Rydberg States Of Atoms Research Articles

Photon-photon interactions in Rydberg-atom arrays

We investigate the interaction of weak light fields with two-dimensional lattices of atoms with high lying atomic Rydberg states. This system features different interactions that act on disparate length scales, from zero-range defect scattering of atomic excitations and finite-range dipole exchange processes to long-range Rydberg-state interactions, which span the entire array and can block multiple Rydberg excitations. Analyzing their interplay, we identify conditions that yield a nonlinear quantum mirror which coherently splits incident fields into correlated photon-pairs in a single transverse mode, while transmitting single photons unaffected. In particular, we find strong anti-bunching of the transmitted light with equal-time pair correlations that decrease exponentially with an increasing range of the Rydberg blockade. Such strong photon-photon interactions in the absence of photon losses open up promising avenues for the generation and manipulation of quantum light, and the exploration of many-body phenomena with interacting photons.

Cavity-driven Rabi oscillations between Rydberg states of atoms trapped on a superconducting atom chip

Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave-to-optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric-dipole transitions. Here we report on the experimental realization of coherent coupling of a Rydberg transition of ultracold atoms, trapped on an integrated superconducting atom chip, to the microwave field of an on-chip coplanar waveguide resonator. Close to the chip surface, stray electric fields lead to inhomogeneous Rydberg level shifts, which would hinder coherent interactions of atoms in a cloud with the Rydberg excitation lasers and the microwave cavity field. We, however, use optical excitation of a Rydberg state of atoms in a narrow layer with nearly constant electric field, which allows for resonant coupling of the atoms to the cavity microwave field on an appropriate Rydberg transition. We also achieve state-selective detection of the energetically close Rydberg states. We then observe and characterize cavity-driven Rabi oscillations between a pair of atomic Rydberg states. The residual damping of the oscillations is dominated by the spread of Rabi frequencies of atoms in different positions of the resonant cavity mode, as revealed by our model. Despite the technical challenges, our studies demonstrate the feasibility of coherent-state manipulation of Rydberg atoms interacting with superconducting circuits, paving the way for realization of capable hybrid quantum systems.

Sensitive detection of radio-frequency field phase with interacting dark states in Rydberg atoms.

An efficient scheme of phase measurement of a radio-frequency (RF) field is proposed by interacting dark states. Under the condition of electromagnetically induced transparency (EIT), the four-level Rydberg atom exhibits two windows. Compared with the transmission spectrum on resonance, the linewidths of absorption peaks off resonance are very narrow due to the interaction of double dark states. It is interesting to find that the distance of absorption peaks shifts approximately linearly with the phase of an RF field, which can be used to measure the RF field phase. Simulation results show that the linewidth of an absorption peak can be narrowed by more than one order of magnitude, and a narrow linewidth improves the detectable minimum phase difference by more than six times. It helps to reduce analyzation complexity and increase sensing resilience. The dependence of phase measurement on the control field and RF field is also investigated.

Erratum to: Machine learning identification of symmetrized base states of Rydberg atoms

Erratum to: Machine learning identification of symmetrized base states of Rydberg atoms

Orbital effects in strong-field Rydberg state excitation of N2, Ar, O2 and Xe

Rather than being freed to the continuum, the strong-field tunneled electrons can make a trajectory driven by the remaining laser fields and have certain probability to be captured by the high lying Rydberg states of the parent atoms or molecules. To explore the effect of molecular orbital on Rydberg state excitation, the ellipticity dependence of Rydberg state yields of N2 and O2 molecules are experimentally investigated using cold target recoil ion momentum spectroscopy and are compared with their counterpart atoms Ar and Xe with comparable ionization potentials. We found the generation probability of the neutral Rydberg fragment O2* was orders of magnitude higher than that of Xe* due to the butterfly-shaped highest occupied molecular orbital of O2. Meanwhile, our experimental and simulation results reveal that it is the initial momentum distribution (determined by the detailed characteristics of orbitals) that finally leads to the tendency that the Rydberg state yield of O2 (Ar) decreased slower than that obtained for Xe (N2) when the ellipticity of the excitation laser field is increased.

Multipartite entanglement and quantum criticality of Rydberg atoms trapped in a two-dimensional optical lattice.

We investigate the multipartite entanglement and quantum criticality of neutral atoms on a two-dimensional square lattice, interacting via laser excitation to atom Rydberg states. It is found that the first derivative of residual entanglement with respect to detuning has peaks near the critical point, and corresponding critical behaviors are shown to obey conventional finite-sized scaling, from which we numerically determine the quantum critical point and the critical exponent of the associated correlation length. We also show that there is a sharp peak in the fidelity susceptibility near the critical point, and the critical exponent of the associated correlation length is obtained based on the finite size analysis.

