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A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials., (© 2022. The Author(s).)

The use of autoionization as a tool to quantitatively analyze transitions between high-n strontium Rydberg states with low-to-intermediate values of L is described and is demonstrated through observations of Rabi oscillations when driving 5snf 1 F 3 → 5s(n + 1)g 1 G 4 , 5snf 1 F 3 → 5s(n + 2)h 1 H 5 , and 5snp 1 P 1 → 5s(n + 1)d 1 D 2 transitions using microwave fields. The technique is shown to offer advantages when compared to selective field ionization and can be used with other alkaline-earth and alkaline-earth-like metals.

Earlier studies of the velocity distributions of heavy-Rydberg ion-pair states formed in collisions between potassium Rydberg atoms with low-to-intermediate values of n , 10 ≲ n ≲ 15, and targets that attach free low-energy electrons have shown that such measurements can provide a window into the dynamics of dissociative electron capture. Here we propose that the reaction dynamics can be explored in much greater detail through studies using hyperthermal Rydberg atoms. This is demonstrated using, as an example, helium Rydberg atoms and a semi-classical Monte Carlo collision code developed specifically to model the dynamics of Rydberg electron transfer in collisions between Rydberg atoms and attaching targets. The simulations show that the outcome of collisions is sensitive not only to the lifetime and decay energetics of the excited intermediate negative ion formed upon initial Rydberg electron capture but also to the radial electron probability density distribution in the Rydberg atom itself, i.e., to its ℓ value.

We report spectroscopic observation of Rydberg polarons in an atomic Bose gas. Polarons are created by excitation of Rydberg atoms as impurities in a strontium Bose-Einstein condensate. They are distinguished from previously studied polarons by macroscopic occupation of bound molecular states that arise from scattering of the weakly bound Rydberg electron from ground-state atoms. The absence of a p-wave resonance in the low-energy electron-atom scattering in Sr introduces a universal behavior in the Rydberg spectral line shape and in scaling of the spectral width (narrowing) with the Rydberg principal quantum number, n. Spectral features are described with a functional determinant approach (FDA) that solves an extended Fröhlich Hamiltonian for a mobile impurity in a Bose gas. Excited states of polyatomic Rydberg molecules (trimers, tetrameters, and pentamers) are experimentally resolved and accurately reproduced with a FDA.

Electron transfer in collisions between low-n, n = 12, Rydberg atoms and targets that attach low-energy electrons can lead to the formation of heavy-Rydberg ion-pair states comprising a weakly-bound positive-negative ion pair that orbit each other at large separations. Measurements of the velocity and angular distribution of ion-pair states produced in collisions with 1,1,1-C 2 Cl 3 F 3 , CBrCl 3 , BrCN, and Fe(CO) 5 are used to show that electron transfer reactions furnish a new technique with which to examine the lifetime and decay energetics of the excited intermediates formed during dissociative electron capture. The results are analyzed with the aid of Monte Carlo simulations based on the free electron model of Rydberg atom collisions. The data further highlight the capabilities of Rydberg atoms as a microscale laboratory in which to probe the dynamics of electron attachment reactions.

We develop an approach to generate finite-range atomic interactions via optical Rydberg-state excitation and study the underlying excitation dynamics in theory and experiment. In contrast to previous work, the proposed scheme is based on resonant optical driving and the establishment of a dark state under conditions of electromagnetically induced transparency (EIT). Analyzing the driven dissipative dynamics of the atomic gas, we show that the interplay between coherent light coupling, radiative decay, and strong Rydberg-Rydberg atom interactions leads to the emergence of sizable effective interactions while providing remarkably long coherence times. The latter are studied experimentally in a cold gas of strontium atoms for which the proposed scheme is most efficient. Our measured atom loss is in agreement with the theoretical prediction based on binary effective interactions between the driven atoms.

