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We review Rydberg aggregates, assemblies of a few Rydberg atoms exhibiting energy transport through collective eigenstates, considering isolated atoms or assemblies embedded within clouds of cold ground-state atoms. We classify Rydberg aggregates, and provide an overview of their possible applications as quantum simulators for phenomena from chemical or biological physics. Our main focus is on flexible Rydberg aggregates, in which atomic motion is an essential feature. In these, simultaneous control over Rydberg-Rydberg interactions, external trapping and electronic energies, allows Born-Oppenheimer surfaces for the motion of the entire aggregate to be taylored as desired. This is illustrated with theory proposals towards the demonstration of joint motion and excitation transport, conical intersections and non-adiabatic effects. Additional flexibility for quantum simulations is enabled by the use of dressed dipole-dipole interactions or the embedding of the aggregate in a cold gas or BEC environment. Finally we provide some guidance regarding the parameter regimes that are most suitable for the realization of either static or flexible Rydberg aggregates based on Li or Rb atoms. The current status of experimental progress towards enabling Rydberg aggregates is also reviewed., Comment: 32 pages, 14 figures, review article, feedback welcome

Nano-mechanical oscillators as well as Rydberg-atomic waveguides hosted on micro-fabricated chip surfaces hold promise to become pillars of future quantum technologies. In a hybrid platform with both, we show that beams of Rydberg atoms in waveguides can quantum-coherently interrogate and manipulate nanomechanical elements, allowing full quantum state tomography. Central to the tomography are quantum non-demolition measurements using the Rydberg atoms as probes. Quantum coherent displacement of the oscillator is also made possible, by driving the atoms with external fields while they interact with the oscillator. We numerically demonstrate the feasibility of this fully integrated on-chip control and read-out suite for quantum nano-mechanics, taking into account noise and error sources., Comment: 11 pages, 5 figures, 1 table

We provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. We show that the long-range character of these interactions does not further increase the limitations of these methods, in contrast to the situation for alternatives such as the density matrix renormalisation group. Furthermore, stochastic gauge techniques can also successfully extend simulation times in the long-range-interaction case, by making using of parameters that affect the noise properties of trajectories, without affecting physical observables. We derive essential results that significantly aid the use of these methods: estimates of the available simulation time, optimized stochastic gauges, a general form of the characteristic stochastic variance and adaptations for very large systems. Testing the performance of particular drift and diffusion gauges for nonlocal interactions, we find that, for small to medium systems, drift gauges are beneficial, whereas for sufficiently large systems, it is optimal to use only a diffusion gauge. The methods are illustrated with direct numerical simulations of interaction quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg states in a Bose-Einstein condensate, also without the need for the typical frozen gas approximation. We demonstrate that gauges can indeed lengthen the useful simulation time., Comment: 19 pages, 11 appendix, 3 figures

We demonstrate that through localised Rydberg excitation in a three-dimensional cold atom cloud atomic motion can be rendered directed and nearly confined to a plane, without spatial constraints for the motion of individual atoms. This enables creation and observation of non-adiabatic electronic Rydberg dynamics in atoms accelerated by dipole-dipole interactions under natural conditions. Using the full $l=0,1$ $m=0,\pm1$ angular momentum state space, our simulations show that conical intersection crossings are clearly evident, both in atomic position information and excited state spectra of the Rydberg system. Hence, flexible Rydberg aggregates suggest themselves for probing quantum chemical effects in experiments on length scales much inflated as compared to a standard molecular situation., Comment: 10 pages, 8 figures. arXiv admin note: text overlap with arXiv:1612.07858

