tunnel ionization rates. Despite this we show that the electric fields in which different Ps states are ionized are sufficiently separated to allow selective field-ionization methods to be used in typical experimental conditions.

A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions ($\overline{p}\mathrm{H}$), which in the separated atom limit correlate with $\overline{p}+\mathrm{H}(n=2)$ ($n$ being the principal quantum number). The $\overline{p}\mathrm{H}$ molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the $\overline{p}\mathrm{H}$ molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the $\mathrm{H}$ atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of $\overline{p}+\mathrm{H}(n=2)$ behaves as $1/{R}^{2}$ ($R$ being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the $\overline{p}\mathrm{H}$ molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The $\overline{p}\mathrm{H}$ system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the $\overline{p}\mathrm{H}$ molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with $\overline{p}$ beams.

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a $^{87}$Rb Rydberg atom whose outer electron interacts via spin-dependent $s$- and p-wave scattering with a polarizable $^{87}$Rb ground state atom. Our model includes also the hyperfine structure of the ground state atom as well as spin-orbit couplings of the Rydberg and ground state atom. We focus on $d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gau{\ss}. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both, weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model., Comment: 10 pages, 9 figures

We theoretically investigate long-range interactions between an excited $L$-state He atom and two identical $S$-state He atoms for the cases of the three atoms all in spin-singlet states or all in spin-triplet states, denoted by He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{'}\ensuremath{\lambda}}L$), with ${n}_{0}$ and ${n}_{0}^{\ensuremath{'}}$ principal quantum numbers, $\ensuremath{\lambda}=1$ or 3 the spin multiplicity, and $L$ the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients ${C}_{3}$ of the first-order dipolar interactions and the coefficients ${C}_{6}$ and ${C}_{8}$ of the second-order additive and nonadditive interactions. Both the dipolar and dispersion interaction coefficients, for these three-body degenerate systems, show dependences on the geometrical configurations of the three atoms. The nonadditive interactions start to appear in second-order. To demonstrate the results and for applications, the obtained coefficients ${C}_{n}$ are evaluated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates for $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)$, $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, and $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}P)$. The calculations are given for three like nuclei for the cases of hypothetical infinite mass He nuclei, and of real finite mass $^{4}\mathrm{He}$ or $^{3}\mathrm{He}$ nuclei. The special cases of the three atoms in equilateral triangle configurations are explored in detail, and for the cases in which one of the atoms is in a $P$ state, we also present results for the atoms in an isosceles right triangle configuration or in an equally spaced collinear configuration. The results can be applied to construct potential energy surfaces for three helium atom systems.

The $1snp\phantom{\rule{0.16em}{0ex}}^{3}P_{J}$ fine structure of high Rydberg states in helium has been measured by microwave spectroscopy of single-photon transitions from $1sns\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ levels in pulsed supersonic beams. For states with principal quantum numbers in the range from $n=34$ to 36, the $J=0\ensuremath{\rightarrow}2$ and $J=1\ensuremath{\rightarrow}2$ fine structure intervals were both observed. For values of $n$ between 45 and 51 only the larger $J=0\ensuremath{\rightarrow}2$ interval was resolved. The experimental results are in good agreement with theoretical predictions. Detailed characterization of residual uncanceled electric and magnetic fields in the experimental apparatus and calculations of the Stark and Zeeman structures of the Rydberg states in weak fields were used to quantify systematic contributions to the uncertainties in the measurements.

It is well known that the lanthanide and actinide elements are formed by the filling of $4f$ and $5f$ subshells which occurs after the filling of $5d$ and $6d$ subshells, respectively, has begun. With increasing ionization one expects the energy levels to eventually regroup to their hydrogenic ordering, i.e., in terms of principal quantum number. In the lanthanides, the $4f$ electron binding energy overtakes that of $5p$ near the 6th or 7th ion stage and $5s$ near the 14th or 15th ion stage, leading to dramatic rearrangements of ground-state configurations. In this paper we report on the results of a study to explore the effects of increasing ionization on the ground-state configurations of actinide ions as a result of $5f$ and $6p$ or $6s$ level crossings. It is seen that the effects generally occur later and are more strongly influenced by spin-orbit splitting than in the lanthanides. The near degeneracies of $5f$ and $6l$ energies in these stages lead to configuration interaction (CI) amongst configurations with variable numbers of $5f$ and $6p$ electrons. The effects of CI on the level complexity are explored for ions along the Rn I sequence and are found to lead to the formation of ``compound states'' as predicted for the lanthanides. The extreme ultraviolet and soft x-ray spectra of medium and highly charged lanthanides are dominated by emission from unresolved transition arrays (UTAs) of the type $\mathrm{\ensuremath{\Delta}}n=0$, $4{p}^{6}4{d}^{N+1}\ensuremath{-}4{p}^{5}4{d}^{N+2}+4{p}^{6}4{d}^{N}4f$, which, in general, overlap in adjacent ion stages of a particular element. Here, the corresponding $\mathrm{\ensuremath{\Delta}}n=0$, $5{p}^{6}5{d}^{N+1}\ensuremath{-}5{p}^{5}5{d}^{N+2}+5{p}^{6}5{d}^{N}5f$ UTAs have been studied theoretically with the aid of Hartree-Fock with configuration interaction calculations. As well as predicting the wavelengths and spectral details of the anticipated features, the calculations show that the effects of configuration interaction are quite different for the two different families of $\mathrm{\ensuremath{\Delta}}n=0$ transitions and, once more, spin-orbit interactions play a major role.

