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The Hawking temperature and Entropy of Reissner-Nordstrom (RN) black hole can be derived from energy quantization of the test particle moving around different circular orbits which is analog to the Bohr’s atomic model. Energy transitions (recall the Rydberg formula) can lead to radiations that can be experimentally detected in the future. Following gravitoelectromagnetism (GEM) it is possible to split the upper bound of energy without the quantization effects on energy level splitting in atoms and molecules due to the hypothetical nature of the gravitipole. Here we have mentioned the entropy and other thermodynamic properties of RN black holes within string theory going well beyond the thermodynamic limit.

We have theoretically investigated the modulation structures of the excited-state population of an argon atom exposed to a linearly polarized 800-nm laser pulse in the tunneling region. The numerical result identifies a nearly opposite phase modulation structure between the low-lying n = 4–7 states and over all higher $$n>7$$ states. This phase-dependent alternating population phenomenon is found to be related to the periodic channel-closing effect that results from ac-Stark-shifted multiphoton resonances. Moreover, the angular momentum states attributed to different parities have a similar alternating effect, which confirms a multiphoton process in the tunneling region. We introduce a mechanism of two-photon $$\Lambda $$ -type Raman transitions involving Rydberg and continuum states with a simultaneous redistribution of states to account successfully for this observed out-of-phase angular momentum state population.

In this paper, we proposed a model based on Rydberg atoms for controlling the optical bistability (OB) and optical multistability (OM) in a ring cavity. The atoms interact with an elliptical polarized probe light and a strong coupling light in the presence of external magnetic field. We realized that the threshold of OB can be controlled by elliptical polarized parameter when the first excited states of the atoms interact with Rydberg state. Also, we found that by adjusting the elliptical parameter of probe light, the switching from OB to OM is possible when we consider the strong coupling between Rydberg level and first excited state of the atomic system. We find that when the probe light becomes linearly the OB and OM disappear due to Rydberg electromagnetically induced transparency. However, by adjusting the polarized parameter of the probe light the threshold of OB can be controlled due to Rydberg electromagnetically absorption. Our proposed model can be used as an all-optical device for switching between OB and OM with potential applications in optical communication.

Highly sensitive phase- and frequency-resolved detection of microwave electric fields is of central importance in a wide range of fields, including cosmology1,2, meteorology3, communication4 and microwave quantum technology5. Atom-based electrometers6,7 promise traceable standards for microwave electrometry, but their best sensitivity is currently limited to a few μV cm−1 Hz−1/2 (refs. 8,9) and they only yield information about the field amplitude and polarization10. Here, we demonstrate a conceptually new microwave electric field sensor—the Rydberg-atom superheterodyne receiver (superhet). The sensitivity of this technique scales favourably, achieving even 55 nV cm−1 Hz−1/2 with a modest set-up. The minimum detectable field of 780 pV cm−1 is three orders of magnitude smaller than what can be reached by existing atomic electrometers. The Rydberg-atom superhet allows SI-traceable measurements, reaching uncertainty levels of 10−8 V cm−1 when measuring a sub-μV cm−1 field, which has been inaccessible so far with atomic sensors. Our method also enables phase and frequency detection. In sensing Doppler frequencies, sub-μHz precision is reached for fields of a few hundred nV cm−1. This work is a first step towards realizing electromagnetic-wave quantum sensors with quantum projection noise-limited sensitivity. Such a device will impact diverse areas like radio astronomy, radar technology and metrology. The Rydberg-atom superhet, based on microwave-dressed Rydberg atoms and a tailored electromagnetically induced transparency spectrum, allows SI-traceable measurements of microwave electric fields with unprecedented sensitivity.

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 fidelities for Rydberg state detection, single-atom Rabi operations, and two-atom entanglement surpassing previously published values. Our results pave the way for novel applications, including programmable quantum metrology and hybrid atom-ion systems, and set the stage for alkaline-earth based quantum computing architectures., ISM and JPC contributed equally to this work

We report on the results of studying the radio emission of the Rydberg states of atoms and molecules in the Earth’s upper atmosphere at ionospheric altitudes when the ionosphere is modified by high-power HF radio waves radiated by the Sura heating facility. Radio emission from the upper atmosphere, caused by the emission of highly excited Rydberg atoms and molecules with the principal quantum number n = 163–169 and n = 225 (decimeter wavelength range) and two spectral features that coincide with the frequencies of transitions between Rydberg states m = 169 → n = 168 with the transition frequency νn = 1375.35 MHz and m = 166 → n = 165 with νn = 1451.5 MHz were detected. Characteristic altitudes of the Rydberg radiation generation region were 150–250 km. The radio emission intensity corresponds to 10–45 K, which is comparable with the intensity of the radio emission generated during solar flares.

