We present quantum mechanical calculations of Auger decay rates for two Rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis of the two-electron state space. We consider large sets of two-atom states with randomly chosen quantum numbers and find that the charge overlap between the two Rydberg electrons allows one to characterise the magnitude of the Auger decay rates. If the electron clouds overlap by more than one percent, the Auger decay rates increase approximately exponentially with the charge overlap. This finding is independent of the energy of the initial state.
In high orbital angular momentum ($\ell \geq 3$) Rydberg states, the centrifugal barrier hinders close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-$\ell$ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular …
Using ultrafast extreme ultraviolet pulses, we performed a direct measurement of the relaxation dynamics of neutral superexcited states corresponding to the nlσ_g(c^4Σ_u^-) Rydberg series of O_2. An XUV attosecond pulse train was used to create a temporally localized Rydberg wavepacket and the ensuing electronic and nuclear dynamics were probed using a time-delayed femtosecond near-infrared pulse. We investigated the competing predissociation and autoionization mechanisms for superexcited molecules and found that autoionization is dominant for the low n Rydberg states. We measured an autoioniz…
Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a $4D$ metastable level are impervious to autoionization over more than a few millisecond t…
We investigate a possible mechanism for the autoionization of ultracold Rydberg gases, based on the resonant coupling of Rydberg pair states to the ionization continuum. Unlike an atomic collision where the wave functions begin to overlap, the mechanism considered here involves only the long-range dipole interaction and is in principle possible in a static system. It is related to the process of intermolecular Coulombic decay (ICD). In addition, we include the interaction-induced motion of the atoms and the effect of multi-particle systems in this work. We find that the probability for this io…
We study isolated core excitation of ultra cold ytterbium Rydberg atoms of high orbital quantum number. Measurements were performed on the $6s_{1/2} 40l \rightarrow 6p_{1/2} 40l $ transition with $l=5-9$. The extracted energy shifts and autoionization rates are in good agreement with a model based on independant electrons, taking into account interactions in a perturbative approach. We reveal a particularly long persistence of the autoionization rates with the orbital quantum number, explained by the strong coupling of the $6p_{1/2}nl$ autoionizing state with the $5d_{3/2}εl'$ continua compare…
Autoionization of Rydberg states of HfF, prepared using the optical-optical double resonance (OODR) technique, holds promise to create HfF+ in a particular Zeeman level of a rovibronic state for an electron electric dipole moment (eEDM) search. We characterize a vibronic band of Rydberg HfF at 54 cm-1 above the lowest ionization threshold and directly probe the state of the ions formed from this vibronic band by performing laser-induced fluorescence (LIF) on the ions. The Rydberg HfF molecules show a propensity to decay into only a few ion rotational states of a given parity and are found to p…
Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or …
We present a study of a cold strontium Rydberg gas. The narrowband laser excitation of Rydberg states in the range n=20-80 from a 6~mK cloud of strontium atoms is detected using the spontaneous ionization of the Rydberg atoms. Using a high-resolution step-scanning technique, we perform detailed measurements of the Stark maps of selected Rydberg states. We find excellent agreement between the measured Stark maps and a numerical calculation based on an independent-electron model. Finally we show that excitation of the second valence electron can be used to probe the dynamics of the Rydberg gas w…
Scalable, local control over gate operations is an outstanding challenge in the field of quantum computing and programmable quantum simulation with Rydberg atom arrays. One approach is to use a global field to excite atoms to the Rydberg state, and tune individual atoms in and out of resonance via local light shifts. In this work, we point out that photon scattering errors from light shifts can be significantly reduced if the light shift is applied to the Rydberg state instead of the ground state, which can be realized in Rydberg states of alkaline earth atoms using optical transitions in the …
New experimental quantum simulation platforms have recently been implemented with divalent atoms trapped in optical tweezer arrays with promising performance. The second valence electron also brings new propects through the so-called Isolated Core Excitation (ICE), however autoionization presents a strong limitation to this use. In this study, we propose and demonstrate a new approach to applying a sizable light shift to a Rydberg state with close-to-resonant ICE while avoiding auto-ionization. In particular, we have investigated ICE of ytterbium atoms in $^1S_0$ Rydberg states. Spectroscopic …
We investigate a hybrid electro-mechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocol for the mechanical oscilla…
We demonstrate finite range binding potentials between pairs of Rydberg atoms interacting with each other via attractive and repulsive van der Waals potentials and driven by a microwave field. We show that, using destructive quantum interference to cancel single-atom Rydberg excitation, the Rydberg-dimer states can be selectively and coherently populated from the two-atom ground state. This can be used to realize a two-qubit interaction gate which is not susceptible to mechanical forces between the atoms and is therefore immune to motional decoherence.