We study the link between atomic motion and exciton transport in flexible Rydberg aggregates, assemblies of highly excited light alkali atoms, for which motion due to dipole-dipole interaction becomes relevant. In two one-dimensional atom chains crossing at a right angle adiabatic exciton transport is affected by a conical intersection of excitonic energy surfaces, which induces controllable non-adiabatic effects. A joint exciton/motion pulse that is initially governed by a single energy surface is coherently split into two modes after crossing the intersection. The modes induce strongly different atomic motion, leading to clear signatures of non-adiabatic effects in atomic density profiles. We have shown how this scenario can be exploited as an exciton switch, controlling direction and coherence properties of the joint pulse on the second of the chains [K.~Leonhardt {\it et al.}, Phys.~Rev.~Lett. {\bf 113} 223001 (2014)]. In this article we discuss the underlying complex dynamics in detail, characterise the switch and derive our isotropic interaction model from a realistic anisotropic one with the addition of a magnetic bias field., Comment: 14 pages, 12 figures

We theoretically investigate the coupling of an ultracold three-level atomic gas and a nano-mechanical mirror via classical electromagnetic radiation. The radiation pressure on the mirror is modulated by absorption of a probe light field, caused by the atoms which are electromagnetically rendered nearly transparent, allowing the gas to affect the mirror. In turn, the mirror can affect the gas as its vibrations generate opto-mechanical sidebands in the control field. We show that the sidebands cause modulations of the probe intensity at the mirror frequency, which can be enhanced near atomic resonances. Through the radiation pressure from the probe beam onto the mirror, this results in resonant driving of the mirror. Controllable by the two photon detuning, the phase relation of the driving to the mirror motion decides upon amplification or damping of mirror vibrations. This permits direct phase locking of laser amplitude modulations to the motion of a nano-mechanical element opening a perspective for cavity-free cooling through coupling to an atomic gas., Comment: 8 pages, 5 figs

Electrons released from clusters through strong Xray pulses show broad kinetic-energy spectra, extending from the atomic excess energy down to the threshold, where usually a strong peak appears. These low-energy electrons are normally attributed to evaporation from the nano-plasma formed in the highly-charged clusters. Here, it is shown that also directly emitted photo electrons generate a pronounced spectral feature close to threshold. Furthermore, we give an analytical approximation for the direct photo-electron spectrum., Comment: 8 pages, 3 figures

Exciton pulses transport excitation and entanglement adiabatically through Rydberg aggregates, assemblies of highly excited light atoms, which are set into directed motion by resonant dipole-dipole interaction. Here, we demonstrate the coherent splitting of such pulses as well as the spatial segregation of electronic excitation and atomic motion. Both mechanisms exploit local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The intersection provides a sensitive knob controlling the propagation direction and coherence properties of exciton pulses. The fundamental ideas discussed here have general implications for excitons on a dynamic network., Comment: Letter with 4 pages and 4 figures. Supplemental material with 4 pages and 4 figures

Two ultracold atom clouds, each separately in a dipole-blockade regime, realize a source of entangled atom pairs that can be ejected on demand. Entanglement generation and ejection is due to resonant dipole-dipole interactions, while van-der-Waals interactions are predominantly responsible for the blockade that ensures the ejection of a single atom per cloud. A source of entangled atoms using these effects can operate with a 10 kHz repetition rate producing ejected atoms with velocities of about 0.5 m/s., Comment: 7 pages, 4 figures

We consider two clouds of ground state alkali atoms in two distinct hyperfine ground states. Each level is far off-resonantly coupled to a Rydberg state, which leads to dressed ground states with a weak admixture of the Rydberg state properties. Due to this admixture, for a proper choice of the Rydberg states, the atoms experience resonant dipole-dipole interactions that induce mechanical forces acting on all atoms within both clouds. This behavior is in contrast to the dynamics predicted for bare dipole-dipole interactions between Rydberg superatoms, where only a single atom per cloud is subject to dipole-dipole induced motion [Phys. Rev. A {\bf 88} 012716 (2013)]., Comment: 15 pages, 2 figures