Elastic electron–proton scattering (e–p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, rp. In 2010, a new method using muonic hydrogen atoms1 found a substantial discrepancy compared with previous results2, which became known as the ‘proton radius puzzle’. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen3,4. Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e–p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e–p experiments and enabled measurements at very small forward-scattering angles. Our result, rp = 0.831 ± 0.007stat ± 0.012syst femtometres, is smaller than the most recent high-precision e–p measurement5 and 2.7 standard deviations smaller than the average of all e–p experimental results6. The smaller rp we have now measured supports the value found by two previous muonic hydrogen experiments1,7. In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant8—one of the most accurately evaluated fundamental constants in physics. A magnetic-spectrometer-free method for electron–proton scattering data reveals a proton charge radius 2.7 standard deviations smaller than the currently accepted value from electron–proton scattering, yet consistent with other recent experiments.

The relativistic energies and Auger transition rates for the Rydberg series 1s23lnl′ 1,3F° (n = 3–6) of Be-like oxygen ions are determined by the saddle-point variation and saddle-point complex-rotation methods. Relativistic corrections and mass polarization effects are considered to improve the computational accuracy of the energy. The Auger branching ratios of the 1s22s and 1s22p decay channels for these Rydberg series are calculated. The accurate Auger electron energies are compared with high-resolution electron spectroscopy. The results will provide useful data for the identification of spectral lines arising from the Be-like oxygen ions and experimental studies in future work.

We study effects of a magnetic field on the classical bound motion of a highly excited (Rydberg) electron around a polar molecule, the latter being treated as the point-like electric dipole. We consider the magnetic field B to be parallel or antiparallel to the electric dipole, so that the system has the axial symmetry. (The $${B} = 0$$ case was studied analytically in one of our previous papers.) We obtain analytical results for the arbitrary strength of the magnetic field. We show that the presence of the magnetic field opens up new ranges of the bound oscillatory-precessional motion of the Rydberg electron, the oscillations being in the meridional direction ( $$\theta $$ -direction) and the precession being along parallels of latitude ( $$\varphi $$ -direction). In particular, it turns out that in one of the new ranges of the motion, the period of the $$\theta $$ -oscillations has the non-monotonic dependence on primary parameter of the system. This is a counterintuitive result.

We study the Rydberg excitation of a square atomic lattice driven by a pumping and a coupling fields into the ladder configuration via Monte Carlo simulations based on density matrix equations. Single-atom Rydberg population can be very close to unit benefiting from the formation of a dark state such that the antiferromagnet (AFM) phase has been observed at finite two-photon detunings owing to moderate van der Waals (vdW) interactions. We note in particular that the pumping Rabi frequency is more important than the coupling Rabi frequency in manipulating the AFM phase to occur for specific pumping detunings, coupling detunings, and nearest-neighbor vdW potentials. Moreover, the AFM phase may enter a saturation regime in terms of its parameter region when the boundary effect of vdW interactions is negligible for a large enough lattice size.

We present an improved version of the superatom (SA) model to examine the slow-light dynamics of a few-photons signal field in cold Rydberg atoms with van der Waals (vdW) interactions. A main feature of this version is that it promises consistent estimations on total Rydberg excitations based on dynamic equations of SAs or atoms. We consider two specific cases in which the incident signal field contains more photons with a smaller detuning or less photons with a larger detuning so as to realize the single-photon-level light storage. It is found that vdW interactions play a significant role even for the slow-light dynamics of a single-photon signal field as distributed Rydberg excitations are inevitable in the picture of dark-state polariton. Moreover, the stored (retrieved) signal field exhibits a clearly asymmetric (more symmetric) profile because its leading and trailing edges undergo different (identical) traveling journeys, and higher storage/retrieval efficiencies with well preserved profiles apply only to weaker and well detuned signal fields. These findings are crucial to understand the nontrivial interplay of single-photon-level light storage and distributed Rydberg excitations.[Figure not available: see fulltext.].

A dynamics regime of Rydberg atoms, unselective ground-state blockade (UGSB), is proposed in the context of Rydberg antiblockade (RAB), where the evolution of two atoms is suppressed when they populate in an identical ground state. UGSB is used to implement a SWAP gate in one step without individual addressing of atoms. Aiming at circumventing common issues in RAB-based gates including atomic decay, Doppler dephasing, and fluctuations in the interatomic coupling strength, we modify the RAB condition to achieve a dynamical SWAP gate whose robustness is much greater than that of the nonadiabatic holonomic one in the conventional RAB regime. In addition, on the basis of the proposed SWAP gates, we further investigate the implementation of a three-atom Fredkin gate by combining Rydberg blockade and RAB. The present work may facilitate to implement the RAB-based gates of strongly coupled atoms in experiment., to appear in Frontiers of Physics

In this study, the potential energy curves of the ground and the excited states of molecular fluorine anion (F $_{2}^{-}$ ) were investigated at multireference configuration interaction (MRCISD) with Davidson size-extensivity correction (denoted as +Q) within fully relativistic four-component relativistic framework including Breit interaction. Spectroscopic constants (Re, ωe, ωexe, ωeye, De,D0,Be, αe, βe, γe ), accurate extended Rydberg analytical form and rovibrational levels for ground state X: $^{2}{\varSigma }_{u,1/2}^{+} $ are presented, as well as spectroscopic constants for non dissociative excited states. For most states these spectroscopic constants are presented for the first time in literature and they are of interest for experimental studies, specially regarding electron attachment of F2. Results suggest that inclusion of relativistic effects at 4-component level and correlation effects treated at MRCISD+Q level are needed to obtain reliable results, which we report for X: $^{2}{\varSigma }_{u,1/2}^{+} $ ground state’s Re, ωe and De the values of 1.999 A, 391 cm− 1 and 1.22 eV, respectively.