We present time-resolved spectroscopic measurements of Rydberg-Rydberg interactions in an ultracold gas, revealing the pair dynamics induced by long-range van der Waals interactions between the atoms. By detuning the excitation laser, a specific pair distribution is prepared. Penning ionization on a microsecond timescale serves as a probe for the pair dynamics under the influence of the attractive long-range forces. Comparison with a Monte Carlo model not only explains all spectroscopic features but also gives quantitative information about the interaction potentials. The results imply that th…
In a recent work [Phys. Rev. Lett. 98, 023004 (2007)] we have investigated the influence of attractive van der Waals interaction on the pair distribution and Penning ionization dynamics of ultracold Rydberg gases. Here we extend this description to atoms initially prepared in Rydberg states exhibiting repulsive interaction. We present calculations based on a Monte Carlo algorithm to simulate the dynamics of many atoms under the influence of both repulsive and attractive longrange interatomic forces. Redistribution to nearby states induced by black body radiation is taken into account, changing…
We explore the possibility of engineering quantum states of a charged mechanical oscillator by coupling it to a stream of atoms in superpositions of high-lying Rydberg states. Our scheme relies on the driving of a two-phonon resonance within the oscillator by coupling it to an atomic two-photon transition. This approach effectuates a controllable open system dynamics on the oscillator that permits the dissipative creation of squeezed and other non-classical states which are central to applications such as sensing and metrology or for studies of fundamental questions concerning the boundary bet…
We present a theoretical analysis of the implementation of an entangling quantum gate between two trapped Ca$^+$ ions which is based on the dipolar interaction among ionic Rydberg states. In trapped ions the Rydberg excitation dynamics is usually strongly affected by mechanical forces due to the strong couplings between electronic and vibrational degrees of freedom in inhomogeneous electric fields. We demonstrate that this harmful effect can be overcome by using dressed states that emerge from the microwave coupling of nearby Rydberg states. At the same time these dressed states exhibit long r…
We discuss a method for scaling a neutral atom Rydberg gate quantum processor to a large number of qubits. Limits are derived showing that the number of qubits that can be directly connected by entangling gates with errors at the $10^{-3}$ level using long range Rydberg interactions between sites in an optical lattice, without mechanical motion or swap chains, is about 500 in two dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller number of sites can be obtained using collective register encoding in the hyperfine ground states of the rare earth atom Holmium. We present…
We show that sizeable Abelian and non-Abelian gauge fields arise in the relative motion of two dipole-dipole interacting Rydberg atoms. Our system exhibits two magnetic monopoles for adiabatic motion in one internal two-atom state. These monopoles occur at a characteristic distance between the atoms that is of the order of one micron. The deflection of the relative motion due to the Lorentz force gives rise to a clear signature of the effective magnetic field. In addition, we consider non-adiabatic transitions between two near-degenerate internal states and show that the associated gauge field…
We develop and study quantum and semi-classical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in any other spectroscopic scheme, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a novel type of sub-Doppler mechanism, which we explain in detail. In our exact quantum model, we solve the time-dependent Schrödinger equation in the product space of center-of-mass (COM)…
In the combination of crossed electric and magnetic fields and the Coulomb field of the atomic nucleus the spectrum of the Rydberg electron in the vicinity of the Stark saddle-point are investigated at a quantum mechanical level. The results expose a quantum anomaly dissociation: quasibound states near and above the saddle-point ionization limit predicted at the semi-classical level disappear at a quantum mechanical level.