The lifetimes and decay channels of ultralong-range Rydberg molecules created in a dense Bose-Einstein condensate are examined by monitoring the time evolution of the Rydberg population using field ionization. Studies of molecules with values of the principal quantum number, $n$, in the range $n=49$ to $n=72$ that contain tens to hundreds of ground-state atoms within the Rydberg electron orbit show that their presence leads to marked changes in the field ionization characteristics. The Rydberg molecules have lifetimes of $\ensuremath{\sim}1\ensuremath{-}5\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$, their destruction being attributed to two main processes: formation of ${\mathrm{Sr}}_{2}{}^{+}$ ions through associative ionization and dissociation induced through $L$-changing collisions. The observed loss rates are consistent with a reaction model that emphasizes the interaction between the Rydberg core ion and its nearest-neighbor ground-state atom. The measured lifetimes place strict limits on the time scales over which studies involving Rydberg species in cold, dense atomic gases can be undertaken and limit the coherence times for such measurements.

The van der Waals coefficient ${C}_{6}(\ensuremath{\theta};nlJM)$ of two like Rydberg atoms in their identical Rydberg states $|nlJM\ensuremath{\rangle}$ is resolved into four irreducible components called scalar ${R}_{ss}$, axial (vector) ${R}_{aa}$, scalar-tensor ${R}_{sT}={R}_{Ts}$, and tensor-tensor ${R}_{TT}$ parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of ${C}_{6}(\ensuremath{\theta};nlJM)$ on the angle $\ensuremath{\theta}$ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components ${R}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of atoms in their Rydberg series of doublet states of the low angular momenta ($^{2}S, ^{2}P, ^{2}D, ^{2}F$). The polynomial presentations in powers of the Rydberg-state principal quantum number $n$ taking into account the asymptotic dependence ${C}_{6}(\ensuremath{\theta};nlJM)\ensuremath{\propto}{n}^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{S}_{1/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{P}_{1/2,3/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{D}_{3/2,5/2}$, and $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{F}_{5/2,7/2}$ Rydberg states of arbitrary high $n$. The transformation of the van der Waals interaction law $\ensuremath{-}{C}_{6}/{R}^{6}$ into the dipole-dipole law ${C}_{3}/{R}^{3}$ in the case of close dipole-connected two-atomic states (the F\"orster resonance) is considered and the dependencies on the magnetic quantum numbers $M$ and on the angle $\ensuremath{\theta}$ of the constant ${C}_{3}(\ensuremath{\theta};nlJM)$ are determined together with the ranges of interatomic distances $R$, where the transformation appears.

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties such as the prevalence of long-range oscillatory tails and the emergence of numerically large van der Waals ${C}_{6}$ coefficients. Furthermore, the energetically quasidegenerate $nP$ states require special attention and lead to mathematical subtleties. Here we analyze the interaction of excited hydrogen atoms in $nS$ states ($3\ensuremath{\le}n\ensuremath{\le}12$) with ground-state hydrogen atoms and find that the ${C}_{6}$ coefficients roughly grow with the fourth power of the principal quantum number and can reach values in excess of $240\phantom{\rule{0.16em}{0ex}}000$ (in atomic units) for states with $n=12$. The nonretarded van der Waals result is relevant to the distance range $R\ensuremath{\ll}{a}_{0}/\ensuremath{\alpha}$, where ${a}_{0}$ is the Bohr radius and $\ensuremath{\alpha}$ is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range ${a}_{0}/\ensuremath{\alpha}\ensuremath{\ll}R\ensuremath{\ll}\ensuremath{\hbar}c/\mathcal{L}$, where $\mathcal{L}$ is the Lamb shift energy. In this range, the contribution of quasidegenerate excited $nP$ states remains nonretarded and competes with the $1/{R}^{2}$ and $1/{R}^{4}$ tails of the pole terms, which are generated by lower-lying $mP$ states with $2\ensuremath{\le}m\ensuremath{\le}n\ensuremath{-}1$, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range $R\ensuremath{\gg}\ensuremath{\hbar}c/\mathcal{L}$. The familiar $1/{R}^{7}$ asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation for highly excited states.