The photoionization dynamics of Rydberg hydrogen atom in a space-dependent magnetic field has been studied for the first time. Because of the non-uniform magnetic field, this system is non-integrable, and its dynamics becomes more complex than that in a uniform magnetic field. The exact analytic electron wave function can not be obtained by solving the Schrodinger equation quantum mechanically, instead, it can be constructed within the framework of the semiclassical EBKM scheme, which gives the correspondence between the quantum wave function and a family of classical electron trajectories. The observed oscillatory structures in the electron probability density distributions on the detector plane can be understood by considering the accumulated phase among different classical trajectories by which the electron moves from the atom to the detector. The calculation results suggest that the patterns of the photoionization microscopy can be modulated by changing the scaled energy, the position of the detector plane and the initial state wave function. Once the photoionization microscopy image on the detector has been measured in the experiment, it can be used to recover the angular distribution of the electron wave function. Our work provides a convincing semiclassical interpretation of the photoionization microscopy image and the underlying classical dynamics, and may guide future experimental study on the photoionization microscopy of the Rydberg atom in the non-uniform magnetic fields.

Exploring the dynamics of inelastic and reactive collisions on the quantum level is a fundamental goal in quantum chemistry. Such collisions are of particular importance in connection with Rydberg atoms in dense environments since they may considerably influence both the lifetime and the quantum state of the scattered Rydberg atoms. Here, we report on the study of state-changing collisions between Rydberg atoms and ground state atoms. We employ high-resolution momentum spectroscopy to identify the final states. In contrast to previous studies, we find that the outcome of such collisions is not limited to a single hydrogenic manifold. We observe a redistribution of population over a wide range of final states. We also find that even the decay to states with the same angular momentum quantum number as the initial state, but different principal quantum number is possible. We model the underlying physical process in the framework of a short-lived Rydberg quasi-molecular complex, where a charge exchange process gives rise to an oscillating electric field that causes transitions within the Rydberg manifold. The distribution of final states shows a diffusive-like behavior., Here, the authors discuss state-changing inelastic collisions between rubidium Rydberg and ground state atoms. They employ high-resolution magneto-optical trap recoil-ion momentum spectroscopy to measure the distribution of the final states.

This work is dedicated to the theoretical investigation of the influence of water clusters’ organisation and size on the electronic spectrum of an interacting benzene (Bz) molecule using both TD-DFT and CASPT2 approaches. Two series of geometries, namely $$Geo_{IEI}$$ and $$Geo_{IED}$$ were extracted from two Bz-hexagonal ice configurations leading to maximum and minimum ionization energies respectively. An appropriate basis set containing atomic diffuse and polarisation orbitals and describing the Rydberg states of Bz was determined. The TD-DFT approach was carefully benchmarked against CASPT2 results for the smallest systems. Despite some discrepancies, the trends were found to be similar at both levels of theory: the positions and intensities of the main $$\pi \rightarrow \pi ^{\star }$$ transitions were found slightly split due to symmetry breaking. For the smallest systems, our results clearly show the dependence of the electronic transitions on the clusters’ structures. Of particular interest, low energy transitions of non negligible oscillator strength from a Bz $$\pi$$ orbital to a virtual orbital of Rydberg character, also involving atomic diffuse functions and partially expanded on the water cluster, were found for the $$Geo_{IED}$$ series. The energies of such transitions were determined to be more than 2 eV below the ionization potential of Bz. When the cluster’s size increases, similar transitions were found for all structures, the virtual orbitals becoming mainly developed on the H atoms of the water molecules at the edge of the cluster. Given their nature and energy, such transitions could play a role in the photochemistry of aromatic species in interaction with water clusters or ice, such processes being of astrophysical interest.

We present a diabatic representation of the potential energy curves (PECs) for the $$^4{{\Pi}} $$ 4 Π states of $$\mathrm {SH}$$ SH . Multireference, configuration interaction (MRCI) calculations were used to determine high-accuracy adiabatic PECs of both $$\mathrm {SH}$$ SH and $${\mathrm {SH}}^+$$ SH + from which the diabatic representation is constructed for $$\mathrm {SH}$$ SH . The adiabatic PECs exhibit many avoided crossings due to strong Rydberg-valence mixing. We employ the block diagonalization method, an orthonormal rotation of the adiabatic Hamiltonian, to disentangle the valence autoionizing and Rydberg $$^4\Pi $$ 4 Π states of $$\mathrm {SH}$$ SH by constructing a diabatic Hamiltonian. The diagonal elements of the diabatic Hamiltonian matrix at each nuclear geometry render the diabatic PECs and the off-diagonal elements are related to the state-to-state coupling. Care is taken to assure smooth variation and consistency of chemically significant molecular orbitals across the entire geometry domain.