ДОСЛІДЖЕННЯ СПЕКТРУ АТОМІВ Zn I В ТРИПЛЕТНИХ РІДБЕРГІВСЬКИХ СТАНАХ

Purpose: This work aims at investigating the zinc atoms in the triplet preionization – Rydberg states. The energy levels of atoms having two electrons outside the closed shell were studied mainly by the optical spectroscopy methods. However, just using the microwave spectroscopy to measure the frequency of transitions between the two Rydberg states allows to increase the accuracy of measurements in two or more orders of magnitude. Disign/methodology/approach:A line of three dye lasers is used to excite the zinc atoms into the triplet Rydberg states with a predetermined set of quantum numbers. The radiation of the first two of them is transformed into the second harmonic in nonlinear crystals. Dye lasers are excited by the radiation of the second harmonic of one YAG: ND3+ laser. All three radiations are reduced to the zone of interaction with the laser and the microwave radiation, which is located between the plates of the ionization cell, where the pulsed electric field is created. The excited Rydberg atoms are recorded with the field ionization procedure. The beam of neutral atoms is created by an effusion cell under the vacuum conditions, the residual pressure does not exceed 10-5 mm Hg. A pulsed electric field of some certain intensity results inionization of atoms excited by microwave radiation and in acceleration of electrons, which have appeared in the direction of the secondary electron multiplier, though being insufficient for ionization of atoms excited only by the laser radiation and which are initial for interaction with microwaves. By scanning the microwave radiation frequency with the given step and measuring the signal intensity of the secondary electron multiplier, the excitation spectrum of the atoms under study can be obtained. Findings: Using the created laser-microwave spectrometer, the frequencies of the F→D, F→F and F→G transitions between the triplet Rydberg states of zinc atoms were measured. From the analysis made of the transition frequencies, the quantum defect decomposition constants were obtained by the Ritz formula for the D, F, and G states of zinc atoms. Conclusions: The frequencies of the F→D, F→F and F→G transitions between the triplet Rydberg states of zinc atoms were measured that allowed obtaining the quantum defect decomposition constants according to the Ritz formula for the D, F and G states of zinc atoms, that in turn had allowed to calculate the energy of these terms and the transition frequencies at least in two orders of magnitude more accurately as against the similar measurements made by the optical spectroscopy. Key words: zinc atom, triplet states of atoms, Rydberg states, laser excitation, microwave radiation

Machine learning identification of symmetrized base states of Rydberg atoms

Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.

Free-bound excitation and predissociation of ytterbium dimers near theS01−P11atomic transition

A continuous excitation band of a free-bound photoassociation transition of ytterbium atoms is observed as a red wing of the $^{1}S_{0}\text{\ensuremath{-}}^{1}P_{1}$ atomic line at 399 nm for a hot thermal vapor. The excitation to the ${0}_{u}^{+}$ molecular state is observed by monitoring fluorescence from the $^{3}P_{1}$ state atoms, which allows us to detect the production of ${\mathrm{Yb}}_{2}$ molecules with high sensitivity. The photoassociation is characterized in comparison with transitions to atomic Rydberg states. The time profile of the fluorescence signal suggests that the ${0}_{u}^{+}$ molecular state predissociates with states correlating to the $^{1}S_{0}+^{3}D_{2}$ atomic states.

Creation of quantum entangled states of Rydberg atoms via chirped adiabatic passage

Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger–Horne–Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms ^{87}Rb interaction with laser pulses, which leads to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of the two-photon excitation, adiabatic for the GHZ and non-adiabatic for the W state, induced by the overlapping chirped pulses and governed by the Rabi frequency, the one-photon detuning, and the strength of the Rydberg–Rydberg interactions.

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole-Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning.

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

Circular Rydberg states of helium atoms or helium-like ions in a high-frequency laser field

Abstract In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z: as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

Quantum phases of Rydberg atoms on a kagome lattice

We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.