Quantum control of the pathway along which a Rydberg electron field ionizes is experimentally and computationally demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The $(1/n^*)^4$ scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing the signal to the desired arrival time, a perturbing electric field produced by an arbitrary waveform generator is added to a slowly rising electric field. A genetic algorithm evolves the perturbing field in an effort to achieve the target time-resolved field ionization signal., Corrected minor typographic errors and changed the title

A pair of neutral atoms separated by several microns and prepared in identical s-states of large principal quantum number experience a van der Waals interaction. If microwave fields are used to generate a superposition of s-states with different principal quantum numbers, a null point may be found at which a specific superposition state experiences no van der Waals interaction. An application of this novel Rydberg state in a quantum controlled-Z gate is proposed, which takes advantage of GHz rate transitions to nearby Rydberg states. A gate operation time in the tens of nanoseconds is predicted., Comment: 17 pages, 12 figures

Rydberg molecules, often exemplified by long-range ``trilobite'' molecules, are a subject of much recent interest at high principal quantum number $n$. States that use the same bonding mechanism can exist at much lower $n$ and less-extreme internuclear separations that are still quite long range. We use a high-resolution pulsed amplifier to study previously detected transitions to a low-$n$ Rydberg molecular state near the $5s+7p$ asymptote in $^{85}\mathrm{Rb}_{2}$. The observed line structure is modeled using precise ground-state positions and a lower bound of $\ensuremath{\tau}g1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ s is set on the excited-state autoionization lifetime.

We have directly detected millimeter wave (mm-wave) free space superradiant emission from Rydberg states ($n \sim 30$) of barium atoms in a single shot. We trigger the cooperative effects with a weak initial pulse and detect with single-shot sensitivity and 20 ps time resolution, which allows measurement and shot-by-shot analysis of the distribution of decay rates, time delays, and time-dependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed values that would correspond to the Doppler width of 250 kHz by a factor of 20 and the spontaneous emission rate of 50 Hz by a factor of $10^5$. The initial superradiant output pulse is followed by evolution of the radiation-coupled many-body system toward complex long-lasting emission modes. A comparison to a mean-field theory is presented which reproduces the quantitative time-domain results, but fails to account for either the frequency-domain observations or the long-lived features., 5 pages, 4 figures

We consider the hydrogen atom $\mathrm{H}(1s)$ exposed to an ultrashort laser pulse with a central frequency ${\ensuremath{\omega}}_{0}$ ranging from several hundreds of eV to 1.5 keV ($\ensuremath{\approx}55$ a.u.) and a peak intensity of $3.51\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{4pt}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. We study the excitation of the atom by stimulated Raman scattering, a process involving pairs of frequencies (${\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2}$). These frequencies are non-negligible components of the pulse Fourier transform and they satisfy the condition ${E}_{g}+\ensuremath{\hbar}{\ensuremath{\omega}}_{1}={E}_{b}+\ensuremath{\hbar}{\ensuremath{\omega}}_{2},{E}_{g}$ and ${E}_{b}\ensuremath{\equiv}{E}_{n}$ being the ground-state and the excited-state energy, respectively. The numerical results obtained by integrating the time-dependent Schr\"odinger equation (TDSE) are compared with calculations in lowest order perturbation theory (LOPT). In LOPT we consider, in the second order of PT, the contribution of the term $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ in the dipole approximation and, in first order of PT, the expression of ${\mathbf{A}}^{2}$ taken for first-order retardation effects. ($\mathbf{A}$ denotes the vector potential of the field and $\mathbf{P}$ is the momentum operator.) We focus on the Raman excitation of bound states with principal quantum numbers $n$ up to $n=13$. The evaluation in perturbation theory of the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution to $1s\ensuremath{-}ns$ and $1s\ensuremath{-}nd$ transition probabilities uses analytic expressions of the corresponding Kramers--Heisenberg matrix elements. At fixed pulse duration $\ensuremath{\tau}=6\ensuremath{\pi}$ a.u. ($\ensuremath{\approx}0.48$ fs), we find that the retardation effects play an important role at high frequencies: they progressively diminish as the frequency decreases until the contribution of $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ dominates over the ${\mathbf{A}}^{2}$ contribution for ${\ensuremath{\omega}}_{0}$ values of a few a.u. We also study the dependence of the Raman process on the pulse duration for several values of ${\ensuremath{\omega}}_{0}$. In the case ${\ensuremath{\omega}}_{0}=13\phantom{\rule{4pt}{0ex}}\mathrm{a}.\mathrm{u}.\phantom{\rule{4pt}{0ex}}(\ensuremath{\approx}354\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ where dipole and nondipole contributions are of the same order of magnitude, we present the Raman excitation probability as a function of the pulse duration for excited $ns,\phantom{\rule{4pt}{0ex}}np$, and $nd$ states.