At the free-electron laser FLASH, multiple ionization of neon atoms was quantitatively investigated at 93.0 eV and 90.5 eV photon energy. For ion charge states up to 6+, we compare the respective absolute photoionization yields with results from a minimal model and an elaborate description. Both approaches are based on rate equations and take into acccout a Gaussian spatial intensity distribution of the laser beam. From the comparison we conclude, that photoionization up to a charge of 5+ can be described by the minimal model. For higher charges, the experimental ionization yields systematically exceed the elaborate rate based prediction., Comment: 10 pages, 3 figures

In Rydberg dressed ultra-cold gases, ground state atoms inherit properties of a weakly admixed Rydberg state, such as sensitivity to long-range interactions. We show that through hyperfine-state dependent interactions, a pair of atom clouds can evolve into a spin and subsequently into a spatial Schr\"odinger's cat state: The pair, containing 20 atoms in total, is in a coherent superposition of two configurations, with cloud locations separated by micrometers. The mesoscopic nature of the superposition state can be proven with absorption imaging, while the coherence can be revealed though recombination and interference of the split wave packets., Comment: 4(+2) pages, 3 figures

We demonstrate ultrafast resonant energy absorption of rare-gas doped He nanodroplets from intense few-cycle (~10 fs) laser pulses. We find that less than 10 dopant atoms "ignite" the droplet to generate a non-spherical electronic nanoplasma resulting ultimately in complete ionization and disintegration of all atoms, although the pristine He droplet is transparent for the laser intensities applied. Our calculations at those intensities reveal that the minimal pulse length required for ignition is about 9 fs.

A simple, semi-analytical model is proposed for non-relativistic Coulomb explosion of a uniformly charged spheroid. This model allows us to derive the time-dependent particle energy distributions. Simple expressions are also given for the characteristic explosion time and maximum particle energies in the limits of extreme prolate and oblate spheroids as well as for the sphere. Results of particle simulations are found to be in remarkably good agreement with the model., Comment: 11 pages, 10 figures

We consider the interplay between excitonic and atomic motion in a regular, flexible chain of Rydberg atoms, extending our recent results on entanglement transport in Rydberg chains [W\"uster et al., Phys.Rev.Lett 105 053004 (2010)]. In such a Rydberg chain, similar to molecular aggregates, an electronic excitation is delocalised due to long range dipole-dipole interactions among the atoms. The transport of an exciton that is initially trapped by a chain dislocation is strongly coupled to nuclear dynamics, forming a localised pulse of combined excitation and displacement. This pulse transfers entanglement between dislocated atoms adiabatically along the chain. Details about the interaction and the preparation of the initial state are discussed. We also present evidence that the quantum dynamics of this complex many-body problem can be accurately described by selected quantum-classical methods, which greatly simplify investigations of excitation transport in flexible chains.

Based on a combined quantum-classical treatment, a complete study of the strong field dynamics of H2+, i.e. including all nuclear and electronic DOF as well as dissociation and ionization, is presented. We find that the ro-vibrational nuclear dynamics enhances dissociation and, at the same time, suppresses ionization, confirming experimental observations by I. Ben-Itzhak et al. [Phys. Rev. Lett. 95, 073002 (2005)]. In addition and counter-intuitively, it is shown that for large initial vibrational excitation ionization takes place favorably at large angles between the laser polarization and molecular axis. A local ionization model delivers a transparent explanation of these findings., Comment: 10 pages, 5 figures

We show how to create long range interactions between alkali-atoms in different hyper-fine ground states, allowing coherent electronic quantum state migration. The scheme uses off resonant dressing with atomic Rydberg states, exploiting the dipole-dipole excitation transfer that is possible between those. Actual population in the Rydberg state is kept small. Dressing offers large advantages over the direct use of Rydberg levels: It reduces ionisation probabilities and provides an additional tuning parameter for life-times and interaction-strengths. We present an effective Hamiltonian for the ground-state manifold and show that it correctly describes the full multi-state dynamics for up to 5 atoms., Comment: 22 pages + 6 pages appendices, 8 figures, replaced with revised version, added journal reference