Energy-conserving, angular momentum-changing collisions between protons and highly excited Rydberg hydrogen atoms are important for precise understanding of atomic recombination at the photon decoupling era, and the elemental abundance after primordial nucleosynthesis. Early approaches to $\ell$-changing collisions used perturbation theory for only dipole-allowed ($Δ\ell=\pm 1$) transitions. An exact non-perturbative quantum mechanical treatment is possible, but it comes at computational cost for highly excited Rydberg states. In this note we show how to obtain a semi-classical limit that is a…
We formulate a three-dimensional semi-classical model to treat three-electron escape dynamics in a strongly-driven linear triatomic molecule, HeH$_{2}^{+}$. Our model includes the Coulomb singularities. Hence, to avoid unphysical autoionization, we employ two criteria to switch off the Coulomb repulsive force between two bound electrons and switch it on when the motion of one electron is mostly determined by the laser field. We investigate triple and "frustrated" triple ionization. In the latter process two electrons escape while one electron remains bound in a Rydberg state. We find that two …
The dynamics of Rydberg states of a hydrogen atom subject simultaneously to uniform static electric field and two microwave fields with commensurate frequencies is considered in the range of small fields amplitudes. In the certain range of the parameters of the system the classical secular motion of the electronic ellipse reveals chaotic behavior. Quantum mechanically, when the fine structure of the atom is taken into account, the energy level statistics obey predictions appropriate for the symplectic Gaussian random matrix ensemble.
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 subj…
The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experiment…
The laser-excitation of Rydberg atoms in ultracold gases is often described assuming that the atomic motion is frozen during the excitation time. We show that this frozen gas approximation can break down for atoms that are held in optical lattices or microtraps. In particular, we show that the excitation dynamics is in general strongly affected by mechanical forces among the Rydberg atoms as well as the spread of the atomic wavepacket in the confining potential. This causes decoherence in the excitation dynamics - resulting in a dissipative blockade effect - that renders the Rydberg excitation…
The standard approach to quantum engines is based on equilibrium systems and on thermodynamic transformations between Gibbs states. However, non-equilibrium quantum systems offer enhanced experimental flexibility in the control of their parameters and, if used as engines, a more direct interpretation of the type of work they deliver. Here we introduce an out-of-equilibrium quantum engine inspired by recent experiments with cold atoms. Our system is connected to a single environment and produces mechanical work from many-body interparticle interactions arising between atoms in highly excited Ry…
We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to e…
Neutral atoms have been observed to survive intense laser pulses in high Rydberg states with surprisingly large probability. Only with this Rydberg-state excitation (RSE) included is the picture of intense-laser-atom interaction complete. Various mechanisms have been proposed to explain the underlying physics. However, neither one can explain all the features observed in experiments and in time-dependent Schrödinger equation (TDSE) simulations. Here we propose a fully quantum-mechanical model based on the strong-field approximation (SFA). It well reproduces the intensity dependence of RSE obta…
Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate to the ponderomotive shift of a free electron in off-resonant fields. We derive and evaluate corrections to the ponderomotive free electron polarizability in the length and velocity (transverse or Coulomb) gauges, which agree exactly as mandated by the gauge invariance. We also show how the free electron value emerges from the Dirac equation through summati…
When atoms are exposed to intense laser or microwave pulses ~10% of the atoms are found in Rydberg states subsequent to the pulse, even if it is far more intense than required for static field ionization. The optical spectra of the surviving Li atoms in the presence of a 38 GHz microwave field suggest how atoms survive an intense pulse. The spectra exhibit a periodic train of peaks 38 GHz apart. One peak is just below the limit, and with a 90 V/cm field amplitude the train extends from 300 GHz above the limit to 3000 GHz below it. The spectra and quantum mechanical calculations imply that the …
A topological $θ$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being …
The dynamics of Rydberg states of atomic hydrogen driven by elliptically polarized microwaves of frequency fulfilling 2:1 classical resonance condition is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical results for quasienergies of the system are shown to be in a good agreement with exact quantum data. The structures of the quantum states are found to reflect the underlying classical dynamics; especially we show the existence of nonspreading wavepackets propagating on elliptical trajectories.
We compare the results of the semi-classical (SC) and quantum-mechanical (QM) formalisms for angular-momentum changing transitions in Rydberg atom collisions given by Vrinceanu & Flannery, J. Phys. B 34, L1 (2001), and Vrinceanu, Onofrio & Sadeghpour, ApJ 747, 56 (2012), with those of the SC formalism using a modified Monte Carlo realization. We find that this revised SC formalism agrees well with the QM results. This provides further evidence that the rates derived from the QM treatment are appropriate to be used when modelling recombination through Rydberg cascades, an important process in u…
The dynamics of Rydberg states of atomic hydrogen illuminated by resonant elliptically polarized microwaves is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical predictions for quasienergies of the system are found to be in a very good agreement with exact quantum data enabling a classification of possible types of motion and their dynamics with the change of the ellipticity of the microwaves. Particular attention is paid to the dynamics of the nonspreading wave packet states which are found to exist for an arbitrary micr…