The effect of a nearby metallic particle on the quantum optical properties of a quantum particle in the four-level double Raman configuration is studied using the quantum Langevin approach. We obtain analytical expressions for the correlated quantum fields of Stokes and anti-Stokes photons emitted from the system and perform analysis on how the interparticle distance, the direction of observation or detection, the strengths of controllable laser fields, the presence of surface plasmon resonance, and the number density of the quantum particle affect the quantum spectra of the Stokes and anti-Stokes fields. We explore the physics behind the quantum-particle\char21{}metallic-nanoparticle interaction within the dipole approximation, that is, when the interparticle distance is much larger than the sizes of the particles. Our results show the dependence of the spectra on the interparticle distance in the form of oscillatory behavior with damping as the interparticle distance increases. At weaker laser fields the enhancement of quantum fields which manifests itself in the form of a Fano dip in the central peak of the spectra becomes significant. Also, the quantum-particle\char21{}metallic-nanoparticle coupling, which is affected by the size of the metallic nanoparticle and the number density of the quantum particle, changes the angular dependence of the spectra by breaking the angular rotational symmetry. In the presence of surface plasmon resonance the oscillatory dependence of the spectra on the interparticle distance and angles of observation becomes even stronger due to the plasmonic enhancement effect.

Effects of weak electric fields on resonant energy transfer between NH$_3$ in the X $^1$A$_1$ ground electronic state, and Rydberg He atoms in triplet states with principal quantum numbers $n = 36$-$41$ have been studied in a crossed beam apparatus. For these values of $n$, electric-dipole transitions between the Rydberg states that evolve adiabatically to the $|ns\rangle$ and $|np\rangle$ states in zero electric field can be tuned into resonance with the ground-state inversion transitions in NH$_3$ using electric fields, with energy transfer occurring via F\"orster resonance. In the experiments the Rydberg He atoms, traveling in pulsed supersonic beams, were prepared by resonant two-photon excitation from the metastable $1s2s\,^3S_1$ level and crossed an effusive beam of NH$_3$ before being detected by state-selective pulsed-electric-field ionization. The resonant-energy-transfer process was identified by monitoring changes in the ionization signal from the $|ns\rangle$ and $|np\rangle$ Rydberg states for each value of $n$. The electric field dependence of the experimental data is in good agreement with the results of calculations in which the resonant dipole-dipole coupling between the collision partners was accounted for., Comment: 6 pages, 4 figures

The antihydrogen formation by charge exchange between cold antiprotons and Rydberg positronium Ps is studied by using the Classical Trajectory Monte Carlo (CTMC) method., Comment: Accepted by Phys. Rev. A

We calculate the bound state spectrum of the highly excited valence electron in the heavy alkali atoms solving the radial Schrodinger eigenvalue problem numerically with an accurate spectral collocation algorithm that applies also for a large principal quantum number $n\gg1$. As an effective single-particle potential we favor the reputable potential of Marinescu \emph{et al}., {[}Phys. Rev.A \textbf{49}, 982(1994){]}. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum $l=0,1,2,...$ overall remarkably well with the results of the numerical calculations, but for the Rydberg states of rubidium and also cesium with $l=3$ this agreement is less fair. The reason for this anomaly is that the potential acquires for $l=3$ deep inside the ionic core a tiny second classical region, thus invalidating a standard WKB calculation with two widely spaced turning points. Comparing then our numerical solutions of the radial Schrodinger eigenvalue problem with the uniform analytic WKB approximation of Langer we observe everywhere a remarkable agreement, apart from a tiny region around the inner turning point. With help of an ansatz proposed by Fock we obtain for the \emph{s}-states a second uniform analytic approximation to the radial wave function complementary to the WKB approximation of Langer, which is exact for $r\to0^{+}$. The value of the radial \emph{s}-wave function at $r=0$ is analytically found, thus validating the Fermi-Segre formula for the magnetic dipole interaction constant $A_{n,j,0}^{\left(\mathrm{HFS}\right)}$.