We find that energy surfaces of more than two atoms or molecules interacting via dipole-dipole po- tentials generically possess conical intersections (CIs). Typically only few atoms participate strongly in such an intersection. For the fundamental case, a circular trimer, we show how the CI affects adiabatic excitation transport via electronic decoherence or geometric phase interference. These phe- nomena may be experimentally accessible if the trimer is realized by light alkali atoms in a ring trap, whose dipole-dipole interactions are induced by off-resonant dressing with Rydberg states. Such a setup promises a direct probe of the full many-body density dynamics near a conical intersection., Comment: 4 pages, 4 figures, replacement to add archive reference

In a regular, flexible chain of Rydberg atoms, a single electronic excitation localizes on two atoms that are in closer mutual proximity than all others. We show how the interplay between excitonic and atomic motion causes electronic excitation and diatomic proximity to propagate through the Rydberg chain as a combined pulse. In this manner entanglement is transferred adiabatically along the chain, reminiscent of momentum transfer in Newton's cradle., Comment: 4 pages, 3 figures. Revised version

Quantum reflection is a pure wave phenomena that predicts reflection of a particle at a changing potential for cases where complete transmission occurs classically. For a chemical bond, we find that this effect can lead to non-classical vibrational turning points and bound states at extremely large interatomic distances. Only recently has the existence of such ultralong-range Rydberg molecules been demonstrated experimentally. Here, we identify a broad range of molecular lines, most of which are shown to originate from two different novel sources: a single-photon associated triatomic molecule formed by a Rydberg atom and two ground state atoms and a series of excited dimer states that are bound by a so far unexplored mechanism based on internal quantum reflection at a steep potential drop. The properties of the Rydberg molecules identified in this work qualify them as prototypes for a new type of chemistry at ultracold temperatures., Comment: 6 pages, 3 figures, 1 table

We show that Rydberg states in an ultra-cold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002]. Near to the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius half-way through the pulse. These correlations lead to large deviations of the atom counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. We finally demonstrate the utility of the omega-expansion for the approximate description of correlation dynamics through an echo sequence., Comment: 8 pages, 6 figures

"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures, related to the distribution of the finite time Lyapunov exponents. We study systematically standard maps from the uncoupled two-dimensional case up to coupled maps of dimension $20$. We find that sticky motion in all unstable directions above a threshold $K_{d}$ of the nonlinearity parameter $K$ for the high dimensional cases $d=10,20$. Moreover, as $K$ increases we can clearly identify the transition from quasiregular to totally chaotic motion which occurs simultaneously in all unstable directions. The results show that all four statistical measures sensitively probe sticky motion in high dimensional systems., Comment: 17 pages, 14 figures, submitted

We investigate theoretically electron dynamics under a VUV attosecond pulse train which has a controlled phase delay with respect to an additional strong infrared laser field. Using the strong field approximation and the fact that the attosecond pulse is short compared to the excited electron dynamics, we arrive at a minimal analytical model for the kinetic energy distribution of the electron as well as the photon absorption probability as a function of the phase delay between the fields. We analyze the dynamics in terms of electron wave packet replicas created by the attosecond pulses. The absorption probability shows strong modulations as a function of the phase delay for VUV photons of energy comparable to the binding energy of the electron, while for higher photon energies the absorption probability does not depend on the delay, in line with the experimental observations for helium and argon, respectively., Comment: 14 pages, 8 figures

We show that nuclear motion of Rydberg atoms can be induced by resonant dipole-dipole interactions that trigger the energy transfer between two energetically close Rydberg states. How and if the atoms move depends on their initial arrangement as well as on the initial electronic excitation. Using a mixed quantum/classical propagation scheme we obtain the trajectories and kinetic energies of atoms, initially arranged in a regular chain and prepared in excitonic eigenstates. The influence of off-diagonal disorder on the motion of the atoms is examined and it is shown that irregularity in the arrangement of the atoms can lead to an acceleration of the nuclear dynamics.