The dynamics of formation of heavy-Rydberg ion-pair states through electron transfer in K(np)-SF6, CCl4 collisions is examined by measuring the velocity, angular, and binding energy distributions of the product ion pairs. The results are analyzed with the aid of a Monte Carlo collision code that models both the initial electron capture and the subsequent evolution of the ion pairs. The model simulations are in good agreement with the experimental data and highlight the factors such as Rydberg atom size, the kinetic energy of relative motion of the Rydberg atom and target particle, and (in the case of attaching targets that dissociate) the energetics of dissociation that can be used to control the properties of the product ion-pair states.

We demonstrate that circular wave packets in high Rydberg states generated by a pulsed electric field applied to extreme Stark states are characterized by a position-dependent energy gradient that leads to a correlation between the principal quantum number n and the spatial coordinate. This correlation is rather insensitive to the initial state and can be seen even in an incoherent mix of states such as is generated experimentally allowing information to be placed into, and extracted from, such wave packets. We show that detailed information on the spatial distribution of a circular wave packet can be extracted by analyzing the complex phase of its expansion coefficients.

Nondispersive localized Trojan wave packets with n(i) ~ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n(f) ~ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.

We present an experimental and theoretical study of the chaotic ionization of quasi-one-dimensional potassium Rydberg wave packets via a classical phase-space turnstile mechanism. Turnstiles form a general transport mechanism for numerous chaotic systems, and this study explicitly illuminates their relevance to atomic ionization. We create time-dependent Rydberg wave packets, subject them to alternating applied electric-field pulses, and measure the electron survival probability. Ionization depends not only on the initial electron energy, but also on the classical phase-space position of the electron with respect to the turnstile--that part of the electron packet inside the turnstile ionizes after the applied ionization sequence, while that part outside the turnstile does not. The survival data thus encode information on the shape and location of the turnstile, in good agreement with theoretical predictions.

A classical trajectory Monte Carlo approach is used to simulate the dissociation of H(+)⋅⋅⋅F(-) and K(+)⋅⋅⋅Cl(-) heavy Rydberg ion pairs induced by a ramped electric field, a technique used experimentally to detect and probe ion-pair states. Simulations that include the effects of the strong short-range repulsive interaction associated with ion-pair scattering are in good agreement with experimental results for Stark wavepackets probed by a ramped field, demonstrating that many of the characteristics of field-induced dissociation can be well described using a quasi-classical model. The data also show that states with a given value of principal quantum number (i.e., binding energy) can dissociate over a broad range of applied fields, the exact field being governed by the initial orbital angular momentum and orientation of the state.

The lifetimes of K(+)..Cl(-), K(+)..CN(-), and K(+)..SF(6)(-) heavy-Rydberg ion-pair states produced through Rydberg electron transfer reactions are measured directly as a function of binding energy using electric field induced detachment and the ion-pair decay channels discussed. The data are interpreted using a Monte Carlo collision code that models the detailed kinematics of electron transfer reactions. The lifetimes of K(+)..Cl(-) ion-pair states are observed to be very long, >100 micros, and independent of binding energy. The lifetimes of strongly bound (>30 meV) K(+)..CN(-) ion pairs are found to be similarly long but begin to decrease markedly as the binding energy is reduced below this value. This behavior is attributed to conversion of rotational energy in the CN(-) ion into translational energy of the ion pair. No long-lived K(+)..SF(6)(-) ion pairs are observed, their lifetimes decreasing with increasing binding energy. This behavior suggests that ion-pair loss is associated with mutual neutralization as a result of charge transfer.