Within the framework of a non-stationary scattering theory formulas for electron scattering cross sections on an arbitrary time-periodic potential are derived. These formulas to a weakly ionized ultracold Rydberg plasma subjected to a perturbation by a terahertz acoustic wave and a laser field are applied. Our result for laser-assisted electron-atom scattering generalizes the Kroll-Watson formula to the case of an elliptically polarized electromagnetic wave. Based on the kinetic approach we discuss a mechanism of the scattering of plasma charges on neutral atoms, vibrating in the field of the external acoustic wave, leading to a renormalization of the electron plasma frequency. Additionally, within the framework of the hydrodynamic approach, we demonstrate the possibility of a parametric resonance amplification of electron and ion density oscillations in weakly ionized two component ultracold Rydberg plasmas under the influence of a laser field and as high-frequency acoustic wave.

The quantum entanglement of the two components of a hydrogenic system with dimensionality $$D\ge 2$$ is investigated for the ground and excited states from first principles, that is, in terms of the Coulomb potential parameters (the dimensionality and the nuclear charge) and the state’s hyperquantum numbers. To quantify this multidimensional entanglement, we use an heuristic quantifier and a practical genuine entanglement measure which are closely related to the variance and disequilibrium of the system in momentum space, respectively. Then, our interest is focused on the multidimensional entanglement of highly excited (Rydberg) states, obtaining at the leading order a simple dependence on the dimensionality and the principal hyperquantum number n which characterizes the state. Applications to various specific low-lying and high-lying hydrogenic states are shown. In particular, it is rigorously shown that the momentum disequilibrium and the entanglement for the Rydberg multidimensional states follow a scaling law of $$n^2\log \,n$$ and $$n^{2(D-1)}$$ type for two-dimensional and D-dimensional ( $$D>2$$ ) systems, respectively.

The potential for spectroscopy in a multilayer cell with rarefied gas medium is theoretically investigated where said cell can be used as a compact analog of a large number of plane-parallel beams of atoms (or molecules) in an optically excited quantum level. In particular, this situation occurs for metastable and highly excited long-lived Rydberg states of atoms and molecules. Velocity selection of atoms (molecules) excited to said quantum level by broadband optical pumping was found to be efficient because of their characteristic transit and collisional relaxation in said cell. Sub-Doppler resonances at the optical transition frequencies from a given level were narrow as a result of the selection when the monochromatic probe light beam was absorbed.

The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties and underpin schemes to control chemical reactions. Considerable progress has been made in understanding vibrational coherence through spectroscopic measurements, but precise, direct measurement of the structure of a vibrating excited-state polyatomic organic molecule has remained unworkable. Here, we measure the time-evolving molecular structure of optically excited N-methylmorpholine through scattering with ultrashort X-ray pulses. The scattering signals are corrected for the differences in electron density in the excited electronic state of the molecule in comparison to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and seems to persist for longer than previously seen using other methods.

A mathematical model which is logically very simple and convenient for programming is proposed for describing and studying the optical spectra of polyatomic molecules from the IR to the UV, including the Rydberg region, with computer simulations. For a specified molecular geometry, the only variable parameters are the elements of the force constant matrices for the ground and electronically excited states and the well depths. The functions for the electrons are specified by sets of principal quantum numbers for the radial components in a hydrogen-like atom. The model can be used to solve both direct and inverse problems.

An theory of charge transfer at intermediate collision velocities is elaborated. Within the framework of the two-wave-function model, we analyze the intermediate stages of the population of the Rydberg states $$\nu _A=(n_A=8,l_A=0-2,m_A=0)$$ of highly charged ions escaping the target ion after atomic collision. The specificity of this approach is reflected in the time-symmetric description of the electron capture process by using two functions. The focus of the work is on determining the transition probabilities and corresponding rates whose analysis can be used to estimate the dominant partial neutralization distances at fixed initial and final states of the ion-ion system under consideration.

We theoretically investigate the single-photon router using two Rydberg atoms embedded in a multi-channel coupled cavity arrays(CCAs) driven by a classical field. It is shown that when the Rydberg interaction is in the proper range, three kinds of photons with different frequencies are absorbed and the quantum routing can be achieved due to the spontaneous emission of the formed dressed states. The Rydberg interaction can also cause photons that are not originally in the energy range to be routed. Furthermore, the total reflection of the single photon is obtained because of the coherent resonance and the existence of the photonic bound states. Based on these characteristics, it is a feasible scheme to generate a multi-frequency photons router and it could be useful for designing the single-photon devices.