Ultracold neutral plasmas, formed by photoionizing laser-cooled atoms near the ionization threshold, have electron temperatures in the 1-1000 kelvin range and ion temperatures from tens of millikelvin to a few kelvin. They represent a new frontier in the study of neutral plasmas, which traditionally deals with much hotter systems, but they also blur the boundaries of plasma, atomic, condensed matter, and low temperature physics. Modelling these plasmas challenges computational techniques and theories of non-equilibrium systems, so the field has attracted great interest from the theoretical and computational physics communities. By varying laser intensities and wavelengths it is possible to accurately set the initial plasma density and energy, and charged-particle-detection and optical diagnostics allow precise measurements for comparison with theoretical predictions. Recent experiments using optical probes demonstrated that ions in the plasma equilibrate in a strongly coupled fluid phase. Strongly coupled plasmas, in which the electrical interaction energy between charged particles exceeds the average kinetic energy, reverse the traditional energy hierarchy underlying basic plasma concepts such as Debye screening and hydrodynamics. Equilibration in this regime is of particular interest because it involves the establishment of spatial correlations between particles, and it connects to the physics of the interiors of gas-giant planets and inertial confinement fusion devices., Comment: 89 pages, 54 images

The main difficulty in utilizing the O(4) symmetry of the Hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wave functions of the states with different energies are proportional to the hyperspherical harmonics (HSH) corresponding to different points on the hypersphere. Thus, the calculation of the matrix elements reduces to the problem of re-expanding HSH in terms of HSH depending on different points on the hypersphere. We solve this problem by applying the technique of multipole expansions for four-dimensional HSH. As a result, we obtain the multipole expansions whose coefficients are the matrix elements of the boost operator taken between hydrogen wave functions (i.e. hydrogen form-factors). The explicit expressions for those coefficients are derived. It is shown that the hydrogen matrix elements can be presented as derivatives of an elementary function. Such an operator representation is convenient for the derivation of recurrency relations connecting matrix elements between states corresponding to different values of the quantum numbers $n$ and $l$., Comment: 26 pages, 2 figures

We investigate the strongly correlated ion dynamics and the degree of coupling achievable in the evolution of freely expanding ultracold neutral plasmas. We demonstrate that the ionic Coulomb coupling parameter $\Gamma_{\rm i}$ increases considerably in later stages of the expansion, reaching the strongly coupled regime despite the well-known initial drop of $\Gamma_{\rm i}$ to order unity due to disorder-induced heating. Furthermore, we formulate a suitable measure of correlation and show th at $\Gamma_{\rm i}$ calculated from the ionic temperature and density reflects the degree of order in the system if it is sufficiently close to a quasisteady state. At later times, however, the expansion of the plasma cloud becomes faster than the relaxation of correlations, and the system does not reach thermodynamic equilibrium anymore.

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.

The ionization dynamics of a Xenon cluster with 40 atoms is analyzed under a pum p probe scenario of laser pulses where an infrared laser pulse of 50 fs length follows with a well defined time delay a VUV pulse of the same length and peak intensity. The mechanism of resonant energy absorption due to the coinc idence of the IR laser frequency with the frequency of collective motion of quasi free electrons in the cluster is mapped out by varying the time delay between the pulses.

We show that the dependence of high-order harmonic generation (HHG) on the molecular orientation can be understood within a theoretical treatment that does not involve the strong field of the laser. The results for H_2 show excellent agreement with time-dependent strong field calculations for model molecules, and this motivates a prediction for the orientation dependence of HHG from the N_2 3s_g valence orbital. For both molecules, we find that the polarization of recombination photons is influenced by the molecular orientation. The variations are particularly pronounced for the N_2 valence orbital, which can be explained by the presence of atomic p-orbitals., Comment: 6 pages 7 figures

A kinetic approach for the evolution of ultracold neutral plasmas including interionic correlations and the treatment of ionization/excitation and recombination/deexcitation by rate equations is described in detail. To assess the reliability of the approximations inherent in the kinetic model, we have developed a hybrid molecular dynamics method. Comparison of the results reveals that the kinetic model describes the atomic and ionic observables of the ultracold plasma surprisingly well, confirming our earlier findings concerning the role of ion-ion correlations [Phys. Rev. A {\bf 68}, 010703]. In addition, the molecular dynamics approach allows one to study the relaxation of the ionic plasma component towards thermodynamical equilibrium.

