I show that the theory developed for quantum delocalization of an excited Hydrogen atom in a two-frequency linearly polarized microwave field can be used with a few adaptions to explain the quantum delocalization of Alkali atoms in a linearly polarized monochromatic field in the regime where it deviates from Hydrogenic behaviour. Comparison with numerical and laboratory experiments is satisfactory: apart from a constant factor, independent from the microwave frequency, the same dependence from the initial quantum number is observed.
A fully classical explanation of the nonhydrogenic ionization threshold for low angular momentum Rydberg states of Alkali-metal atoms in a linearly polarized low frequency monochromatic microwave field is given: the classical equivalent to the quantum rate-limiting step, which is responsible for the n^(-5) scaling and which according to the literature initiates what then continues as essentially classical diffusion, is found.
Intensity modulated optical lattice potentials can change sign for an alkali metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO$_2$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential seen by the Rydberg atom can be made to vanish for atoms in \targeted" Rydberg states. Such state selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices.…
The structure of the Cooper minima in the transition probabilities and photoionization cross-sections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found.
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 …
Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali atoms, Rb and Cs, for the $nS$, $nP_{1/2, 3/2}$, and $nD_{3/2, 5/2}$ states with large principal quantum numbers up to $n = 50$. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semi-empirical core-polarization potential. The obtained results are compared with those from a simpler semi-empirical approach and with available experimental data.
Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of large extent of Ry electron wave function on trapping potentials. We find that when the Ry orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron AC polarizability of Ry electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Ry-ground-state transitions for alkali atoms trapped in infr…
We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\rangle$ and $|np\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$, can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying pertu…
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 sizeable effective inte…
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal \textit{nS}, \textit{n}P and \textit{nD} Rydberg states have been calculated in a wide range of principal quantum numbers $n \le 80$ at the ambient temperatures of 77, 300 and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-in…
The theory is developed for one and two atom interactions when the atom has a Rydberg electron attached to a hyperfine split core state. This situation is relevant for some of the rare earth and alkaline earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, $J$, and a non-zero nuclear spin, $I$. In the alkaline earth atoms there is a single, $s$, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The resulting hyperfine splitting of the c…
We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2L_j$; $L\leq 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^1Σ^+$; $v=0$, $J=0$). We compute the associated $C_6$ dispersion coefficients of atom-molecule pairs involving $^{133}$Cs and $^{85}$Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O(n^7)$ over the range of principal quantum numbers $40\leq n\leq 150$. For all atom-molecule pairs considered, Rydbe…
We identify a fundamental structure in the spectrum of microwave driven alkali Rydberg states, which highlights the remnants of the Coulomb symmetry in the presence of a non-hydrogenic core. Core-induced corrections with respect to the hydrogen spectrum can be accounted for by a perturbative approach.
Target ionization processes of alkali atoms by Positronium impact are investigated. Calculations are performed in the frame work of model potential formalism using the Coulomb distorted eikonal approximation. Interesting qualitative features are noted both in the scattered Ps and the ejected electron distributions in differential as well as double differential levels of the collision cross sections.
We report clear evidence of the role of dipole-dipole interaction in Penning ionization of Rydberg atoms, leading to the formation of an ultracold plasma. Penning ionization of np Rydberg Cesium atoms is prevented for states with in n < 42, which correspond to a repulsive potential, but it does not occur for n larger than 42, corresponding to an attractive potential. Blackbody radiation is mostly responsible for the background and initial ionization, although ion-Rydberg collisions and population transfer due to limited superradiance may have to be considered.