Motivated by recent interest in their applications, we report a systematic study of Cs atomic properties calculated by a high-precision relativistic all-order method. Excitation energies, reduced matrix elements, transition rates, and lifetimes are determined for levels with principal quantum numbers $n \leq 12$ and orbital angular momentum quantum numbers $l \leq 3$. Recommended values and estimates of uncertainties are provided for a number of electric-dipole transitions and the electric dipole polarizabilities of the $ns$, $np$, and $nd$ states. We also report a calculation of the electric quadrupole polarizability of the ground state. We display the dynamic polarizabilities of the $6s$ and $7p$ states for optical wavelengths between 1160 nm and 1800 nm and identify corresponding magic wavelengths for the $6s-7p_{1/2}$, $6s-7p_{3/2}$ transitions. The values of relevant matrix elements needed for polarizability calculations at other wavelengths are provided., Comment: 10 pages, 6 figures

We report measurements of the fluorescence lifetimes of positronium (Ps) atoms with principal quantum numbers $n=10--19$. Ps atoms in Rydberg-Stark states were produced via a two-color two-step $1\phantom{\rule{0.16em}{0ex}}^{3}S\ensuremath{\rightarrow}2\phantom{\rule{0.16em}{0ex}}^{3}P\ensuremath{\rightarrow}n\phantom{\rule{0.16em}{0ex}}^{3}S/n\phantom{\rule{0.16em}{0ex}}^{3}D$ excitation scheme and subsequently detected after traveling 1.2 m. The measured time-of-flight distributions were used to determine the mean lifetimes of the Rydberg levels, yielding values ranging from $3\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$ to $26\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Our data are in accord with the expected radiative lifetimes of Rydberg-Stark states of Ps.

The time dynamics of quantum correlations in the quantum transverse anisotropic $XY$ spin chain of infinite length is studied at zero and finite temperatures. The evolution occurs due to the instantaneous quenching of the coupling constant between the nearest-neighbor spins of the model, which is performed either within the same phase or across the quantum phase-transition point connecting the order-disorder phases of the model. We characterize the time-evolved quantum correlations, viz., entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the quenching scheme. We show that the system is endowed with enhanced nearest-neighbor bipartite quantum correlations compared to that of the initial state, when quenched from the ordered to the deep disordered phase. However, nearest-neighbor quantum correlations are almost washed out when the system is quenched from the disordered to the ordered phase with the initial state being at the zero temperature. We also identify the condition for the occurrence of enhanced bipartite correlations when the system is quenched within the same phase. Moreover, we investigate the bipartite quantum correlations when the initial state is a thermal equilibrium state with finite temperature, which reveals the effects of thermal fluctuation on the phenomena observed at zero temperature. Finally, an analogous analysis is carried out for zero-temperature next-nearest-neighbor quantum correlations.

We have studied the decay of Rydberg excitations in a cold Rb gas. A 10 ns, pulsed-dye-amplified diode laser excites Rb atoms at $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in a magneto-optical trap to $ns$ or $np$ Rydberg states with principal quantum numbers $26\ensuremath{\le}n\ensuremath{\le}40$. Time-delayed state-selective field ionization is used to directly monitor the population in the initial and neighboring Rydberg levels. The measured time dependence of the Rydberg population is well described by numerical simulations which consider only spontaneous emission and population transfer by blackbody radiation. No evidence for collective decay is found at atom densities up to $3\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This result is in contrast to a previous study [Wang et al., Phys. Rev. A 75, 033802 (2007)], in which superradiant decay was theoretically predicted and experimentally inferred for atom density and laser focal volume conditions very similar to those considered here. Suppression of collective emission is likely due to variations in transition energies within the atom sample, dominated by inhomogeneities in dipole-dipole exchange interactions for initial $s$ states, or by a combination of dipole-dipole and electric field inhomogeneities for the initial $p$ states.