Electron transfer in K(np)-C(2)Cl(4) collisions, which leads to formation of both Cl(-) and C(2)Cl(4)(-) anions, is investigated as a function of target temperature over the range of 300-650 K. Measurements at high n (n approximately 30) show that the likelihood of Cl(-) production increases rapidly with temperature indicating the presence of a dissociation barrier. The data yield an activation energy of approximately 0.1 eV. A broad distribution of product C(2)Cl(4)(-) lifetimes is observed that extends from microseconds to milliseconds, this distribution moving toward shorter lifetimes as the target temperature is increased. The measured lifetimes are consistent with the predictions of quasiequilibrium theory. Studies at low n (n approximately 14) show a substantial fraction of the product K(+)-Cl(-) and K(+)-C(2)Cl(4)(-) ion pairs is electrostatically bound leading to creation of heavy-Rydberg ion-pair states. Variations in target temperature lead to changes in kinetic energy of relative motion of the reactants that can result in marked changes in the fraction of ion pairs that is bound, especially at low Rydberg atom velocities. In the case of bound K(+)-C(2)Cl(4)(-) ion pairs a few percent subsequently dissociate by the conversion of internal energy in the anion into translational energy of the ion pair. Analysis of the data points to a mean energy conversion of approximately 60-90 meV, much less than the available excess energy of reaction, approximately 0.7 eV.

The formation of heavy-Rydberg ion-pair states through electron transfer in collisions between K(np) Rydberg atoms and molecules that attach low-energy electrons is investigated. The measurements show that low-n collisions with a wide variety of target species (SF(6), c-C(7)F(14), C(6)F(6), and CCl(4)) can lead to formation of bound ion-pair states and that, under appropriate conditions, a small fraction of these can subsequently dissociate as free ions through internal-to-translational energy transfer. Analysis of the data suggests that those ion pairs that do dissociate typically have lifetimes of approximately 1 micros, although some can have lifetimes of 5 micros or longer.

The formation of long-lived (tau less, similar10 mus) dipole-bound CH(3)CN(-) ions through electron transfer in K(14p)CH(3)CN collisions is investigated as a function of target temperature. The rate for their formation is observed to decrease steadily with increasing target temperature. The results are consistent with earlier suggestions that only target molecules in the ground vibrational state and low-lying rotational states can form long-lived dipole-bound anions. For CH(3)CN, the data indicate that creation of long-lived ions requires that the target molecules be in states with rotational quantum numbers j less, similar20. The measurements further demonstrate that the lifetime of the longest-lived (tau greater, similar50 mus) ions is limited by blackbody-radiation-induced photodetachment.

We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.

A protocol for steering Rydberg electrons towards targeted final states is realized with the aid of a chirped train of half-cycle pulses (HCPs). Its novel capabilities are demonstrated experimentally by transporting potassium atoms excited to the lowest-lying quasi-one-dimensional states in the n(i)=350 Stark manifold to a narrow range of much higher-n states. We demonstrate that this coherent state transfer is, to a high degree, reversible. The protocol allows for remarkable selectivity and is highly efficient, with typically over 80% of the parent atoms surviving the HCP sequence.

The autodetachment lifetimes of SF6-* and C6F6-* ions formed by charge transfer in K(np)/SF6, C6F6 collisions are measured as a function of target temperature over the range of approximately 300-600 K with the aid of time-of-flight techniques and a Penning ion trap. At room temperature only formation of long-lived SF6 -* ions with lifetimes tau >or similar to 1 ms is seen. As the temperature is increased the lifetime of these long-lived ions is reduced, some having lifetimes as short as approximately 0.4 ms. The appearance of a short-lived, tau

We report the first observation of echoes in the electric dipole moment of an ensemble of Rydberg atoms precessing in an external electric field F. Rapid reversal of the field direction is shown to play a role similar to that of a pi pulse in NMR in rephasing a dephased ensemble of electric dipoles resulting in the buildup of an echo. The mechanisms responsible for this are discussed with the aid of classical trajectory Monte Carlo simulations.

A simple compact retarding-potential Mott polarimeter is described that operates at an electron accelerating voltage of 25 kV. With a thorium target the instrument provides efficiencies eta [=S2eff(I/I0), where Seff is the effective asymmetry (Sherman) function and I/I0 is the scattering efficiency] of approximately 1.3 x 10(-4) which are similar to the best values obtained using earlier Mott polarimeters. The present instrument, however, occupies a much smaller volume and is suitable for a wide range of applications involving angle- and/or energy-resolved polarization measurements.