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale \emph{inversely} with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both 3D classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schrödinger equation. More surprisingly, t…
Rydberg atoms are ideal tools for quantum technologies. Due to their large size, their dipole-dipole interaction at micrometer-scale distances and their coupling to external fields are huge. Recent experiments vividly exhibit their interest for quantum simulation, in spite of limitations due to the relatively short lifetime of optically-accessible Rydberg levels. These limitations motivate a renewed interest for the long-lived circular Rydberg states . However, detecting them is so far either destructive or complex. Moreover, alkali circular states can be manipulated only by microwave fields, …
Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this work, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb$^+$ ion core. Using the previo…
We experimentally studied the Rydberg level shift caused by the electric field, which is generated by Rydberg atom collision induced ionization in a cesium atomic ensemble. The density of charged particles caused by collisions between Rydberg atoms is changed by controlling the ground-state atomic density and optical excitation process. We measured the Rydberg level shift using Rydberg electromagnetically-induced-transparency (EIT) spectroscopy, and interpreted the physical origin using a semi-classical model. The experimental results are in good agreement with the numerical simulation. These …
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 …
Trapped neutral atoms have become a prominent platform for quantum science, where entanglement fidelity records have been set using highly-excited Rydberg states. However, controlled two-qubit entanglement generation has so far been limited to alkali species, leaving the exploitation of more complex electronic structures as an open frontier that could lead to improved fidelities and fundamentally different applications such as quantum-enhanced optical clocks. Here we demonstrate a novel approach utilizing the two-valence electron structure of individual alkaline-earth Rydberg atoms. We find fi…
The results of a theoretical investigation of prompt many-body ionization are reported. Our calculations address an experiment that reported ionization in Rydberg gases for densities two orders of magnitude less than expected from ionization between pairs of atoms. The authors argued that the results were due to the simultaneous interaction between many atoms. We performed classical calculations for many interacting Rydberg atoms with the ions fixed in space and have found that the many atom interaction does allow ionization at lower densities than estimates from two atom interactions. However…
Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, there can exist a difference of a factor of up to $\sim2.5$ in the ionization cross section between the orientation with the highest and the lowest ion…
Tunnel ionization rates of triplet Rydberg states in helium with principal quantum numbers close to 37 have been measured in electric fields at the classical ionization threshold of $\sim197$ V/cm. The measurements were performed in the time domain by combining high-resolution continuous-wave laser photoexcitation and pulsed electric field ionization. The observed tunnel ionization rates range from $10^5$ s$^{-1}$ to $10^7$ s$^{-1}$ and have, together with the measured atomic energy-level structure in the corresponding electric fields, been compared to the results of calculations of the eigenv…
We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to princip…
We present an experimental and theoretical study of the chaotic ionization of quasi-one-dimensional potassium Rydberg wavepackets via a 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 wavepackets, subject them to alternating applied electric-field "kicks", and measure the electron survival probability. Ionization depends not only on the initial electron energy, but also on the phase-space position of the electron with respect …
The PairInteraction Toolkit for Modeling Rydberg Physics in Alkali and Alkaline-Earth-Like Atoms
University of Stuttgart（斯图加特大学）；Atom Computing, Inc.（Atom Computing公司）；Universität Tübingen（蒂宾根大学）；University of Bonn（波恩大学）；Universität Heidelberg（海德堡大学）；Max Planck Computing and Data Facility（马克斯·普朗克计算与数据中心）
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…
We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential energy curves. The wide parameter range accessible by combining the various properties of different alkali atoms often leads to hybridized electronic states accessible via one or two photon ex…
Anomalously enhanced lifetimes of low angular momentum Rydberg states in singly charged alkaline-earth metal ions
Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学与技术中心）；School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（诺丁汉大学物理与天文学学院及量子非平衡系统数学与理论物理中心）
It is well-known from numerical and experimental results that the fraction of Rydberg states (excited neutral atoms) created by tunnel ionization declines dramatically with increasing ellipticity of laser light. We present a method to analyze this dependence on ellipticity, deriving a probability distribution of Rydberg states that agrees closely with recent experimental [1] and numerical results. In particular, contradicting the existing proposed mechanism [1] and general expectations, our results indicate that the dependence of Rydberg yield on laser ellipticity is not caused by a rescatteri…