We calculate interspecies Rydberg-Rydberg interaction strengths for the heavy alkalis Rb and Cs. The presence of strong F\"orster resonances makes interspecies coupling a promising approach for long range entanglement generation. We also provide an overview of the strongest F\"orster resonances for Rb-Rb and Cs-Cs using different principal quantum numbers for the two atoms. We show how interspecies coupling can be used for high fidelity quantum non demolition state measurements with low crosstalk in qubit arrays., Comment: v2 angular dependence corrected, 10 figures

We present magic wavelengths for the $n{S}_{1/2}\text{\ensuremath{-}}n{P}_{1/2,3/2},$ and $n{S}_{1/2}\text{\ensuremath{-}}m{D}_{3/2,5/2}$ transitions in ${\mathrm{Mg}}^{+},$ ${\mathrm{Ca}}^{+},$ ${\mathrm{Sr}}^{+},$ and ${\mathrm{Ba}}^{+}$ alkaline-earth-metal ions, for the principal quantum numbers $n$ and $m$ for the ground and first excited $D$ states, respectively. These wavelengths are presented for linearly polarized light by plotting the dynamic polarizabilities of the $nS,n{P}_{1/2,3/2},$ and $m{D}_{3/2,5/2}$ states of the considered ions. Required dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with available high-precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in ${\mathrm{Ca}}^{+}$ concur with the recent measurements reported by Liu et al. [Phys. Rev. Lett. 114, 223001 (2015)]. Knowledge of these magic wavelengths is propitious to carry out many proposed high-precision measurements trapping the above ions in electric fields with the corresponding frequencies.

The Lamb shift in the light hydrogenlike atoms is evaluated for the state-dependent part of the $S$ states $({n}^{3}\mathrm{\ensuremath{\Delta}}{E}_{n}\ensuremath{-}\mathrm{\ensuremath{\Delta}}{E}_{1})/{n}^{3}$ and ${P}_{1/2}$ states by means of a recently proposed relativistic generalization of multipole expansion. We obtain the results for $Z=1--5$ and $n=2--10$, where $Z$ is the charge of the nucleus and $n$ is the principal quantum number of the state under consideration. The results are in an excellent agreement with the results obtained by means of $Z\ensuremath{\alpha}$ expansion truncated after the $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{6}$ term. The state-dependent part of the $S$ states for $n=2--4$ is evaluated also for the case of moderately strong Coulomb fields, $Z=10--50$. It is argued that the present results for the state-dependent part of the $S$ states for low $Z$ are the most accurate results given so far in the literature. In the case of hydrogen the uncertainty is significantly less than 1 Hz. Finally, the extrapolation of the results to infinite $n$ is performed.

X rays originating from transitions from high Rydberg states to the $M$ shell (here called Rydberg-to-$M$-shell x rays) have been measured in the interaction of ${\text{Xe}}^{q+}(q=27--30)$ ions with aluminum, molybdenum, and beryllium surfaces in the energy range of 350--600 keV, by using a Si(Li) detector. The transition energy calculation by Cowan's program with relativistic correlation indicates that such x rays are mainly from the transition of the higher quantum states, with the principal quantum number from 6 up to 30, directly to $M$ shell of xenon. The yield of the x ray per vacancy in $M$ shell decreases slightly with increasing the projectile energies and is inversely proportional to the work functions of metallic surfaces used. However, it increases rapidly with the increase of the projectile charge states. All of these experimental facts combined with the transition rate calculations indicate that the measured Rydberg-to-$M$-shell x rays come from the ``above the surface'' hollow Xe atoms or ions deexcitation, when the inner shells such as $N$ and $O$ have not been filled.

We propose a concept of fractional quantum resonances based on an idea of driving a quantum system by an external field in the form of a repetitive pulse sequence. We show that, in addition to intuitively expected resonance at repetition rate ${\ensuremath{\omega}}_{\text{Rep}}$ equal to the internal quantum frequency $\ensuremath{\omega}$, the system exhibits less intuitive fractional quantum resonances at ${\ensuremath{\omega}}_{\text{Rep}}=\ensuremath{\omega}/n$, with $n$ being an integer. It is a nonintuitive phenomenon since the external repetition rate has no quantum character, yet the atom responds to it, if the rate is equal to $1/n$ of its eigenfrequency. This result is in good agreement with recent magnetometer experiments. It is also found that other resonances are possible at pulse-repetition-rate frequencies equal to $1/n$ of combination frequencies involving the internal system frequencies and Rabi frequencies. We show that quantum-interference-related phenomena of gain without population inversion and absorption with inversion are observed at these unique resonances. Fractional quantum resonances provide a spectroscopy tool, allowing us to measure optical frequency on one transition through detection of resonances on another transition. We believe that our results will have implications in other quantum-related processes, such as laser-assisted resonant enhancement of chemical reactions and biological processes.