Nonadiabatic holonomic quantum computing has received great attention due to its advantages of avoiding long-term evolution of the system and maintaining the robustness of holonomic gates to control errors. In this paper, we study a scheme for implementing nonadiabatic holonomic computation using two blockaded Rydberg atoms. With the presence of the Rydberg blockade effect, we realized controlled-phase gates, which play an irreplaceable role in quantum computation and quantum information processing. Therefore, the current scheme may open up new prospects for the design of new types of effective Rydberg quantum gate devices.

Antihydrogen atoms are produced at CERN in highly excited Rydberg states. However, precision measurements require anti-atoms in ground state. Whereas experiments currently rely on spontaneous emission only, simulations have shown that THz light can be used to stimulate the decay towards ground state and thus increase the number of anti-atoms available for measurements. We review different possibilities at hand to generate light in the THz range required for the purpose of stimulated deexcitation. We demonstrate the effect of a blackbody type light source, which however presents drawbacks for this application including strong photoionization. Further, we report on the first THz transitions in a beam of Rydberg caesium atoms induced by photomixers and conclude with the implications of the results for the antihydrogen case.[graphic not available: see fulltext][graphic not available: see fulltext] Antihydrogen atoms are produced at CERN in highly excited Rydberg states. However, precision measurements require anti-atoms in ground state. Whereas experiments currently rely on spontaneous emission only, simulations have shown that THz light can be used to stimulate the decay towards ground state and thus increase the number of anti-atoms available for measurements. We review different possibilities at hand to generate light in the THz range required for the purpose of stimulated deexcitation. We demonstrate the effect of a blackbody type light source, which however presents drawbacks for this application including strong photoionization. Further, we report on the first THz transitions in a beam of Rydberg caesium atoms induced by photomixers and conclude with the implications of the results for the antihydrogen case.

This paper investigates the Penning ionization (PI) processes in cold gas media of alkali atoms. The PI autoionization widths of atomic pairs show a drastic dependence (by orders of magnitude) on the orbital quantum numbers of Rydberg atoms involved in a long-range dipole-dipole interaction. The nontrivial dependence of the PI efficiency on the size of colliding particles was considered, with a particular accent to the applications in the research of cold matter created in the experiments with magneto-optical traps. We have analytically described the optimal, highly asymmetric configurations of atomic Rydberg pairs, which lead to an explosive intensification (by several orders of magnitude) of a free-electron escaping due to PI. The excited states of atoms in the optimal pairs turn out to have a strong difference in atomic shell sizes. The optimal pairs’ properties may be favorable for the generation of primary (seeding) charged particles when a cold Rydberg medium evolves into a cold plasma. Within the framework of the semiclassical approach, we have obtained universal analytical formulas containing two adjustable parameters and present here their values in tabulated form, which allows estimating the PI rate constants for various pairs of alkali metal atoms.

In the paper, we propose a scheme for fast preparation of Bell state and W state based on quantum Zeno dynamics and shortcuts to adiabaticity with Rydberg superatom. The quantum information is encoded in the collective state of superatom which contains n individual ladder-type Rydberg atoms. When the Rabi frequencies of classical fields are appropriately regulated, the scheme can be achieved within one step. Moreover, the effects of imperfections induced by leakage of the cavity and atomic spontaneous emission are also taken into account. The numerical simulation result shows that this scheme is robust against both cavity leakage and atomic spontaneous emission.

We perform a study of the molecular anisotropy for the H2⋯H2 van der Waals system using a spherical harmonics expansion. We use six leading stable configurations to construct our analytical potential energy surface (PES) from ab initio calculations guided qualitatively by the symmetry-adapted perturbation theory (SAPT) analyses. We extrapolate the energies of the PES performed at the CCSD(T)/aug-cc-pVnZ (n = 2 and 3) levels to the complete basis set (CBS) limit. To best fit the shallow potential energy surface of each leading configuration with the intermolecular distance, it was employed an extended version of the Rydberg potential. To assess the quality of our extrapolated analytical PES, we calculate the second virial coefficients, which are in relatively good agreement with the experimental data. As a result, the spherical harmonics coefficients obtained might be of considerable relevance in spectroscopy and dynamics applications.

The long-range interaction between Rydberg-excited atoms endows a medium with large optical nonlinearity. Here, we demonstrate an optical switch to operate on a single photon from an entangled photon pair under a Rydberg electromagnetically induced transparency configuration. With the presence of the Rydberg blockade effect, we switch on a gate field to make the atomic medium nontransparent thereby absorbing the single photon emitted from another atomic ensemble via the spontaneous four-wave mixing process. In contrast to the case without a gate field, more than 50% of the photons sent to the switch are blocked, and finally achieve an effective single-photon switch. There are on average 1-2 gate photons per effective blockade sphere in one gate pulse. This switching effect on a single entangled photon depends on the principal quantum number and the photon number of the gate field. Our experimental progress is significant in the quantum information process especially in controlling the interaction between Rydberg atoms and entangled photon pairs., 9 pages, 8 figures

The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and Renyi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, D) and the hyperquantum numbers $$(n_r,\mu _1,\mu _2,\ldots ,\mu _{D-1})$$ which characterize the state. Emphasis is placed on the highly excited Rydberg (high radial hyperquantum number $$n_r$$ , fixed D) and the high-dimensional (high D, fixed hyperquantum numbers) states. We have used a methodology where the theoretical determination of the integral functionals of the Laguerre and Gegenbauer polynomials, which describe the spreading quantities, leans heavily on the algebraic properties and asymptotical behavior of some weighted $${\mathfrak {L}}_{q}$$ -norms of these orthogonal functions.