ARC 3.0: An expanded Python toolbox for atomic physics calculations

ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library (Šibalić et al., 2017), which focused on Rydberg states of alkali atoms, this major upgrade introduces support for divalent atoms. It also adds new methods for working with atom–surface interactions, for modelling ultracold atoms in optical lattices and for calculating valence electron wave functions and dynamic polarisabilities. Such calculations have applications in a variety of fields, e.g., in the quantum simulation of many-body physics, in atom-based sensing of DC and AC fields (including in microwave and THz metrology) and in the development of quantum gate protocols. ARC 3.0 comes with an extensive documentation including numerous examples. Its modular structure facilitates its application to a wide range of problems in atom-based quantum technologies. Program summaryProgram Title: ARC 3.0CPC Library link to program files:https://doi.org/10.17632/c4z4n2cdf7.1Licencing provisions: BSD-3-ClauseProgramming language: PythonExternal Routines: NumPy [1], SciPy [1], Matplotlib [2], SymPy [3], LmFit [4]Nature of problem: The calculation of atomic properties of alkali and divalent atoms including energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated through a variety of means.Solution method: Dipole matrix elements are calculated using an analytical semi-classical approximation or wave functions obtained by numerical integration of the radial Schrödinger equation for a one-electron model potential. Interaction energies and shifts due to external fields are calculated using second order degenerate perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Additional comments including restrictions and unusual features: External electric and magnetic field must be parallel to the quantisation axis. The accuracy of short range (≲1μm) atom - atom interaction potentials is limited by the truncation of the basis. Only weak magnetic fields are supported as only linear Zeeman shifts are taken into account. Calculations for divalent atoms use a single-electron approximation and calculation of their wave functions is not supported.

Диффузионная динамика ридберговских состояний в поле излучения с непрерывным спектром

Redistribution of population and ionization of atomic Rydberg states due to multistep cascade transitions between states under the influence of radiation with continuous spectrum is considered. Consideration is carried up both by simulation of kinetic equations for state populations and with the use of a diffusion approximation based on the Fokker-Planck equation. On the example of sodium atom under the influence of radiation with rectangular spectrum a good agreement between the diffusion approximation and the kinetic equation simulation is shown. In the frame of the diffusion approximation some estimations are derived for the state populations, ionization rates and minimal spectral density of radiation necessary for significant ionization.

Theoretical approaches for doubly-excited Rydberg states in quasi-two-electron systems: two-electron dynamics far away from the nucleus

ABSTRACT We report on recent progress regarding the theoretical treatment of doubly-excited Rydberg states of atoms with two valence electrons. Building upon state-of-the-art techniques, we demonstrate that an approach based on configuration interaction with exterior complex scaling (CI-ECS) is capable of describing high Rydberg states () and does not rely on the assumptions of R-matrix multichannel quantum-defect theory. We show that CI-ECS allows the simultaneous, accurate treatment of a range of doubly-excited Rydberg states broader than previously possible. The implementation of the method with numerical basis functions is explained in detail. As an example, CI-ECS calculations of the doubly-excited states of Mg and Sr are presented, and excellent agreement is found with available experimental data. The CI-ECS method opens new perspectives for studying collective two-electron dynamics in doubly-excited Rydberg states of alkaline-earth metal atoms, and is also of interest for the field of Rydberg-based quantum simulation.

Frustrated ionization of atoms in the multiphoton regime

A semiclassical analytic theory which describes the excitation of atomic Rydberg states by intense laser radiation is formulated in the multiphoton limit of ionization. The theory is based on the separation of the electron motion in fast oscillations in the laser field and slow scattering in the Coulomb field of the nucleus. It allows one to calculate classical cut-off positions in the distribution of excited atoms in principal and orbital quantum numbers, and to identify the effect of quantum interference.

Probing time delay of strong-field resonant above-threshold ionization* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11574101, 11674116, 11774111, and 11934006), the Open Fund of Hubei Provincial Key Laboratory of Optical Information and Pattern Recognition (Grant No. 201902), and the International Cooperation Program of Hubei Innovation Fund (Grant No. 2019AHB052).

The high-resolution three-dimensional photoelectron momentum distributions via above-threshold ionization (ATI) of Xe atoms are measured in an intense near circularly polarized laser field using velocity map imaging and tomography reconstruction. Compared to the linearly polarized laser field, the employed near circularly polarized laser field imposes a more strict selection rule for the transition via resonant excitation, and therefore we can selectively enhance the resonant ATI through certain atomic Rydberg states. Our results show the self-reference ionization delay, which is determined from the difference between the measured streaking angles for nonadiabatic ATI via the 4f and 5f Rydberg states, is 45.6 as. Our method provides an accessible route to highlight the role of resonant transition between selected states, which will pave the way for fully understanding the ionization dynamics toward manipulating electron motion as well as reaction in an ultrafast time scale.

Stark–Zeeman and Blokhintsev Spectra of Rydberg Atoms

The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution.

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.