Low-energy electron-impact cross sections of helium among the ground and some low excited states are calculated using the $R$-matrix method. The convergences of the cross sections are checked systematically by using five sets of high-quality target states; i.e., including 5, 11, 19, 29, and 39 physical target states, respectively. Our calculated cross sections are in excellent agreement with the benchmark high-resolution experimental data. Compared with the recommended theoretical data, there is a deviation of about 6%, which suggests the recommended data may need a revision. Based on our calculation results, the influence of the Rydberg target states on the collision cross sections of the excited states is found to be similar to the case of the ground state; i.e., the amplitude of resonance structures will decrease with respect to the principal quantum number $n$ of Rydberg target states. This result should be very useful for providing the cross-section data in the whole energy regions with high quality, which would be of great importance in related scientific fields.

The resonant process of dielectronic recombination (DR) has been applied as a spectroscopic tool to investigate intra-$L$-shell excitations $2s\ensuremath{-}2{p}_{j}$ in Li-like ${}^{136}{\text{Xe}}^{51}+$. The experiments were carried out at the electron cooler of the Experimental Storage Ring of the GSI-Helmholtzzentrum f\"ur Schwerionenforschung, Darmstadt, Germany. The observed center-of-mass energy range (0--505 eV) covers all resonances associated with the $2s+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{(2{p}_{1/2}n{l}_{j})}_{J}$ and ${(2{p}_{3/2}n{l}_{j})}_{J}$ DR processes. Energies and strengths of isolated $2{p}_{1/2}n$ and $2{p}_{3/2}n$ DR-resonance groups were obtained for principal quantum numbers $n$ up to 43 and 36, respectively. The $2s\ensuremath{-}2{p}_{1/2}$ and $2s\ensuremath{-}2{p}_{3/2}$ excitation energies were deduced to be 119.816(42) eV and 492.174(52) eV. The excitation energies are compared with previous measurements of other groups and with recent QED calculations. In addition, the experimental spectra and extracted resonance strengths are compared with multiconfiguration Dirac-Fock calculations. Measurements and theory are found to be in good agreement with each other.

We study the effects of Rydberg-atom interactions on Autler-Townes (AT) spectra in a dense gas of ultracold cesium atoms. The $6{S}_{1/2}$ and $6{P}_{3/2}$ levels of cesium are strongly coupled (Rabi frequency ${\ensuremath{\Omega}}_{c})$, and the resultant AT spectra are probed via excitation into a Rydberg level. Van der Waals interactions between the atoms in the probe Rydberg level give rise to a dephasing rate $({\ensuremath{\gamma}}_{3})$. The interaction-induced dephasing is found to cause characteristic changes in the AT spectra, including a reduction or elimination of the AT splitting, an increase in the critical ${\ensuremath{\Omega}}_{c}$ above which AT splitting occurs, and an increase in the width of the AT spectral lines. Rydberg-atom interactions are controlled by varying the principal quantum number $n$ of the probe Rydberg level; larger values of $n$ correspond to higher dephasing rates ${\ensuremath{\gamma}}_{3}$. Results of numerical calculations are in good agreement with the experiments.

Antihydrogen production has reached such a level that precision spectroscopic measurements of its properties are within reach. In particular, the ground-state level population is of central interest for experiments aiming at antihydrogen spectroscopy. The positron density and temperature dependence of the ground-state yield is a result of the interplay between recombination, collisional, and radiative processes. Considering the fact that antihydrogen atoms with the principal quantum number n=15 or lower quickly cascade down to the ground state within 1ms, the number of such states are adopted as a measure of useful antihydrogen atoms. It has been found that the scaling behaviour of the useful antihydrogen yield is different depending on the positron density and positron temperature.

The non-integrable Dicke model and its integrable approximation, the Tavis-Cummings (TC) model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the previous paper by focusing on the statistical properties of the quantum fluctuations in the energy spectrum and their relation with the excited state quantum phase transitions (ESQPT). These properties are compared with the dynamics observed in the semi-classical versions of the models. The presence of chaos for different energies and coupling constants is exhibited, employing Poincar\'e sections and Peres lattices in the classical and quantum versions, respectively. A clear correspondence between the classical and quantum result is found for systems containing between $\mathcal{N} = 80$ to $200$ atoms. A measure of the Wigner character of the energy spectrum for different couplings and energy intervals is also presented employing the statistical Anderson-Darling test. It is found that in the Dicke Model, for any coupling, a low energy regime with regular states is always present. The richness of the onset of chaos is discussed both for finite quantum systems and for the semi-classical limit, which is exact when the number of atoms in the system tends to infinite.

The optical Ramsey method is employed to investigate molecular electron wave-packet dynamics in the angular coordinate. Time-resolved spectra are presented for vibrationally autoionizing Rydberg electron wave packets with principal quantum numbers $n=17\char21{}21,$ excited between the ${v}^{+}=0$ and ${v}^{+}=1$ ionization limits, in the presence of electric fields in the range 0.7\char21{}1.4 kV ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. A regular, almost dispersion-free beating in the angular coordinate is observed for wave packets created using light which is polarized perpendicular to the direction of the external dc electric field.