Recent experiments with ultracold neutral plasmas show an intrinsic heating effect based on the development of spatial correlations. We investigate whether this effect can be reversed, so that imposing strong spatial correlations could in fact lead to cooling of the ions. We find that cooling is indeed possible. It requires, however, a very precise preparation of the initial state. Quantum mechanical zero-point motion sets a lower limit for ion cooling.

We present long-time simulations of expanding ultracold neutral plasmas, including a full treatment of the strongly coupled ion dynamics. Thereby, the relaxation dynamics of the expanding laser-cooled plasma is studied, taking into account elastic as well as inelastic collisions. It is demonstrated that, depending on the initial conditions, the ionic component of the plasma may exhibit short-range order or even a superimposed long-range order resulting in concentric ion shells. In contrast to ionic plasmas confined in traps, the shell structures are built up from the center of the plasma cloud rather than from the periphery.

We develop a microscopic model for the interaction of small rare gas clusters with soft X-ray radiation. It is shown that, while the overall charging of the clusters is rather low, unexpectedly high atomic charge states can arise due to charge imbalances inside the cluster. The mechanism does not require unusually high absorption rates, and the heating can be described by standard inverse bremsstrahlung formulae., Comment: 4 pages, 4 figures

We numerically compare the semiclassical ``frozen Gaussian'' Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the ``thawed Gaussian'' propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear one-dimensional potentials. The reasons for the lack of long time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy., Comment: 14 pages, 4 figures, corrected typos and figure 1 (d)

The role of shake-off for double ionization of atoms by a single photon with finite energy has become the subject of debate. In this letter, we attempt to clarify the meaning of shake-off at low photon energies by comparing different formulations appearing in the literature and by suggesting a working definition. Moreover, we elaborate on the foundation and justification of a mixed quantum-classical ansatz for the calculation of single-photon double ionization.

A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given., Comment: 4 pages, 3 figures

We account for the different symmetries of the 2^{1,3}S helium excited states in a quasiclassical description of the knockout mechanism augmented by a quantum shakeoff contribution. We are thus able to formulate the separate contribution of the knockout and shakeoff mechanisms for double photoionization for any excess energy from the 2^{1,3}S states. Photoionization ratios and singly differential cross sections calculated for the 2^{1,3}S excited states of helium are found to be in very good agreement with recent theoretical results., Comment: 9 pages, 5 figures

Recent experiments have demonstrated the spontaneous evolution of a gas of ultracold Rydberg atoms into an expanding ultracold plasma, as well as the reverse process of plasma recombination into highly excited atomic states. Treating the evolution of the plasma on the basis of kinetic equations, while ionization/excitation and recombination are incorporated using rate equations, we have investigated theoretically the Rydberg-to-plasma transition. Including the influence of spatial correlations on the plasma dynamics in an approximate way we find that ionic correlations change the results only quantitatively but not qualitatively.

Solving the one-dimensional time-dependent Schr\"odinger equation for simple model potentials, we investigate resonance-enhanced high-order harmonic generation, with emphasis on the physical mechanism of the enhancement. By truncating a long-range potential, we investigate the significance of the long-range tail, the Rydberg series, and the existence of highly excited states for the enhancements in question. We conclude that the channel closings typical of a short-range or zero-range potential are capable of generating essentially the same effects., Comment: 7 pages revtex, 4 figures (ps files)