We demonstrate electromagnetically-induced transparency and giant Kerr nonlinearity in a five-level atomic system where the upper level is a Rydberg-state coupled coherently to a four-level tripod subsystem. Since the high Rydberg states exhibit rather long lifetimes, the system evolves into a dark state that is a superposition of all long-lived states resulting in an optical transparency for the probe field. We solve the relevant density matrix equations for the atomic system in steady-state and utilize the perturbation approach to obtain the expressions for the linear and nonlinear susceptibility. It is shown that depending on the system parameters, the system can exhibit triple, double or single, optical transparency. Therefore, there is a resulting change in the sign of linear dispersion for different parametric situations giving, rise to switching in the group velocity of the probe pulse from superluminal to subluminal or vice versa. We also identify the existence of giant third-order Kerr nonlinearities within regions of optical transparency and under the slow light condition.

We consider classical circular Rydberg states of a hydrogenic atom/ion under collinear electric and magnetic fields of arbitrary strengths, the entire system being immersed into a plasma with the Debye screening. In this way we add a “new dimension” to the results of the previous paper of one of us, where the screening was not taken into account. We show in detail how the screening decreases the value of the critical electric field required for the ionization at different values of the magnetic field. Our results should have a fundamental importance because hydrogenic atoms/ions under external fields remain a test-bench for atomic physics. Also our results could motivate experiments on the magnetic control of the “continuum lowering” in cold Rydberg plasmas, this being of practical importance.

Photoionization (PI) cross sections of the ground state 3s23p 2P°1/2 and metastable state 3s23p 2P°3/2 of Al-like Sc are investigated using the Dirac R-matrix method. The current energy levels and radiative transition rates are consistent with experimental results and previous theory. Our calculated ionization energies of the ground and metastable states are in accordance with the experimental values. The PI cross sections show good agreement between length and velocity forms. Partial-wave contributions to the total PI of ground and metastable states are discussed. Moreover, the PI cross sections are dominated by a large number of resonances from the Rydberg series of autoionizing states. In addition to providing data for the Opacity Project TOPbase, the present work promotes plasma simulation and diagnosis.

The detailed description of electron terms in the field of two stationary Coulomb centers of charges Z and Z′ separated by a distance R is one of the most fundamental problems in quantum mechanics. When the charges Z and Z′ approach each other and share the only one electron that they have, they form a quasimolecule. Such quasimolecules are encountered in various kinds of plasmas and play an important role in theoretical and experimental studies of charge exchange. When the electron is in a highly-excited state, it is a one-electron Rydberg quasimolecule (OERQ). There are extensive analytical studies of the OERQ by the methods of classical mechanics (which are appropriate for Rydberg states). In one of our previous papers we studied the OERQ subjected to a laser field in the situation where the laser frequency was much smaller than the highest frequency of the unperturbed system. In the present paper we consider the situation where the OERQ is subjected to a laser field whose frequency is much greater than the highest frequency of the unperturbed system. For obtaining analytical results we use a generalization of the method of effective potentials. We show that as the amplitude of the laser field increases, in the case of the linearly-polarized laser field, the structure of the energy terms becomes more complex. Moreover the number of the energy terms increases in this case. We also calculated analytically the shift of the radiation frequency of OERQ caused by the laser field. As the amplitude of the laser field increases, so does the shift. The radiation frequency is shifted to the blue in the case of the linearly-polarized laser field, and to the red in the case of the circularly-polarized laser field. For a known amplitude of the laser field, by measuring the relative shift of the radiation frequency it should be possible to determine experimentally the distance of the orbital plane of the electron from the nucleus of the smaller nuclear charge.

11 pags., 4 figs., 2 tabs., The correlation between chemical structure and predissociation dynamics has been evaluated for a series of linear and branched alkyl iodides with increasing structural complexity by means of femtosecond time-resolved velocity map imaging experiments following excitation on the second absorption band (B-band) at around 201 nm. The time-resolved images for the iodine fragment are reported and analyzed in order to extract electronic predissociation lifetimes and the temporal evolution of the anisotropy while the experimental results are supported by ab initio calculations of the potential energy curves as a function of the C-I distance. Remarkable similarities are observed for all molecules consistent with a major predissociation of the initially populated bound Rydberg states 6A″ and 7A′ through a crossing with the purely repulsive states 7A″, 8A′ and 8A″ leading to a major R + I*(P) (R = CH, CH, n-CH, n-CH, i-CH and t-CH) dissociation channel. The reported electronic predissociation lifetimes are found to decrease for an increasing size of the linear radical, reflecting the shifts observed in the position of the crossings in the potential energy curves, and very likely a greater non-adiabatic coupling between the initially populated Rydberg states and the repulsive states leading to dissociation induced by other coordinates associated to key vibrational normal modes. The loss of anisotropy is fully accounted for by the parent molecular rotation during predissociation and the rotational temperature of the parent molecule in the molecular beam is reasonably derived., M.L.M.S. acknowledges fnancial support through a predoctoral contract from Universidad Complutense de Madrid. S.M.P. acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, grant agreement No 842539. Tis work has been fnanced by the Spanish MINECO (grant CTQ2015-65033-P) and Ministerio de Ciencia, Innovación y Universidades (grant PGC2018-096444-B-I00). Te facilities provided by the Center for Ultrafast Lasers of Universidad Complutense de Madrid are acknowledged.