The ability to localize and to steer Rydberg wave packets in phase space using tailored sequences of half-cycle pulses is demonstrated. Classical phase-space portraits are used to explain the method and to illustrate the level of control that can be achieved. This is confirmed experimentally by positioning a phase-space-localized wave packet at the center of a stable island or navigating it around its periphery. This work provides a valuable starting point for further engineering of electronic wave functions.

We show that strongly polarized very-high-n (n approximately 600) potassium Rydberg atoms can be produced by manipulating lower-n (n approximately 350) polarized atoms using a tailored sequence of ultrashort half-cycle pulses (HCPs). The protocol for this involves first a weak HCP that generates transient phase-space localization whereupon a second large HCP of opposite polarity excites the electron to a broad distribution of highly elongated states. This distribution is then refocused by a short periodic train of HCPs using the properties of (un)stable manifolds near fixed points in phase space.

The lifetimes of long-lived C2Cl4(-) ions formed by Rydberg electron transfer in K(np)/C2Cl4 collisions are investigated using a Penning ion trap. Measurements at high n, n > or = 30, show that low-energy electron attachment to C2Cl4 leads to the production of C2Cl4(-) ions with a broad range of lifetimes that extends up to at least 1 ms. This is attributed to capture by molecules in different initial vibrational states. At low n, internal-to-translational energy transfer in postattachment interactions between the product K+ and C2Cl4(-) ions becomes important and leads to a substantial increase in ion lifetimes.

The lifetimes of SF6- ions produced by Rydberg electron transfer in K(np)SF6 collisions at high n, n greater or similar to 30, are examined using a Penning ion trap. The data point to the formation of ions with a range of lifetimes that extends from approximately 1 to greater or similar to 10 ms. Sizable numbers of ions remain in the trap even 40 ms after initial injection and at least part of this signal can be attributed to radiative stabilization. Measurements of free low-energy electron attachment to SF6 in the trap show that the product ions have lifetimes similar to those of SF6- ions formed by electron transfer in high-n collisions.

The nature of electron binding in C6H5NO2- ions produced by Rydberg electron transfer in K(np)C6H5NO2 collisions is investigated through measurements of the number and the lifetimes of the product ions and their dependence on Rydberg atom velocity and principal quantum number n in the range 12

The dynamics of free-ion production through electron transfer in K(np)/CH3CN collisions are examined through measurements using velocity-selected Rydberg atoms. The data show that Rydberg electron transfer leads to the creation of two groups of dipole-bound CH3CN- ions, one long lived (tau>85 micros), the other short lived (tau<1 micros). The velocity dependences associated with the production of both groups of ions are similar, the ion formation rate decreasing markedly with decreasing Rydberg atom velocity, principally as a consequence of postattachment electrostatic interactions between the product ions. The results are in reasonable accord with the predictions of a Monte Carlo collision model that considers the effect of crossings between the diabatic potential curves for the covalent K(np)/CH3CN system and the K+/CH3CN- ion pair. This model also accounts for the relatively small reaction rate constants, approximately 0.5-1.0 x 1.0(-8) cm(3) s(-1), associated with the formation of long-lived CH3CN- ions. No velocity dependence in the lifetime of the CH3CN- ions is observed.

Experiments in which a thermal-energy beam of xenon Rydberg atoms is directed at near grazing incidence onto a flat Au(111) surface are described that provide new insight into charge transfer and electron tunneling during atom/surface interactions. Analysis of the data shows that for the present range of principal quantum number n, 13 < or = n < or = 20, ionization occurs at an atom/surface separation Z(i) = (4.5+/-0.9)n2a0, where n2a0 is the Bohr radius of the atom. This result is in good agreement with the value Z(i) approximately 3.8n2a0 predicted by ab initio hydrogenic theory.

A novel Mott polarization analysis system is described. This system is much simpler than earlier designs and offers improved rejection of electrons inelastically scattered from the gold target foil. In addition the analyzer is capable of ''in-line'' polarization measurements.