Pulsed field ionization of high-$n$ (90 $\leq n \leq$ 150) manifold states in Rb Rydberg atoms has been investigated in high slew-rate regime. Two peaks in the field ionization spectra were systematically observed for the investigated $n$ region, where the field values at the lower peak do not almost depend on the excitation energy in the manifold, while those at the higher peak increase with increasing excitation energy. The fraction of the higher peak component to the total ionization signals increases with increasing $n$, exceeding 80% at $n$ = 147. Characteristic behavior of the peak compo…
We have developed a quite stringent method in selectivity to ionize the low angular- momentum ($\ell$) states which lie below and above the adjacent manifold in highly excited Rb Rydberg atoms. The method fully exploits the pulsed field-ionization characteristics of the manifold states in high slew-rate regime: Specifically the low $\ell$ state below (above) the adjacent manifold is firstly transferred to the lowest (highest) state in the manifold via the adiabatic transition at the first avoided crossing in low slew-rate regime, and then the atoms are driven to a high electric field for ioniz…
Multi-step laser resonance ionization spectroscopy of lutetium (Lu) has been performed at TRIUMF's off-line laser ion source test stand. The even-parity Rydberg series $6s^2nd$ $^2D_{3/2}$, $6s^2nd$ $^2D_{5/2}$ and $6s^2ns$ $^2S_{1/2}$ were observed converging to the 6s$^2$ ionization potential. The experimental results has been compared to previous work. 51 levels of Rydberg series $6s^2nd$ $^2D_{5/2}$ and 52 levels of Rydberg series $6s^2ns$ $^2S_{1/2}$ were reported new. Additionally six even-parity autoionization (AI) series converging to Lu ionic states $5d6s$ $^3D_1$ and $5d6s$ $^3D_2$ w…
We report new frequency-comb-based measurements of Ca Rydberg energy levels. Counter-propagating laser beams at 390 nm and 423 nm excite Ca atoms from the $4s^2~^1\mbox{S}_0$ ground state to $4sns~^1\mbox{S}_0$ Rydberg levels with $n$ ranging from 40 to 110. Near-resonant two-photon two-color excitation of atoms in a thermal beam makes it possible to eliminate the first-order Doppler shift. The resulting lineshapes are symmetric and Gaussian. We verify laser metrology and absolute accuracy by reproducing measurements of well-known transitions in Cs, close to the fundamental wavelengths of our …
We present an object-oriented Python library for computation of properties of highly-excited Rydberg states of alkali atoms. These include single-body effects such as dipole matrix elements, excited-state lifetimes (radiative and black-body limited) and Stark maps of atoms in external electric fields, as well as two-atom interaction potentials accounting for dipole and quadrupole coupling effects valid at both long and short range for arbitrary placement of the atomic dipoles. The package is cross-referenced to precise measurements of atomic energy levels and features extensive documentation t…
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…
Coherent time evolution of highly excited Rydberg states in Rb (98 < n < 150) under pulsed electric field in high slew-rate regime was investigated with the field ionization detection. The electric field necessary to ionize the Rydberg states was found to take discrete values successively depending on the slew rate. Specifically the slew-rate dependence of the ionization field varies with the quantum defect value of the states, i.e. with the energy position of the states relative to the adjacent manifold. This discrete transitional behavior of the ionization field observed for the first time i…
This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions i…
We investigate computationally a method for ultrafast preparation of alkali metal atoms in their Rydberg states using a three-dimensional model potential in the single active electron approximation. By optimizing laser pulse shapes that can be generated with modern waveform synthesizers, we propose pulses for controlling the population transfer from the ground state to a preselected set of Rydberg states. Dynamical processes under the optimized pulses are shown to be much more complicated than in the traditional optical two-photon preparation of Rydberg states.
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…
The electron signals from the field ionization of two closely-spaced Rydberg states of \mbox{rubidium-85} are separated using quantum control. In selective field ionization, the state distribution of a collection of Rydberg atoms is measured by ionizing the atoms with a ramped electric field. Generally, atoms in higher energy states ionize at lower fields, so ionized electrons which are detected earlier in time can be correlated with higher energy Rydberg states. However, the resolution of this technique is limited by the Stark effect. As the electric field is increased, the electron encounter…
We have studied an ionization of alkali-metal Rydberg atoms by blackbody radiation (BBR). The results of the theoretical calculations of ionization rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. Calculations have been performed for nS, nP and nD states which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at the three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ion…
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 …
Ionization energies for Rydberg $^4 \mathrm{He}$ ($1snp\,^{1,3}P$) states using the correlated B-spline basis function method
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新院）；University of Chinese Academy of Sciences（中国科学院大学）
Photoionization spectra of Se have been studied by step-wise resonance laser ionization. The Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_{0,1,2}$ and 4s$^2$4p$^3$($^4$S)np $^5$P$_{1,2,3}$ were measured via different excitation schemes. Using the Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_2$ with n=15-33, the ionization potential of Se was determined with improved precision to 76658.15(2)$_{stat}$(4)$_{sys}$ cm$^{-1}$, which resolved the discrepancy in previous literatures. Autoionizing (AI) spectra between the IP and two neighboring converging limits of the Se ionic states 4s$^2$4p$^3$($^2$D$…