Using time-resolved laser-scanning confocal microscopy and ultrafast optical pump/THz probe spectroscopy, we measure photoluminescence (PL) and THz-conductivity in perovskite micro-crystals and films. PL quenching and lifetime variations occur from local heterogeneity. Ultrafast THz-spectra measure sharp quantum transitions from excitonic Rydberg states, providing weakly bound excitons with a binding energy of ~13.5 meV at low temperatures. Ab-initio electronic structure calculations give a direct band gap of 1.64 eV, a dielectric constant of ~18, heavy electrons, and light holes, resulting in weakly bound excitons, consistent with the binding energies from the experiment. The complementary spectroscopy and simulations reveal fundamental insights into perovskite light-matter interactions.

A novel two-dimensional phase and amplitude electromagnetically induced grating is proposed. This model improves the sensitivity of electromagnetically induced grating to the microwave field. The system experiences electromagnetically induced transparency (EIT) via interacting dark resonances. When two-dimensional standing control fields are applied to a Rydberg five-level EIT system, two sub-EIT systems appear and the central peak in the EIT window is splitted. Frequency splitting of two central absorption peaks is proportional to the microwave field strength. The simulations show that the efficiency of higher orders of two-dimensional EIG could be enhanced compared to a common four-level single-dark-state system without microwave field. Therefore, one can take advantage of the phase modulation to control the probe light dispersing into the required high orders. This proposed model is appropriate to be utilized as an all-optical switch and router in optical networking and communication based on microwave field.

We have theoretically studied the seven lowest triplet states of the disulfur species. For such investigations, analytical potential energy curves (APECs) for $X^{3}\varSigma _{g}^{-}$ ground and $A^{\prime\,3} \Delta _{u}$, $A^{3}\varSigma _{u}^{+}$, $B^{\prime\prime\,3}\varPi _{u}$, and $B^{3}\varSigma _{u}^{-}$ excited electronic states were constructed within the extended Hartree–Fock approximate correlation energy (EHFACE) model by Varandas. Once that these analytical representations are obtained, nuclear properties, such as vibrational energies, classical turning points, and spectroscopic constants were calculated. Particularly, comparisons between these vibrational levels with those obtained via the Rydberg–Klein–Rees (RKR) methodology as implemented in Le Roy’s RKR1 code are reported. The impact of tight $d$ augmented correlation consistent basis on the energies and frequencies is shown. We also re-examined the vibronic (vibration-electronic) transition parameters as Franck–Condon (FC) factors and $r$-centroids for the bands of the $B^{\prime\prime\,3}\varPi _{u} $–$X^{3}\varSigma _{g}^{-}$, $B^{3}\varSigma _{u}^{-} $–$X^{3}\varSigma _{g}^{-}$, $C^{3}\varSigma _{u}^{-} $–$X ^{3}\varSigma _{g}^{-}$, and $D^{3}\varPi _{u} - X^{3}\varSigma _{g}^{-}$ systems of the $\mbox{S}_{2}$ molecule. The vibrational levels and turning points of the two Rydberg states $C^{3}\varSigma _{u}^{-}$ and $D^{3}\varPi _{u}$ were computed only with the RKR method. Our results can be employed in rationalizations of astrochemical and astrophysical observations.

We study power broadening of coherent two-photon resonances on Rydberg transitions in lithium-7 atoms in a magneto-optical trap (MOT). We apply the spectroscopic technique based on the reduction of resonance fluorescence in the MOT. One of the main contributions to the spectral broadening is associated with heating of the trapped atoms by laser cooling beams. We suggest a new nondestructive method to measure the atomic temperature in a working MOT using two-photon spectroscopy with variable directions of probe beams.

Systems of neutral atoms are gradually gaining currency as a promising candidate for realizing large-scale quantum computing. The achievement of a record-high fidelity in quantum operation with alkaline-earth Rydberg atoms is a case in point.