Stabilization of autoionizing states of barium by laser-induced, stimulated emission of light is demonstrated. Relative to purely flourescent stabilization, the data clearly show an enhancement of the stabilization process for laser pulses short compared to the flourescent lifetime of the autoionizing states. Shakeup spectra in which the principal quantum number of both electrons changes during the stimulated emission process are also clearly demonstrated.

High-power, nearly unipolar electromagnetic-field pulses are a useful spectroscopic tool, in particular for studying the dynamics of weakly bound Rydberg electrons. Various experimental @1‐3# and theoretical @4,5# investigations on the interaction between Rydberg atoms and half-cycle pulses ~HCPs! have already been performed. In particular, the theoretical approaches that have been used so far involve either fully quantum-mechanical calculations, purely classical simulations, or simplified one-dimensional model problems. Fully quantum-mechanical treatments are capable of yielding quantitatively exact results, but due to the large spatial extension of highly excited Rydberg states they demand a huge computational effort. Furthermore, they allow only for a restricted qualitative understanding of the system, in general. Purely classical approaches are of interest, as they yield insight into the underlying classical aspects of the motion of the Rydberg electron. But they cannot deal properly with quantum-mechanical interference effects and are therefore also of limited applicability. One-dimensional model problems, finally, are not capable of describing all spatial aspects of the excitation process. Thus the natural question arises whether a proper three-dimensional theoretical description of the excitation process can be developed that is numerically highly accurate even for very large principal quantum numbers, which gives direct insight into the underlying classical aspects of the dynamics of the Rydberg electron and which is capable of dealing with all quantum-mechanical interference phenomena properly. In this Rapid Communication it is shown that such a theoretical description can be developed on the basis of a multidimensional semiclassical description of the excitation process. This approach is easily applicable to any spatial or temporal pulse form of the exciting HCP, and it is particularly accurate in the region of high principal quantum numbers, which is difficult to access by fully quantummechanical calculations. Based on this treatment different oscillatory structures are discussed, which appear in energyand angle-resolved ionization spectra and which should be accessible to experimental observation in view of the recently developed imaging method @6#. It is shown that these structures are caused by quantum-mechanical interferences between probability amplitudes that can be associated with classical trajectories of the ionized Rydberg electron. In order to demonstrate the numerical accuracy of the multidimensional semiclassical approach a comparison with numerical results is presented in the impulse approximation. Modifications of these oscillatory structures due to finite pulse durations are also discussed. Let us consider a typical HCP-excitation process. Initially an atom is prepared in a Rydberg state un0l 0m0& with a large principal quantum number n0@1 and a small angularmomentum quantum number l 0!n0. Around t50 a linearly polarized HCP with vector potential A(x,t)ez and duration t interacts with the Rydberg electron. The time evolution of the state c(x,t) of the Rydberg electron is determined by the ‘

We investigate the photon statistics of the light transmitted from a driven optical cavity containing N two-level atoms, with emphasis on the weak driving field limit. This limit is of most interest from the point of view of quantum fluctuations. We find that various types of nonclassical behavior are possible, even with large numbers of atoms in the cavity, under conditions of strong atom-field coupling, which we refer to as the cavity quantum electrodynamics limit. We describe the system with a pure-state formalism valid for weak fields, and also use a Fokker-Planck equation obtained by a small fluctuation linearization. We examine the conditions under which the linearized theory is appropriate, and explore the sensitivity of nonclassical effects in the system to atom number, transit-time broadening, and detunings. @S1050-2947~99!04803-9#

Single and double electron capture from He targets by ${\mathrm{Ar}}^{16+}$ ions have been studied at projectile velocities from 0.3 to 1.5 a.u. Cold-target recoil-ion momentum spectroscopy was used to record the energy gain and scattering angle simultaneously. For single capture, the reaction window is found to spread in width approximately as the square root of the projectile velocity and to shift slightly toward smaller energy-gain values as the velocity increases. The angular distributions center at the half Coulomb angle over most of the velocity range covered, but differ in shape from multichannel Landau-Zener model results. For double capture, transfer ionization dominates and feeds primarily $n$-symmetric states, where n is the principal quantum number. True double capture feeds mainly $n$-asymmetric states. The angular distributions for double capture lie outside the half Coulomb angle, indicating the importance of two-step processes in populating doubly excited states.