We present an experimental setup for creating arbitrary two-dimensional arrays of optical microtraps to trap single atoms for experiments with Rydberg atoms. We use a spatial light modulator to manipulate the spatial phase of a far red-detuned optical dipole trap beam, which allows us to create arbitrary arrays of optical microtraps, by focusing the beam with an in-vacuum high numerical-aperture aspheric lens. We load atoms in the microtraps from a dilute cloud of cold atoms, having at most one atom in each trap due to fast light-assisted collisions. Real-time analysis of the atomic fluorescence with a sensitive CCD camera allows us to determine the filling of each trap individually with a >10 Hz rate. We can create strong interactions between the atoms by exciting them to Rydberg states, with an efficiency of single atom resolved Rydberg detection of >95%.

The Interaction Enhanced Imaging technique allows to detect the spatial distribution of strongly interacting impurities embedded within a gas of background atoms used as a contrast medium [1]. Here we present a detailed study of this technique, applied to detect Rydberg P states. We experimentally realize fast and efficient three-photon excitation of P states, optimized according to the results of a theoretical effective two-level model. Few Rydberg P-state atoms, prepared in a small cloud with dimensions comparable to the blockade radius, are detected with a good sensitivity by averaging over 50 shots. The main aspects of the technique are described with a hard-sphere model, finding good agreement with experimental data. This work paves the way to a non-destructive optical detection of single Rydberg atoms with high spatial and temporal resolution.

Strong interactions between Rydberg excitations in cold gases give rise to strong correlations within these samples. Here we present a series of techniques that allow to visualize such correlations either directly, by varying the degree of interaction between the excitations, or indirectly, through the analysis of the full counting statistics (FCS) of the excitation events. Combining the information obtained by both methods provides a more complete characterization of the system, and allows the study of the correlations emerging in the system as a consequence of the strongly interacting nature of Rydberg excitations.

The strong dipole-dipole coupling and the Stark tunability make Forster resonances an attractive tool for the implementation of quantum gates. In this direction a generalization to a N-body process would be a powerful instrument to implement multi-qubit gate and it will also path the way to the understanding of many-body physics. In this review, we give a general introduction on Forster resonances, also known as two-body FRET, giving an overview of the different application in quantum engineering and quantum simulation. Then we will describe an analogous process, the quasi-forbidden FRET, which is related to the Stark mixing due to the presence of an external electric field. We will then focus on its use in a peculiar four-body FRET. The second part of this review is focused on our study of few-body interactions in a cold gas of Cs Rydberg atoms. After a detailed description of a series of quasi-forbidden resonances detected in the proximity of an allowed two-body FRET we will show our most promising result: the observation of a three-body FRET. This process corresponds to a generalization of the usual two-body FRET, where a third atom serves as a relay for the energy transport. This relay also compensates for the energy mismatch which prevents a direct two-body FRET between the donor and the acceptor, but on the other side allowed a three-body process; for this reason, the three-body FRET observed is a “Borromean” process. It can be generalized for any quantum system displaying two-body FRET from quasi-degenerate levels. We also predict N-body FRET, based on the same interaction scheme. Three-body FRET thus promises important applications in the formation of macro-trimers, implementation of few-body quantum gates, few-body entanglement or heralded entanglement.

We present an overview of our recent investigations of long-range interactions in an ultracold Cs Rydberg gas. These interactions are studied by high-resolution photoassociation spectroscopy, using excitation close to one-photon transitions into np3/2 Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs2 molecules. We observe two types of molecular resonances. The first type originates from the correlated excitation of two atoms into Rydberg-atom-pair states interacting at long range via multipole-multipole interactions. The second type results from the interaction of one atom excited to a Rydberg state with one atom in the electronic ground state. Which type of resonances is observed in the experiments depends on the laser intensity and frequency and on the pulse sequences used to prepare the Rydberg states. We obtain insights into both types of molecular resonances by modelling the interaction potentials, using a multipole expansion of the long-range interaction for the first type of resonances and a Fermi-contact pseudo-potential for the second type of resonances. We analyse the relation of these long-range molecular resonances to molecular Rydberg states and ion-pair states, and discuss their decay channels into atomic and molecular ions. In experiments carried out with a two-colour two-photon excitation scheme, we observe a large enhancement of Rydberg-excitation probability, which we interpret as a saturable autocatalytic antiblockade phenomenon.

We review the field of ultralong-range Rydberg molecules with a focus on recent developments. We briefly revisit the binding mechanism of Rydberg molecules based on electron-atom scattering and give an overview of experimental realizations in different ultracold atomic systems. However the main focus of the manuscript is on Rb2 Rydberg molecules. We discuss different angular momenta of the excited Rydberg states (S and D) and the interaction of the molecules with external electric and magnetic fields. Furthermore, we cover the transition from low atomic densities, where only a single atom is bound by a Rydberg electron, to high densities, where polyatomic bound states can be observed.

Rare isotope (13C, 17O and 18O) substitutions can substantially change absorption line positions, oscillator strengths and photodissociation rates of carbon monoxide (CO) in the vacuum ultraviolet (VUV) region, which has been well accounted for in recent photochemical models for understanding the large isotopic fractionation effects that are apparent in carbon and oxygen in the solar system and molecular clouds. Here, we demonstrate a strong isotope effect associated with the VUV photodissociation of CO by measuring the branching ratios of 12C16O and 13C16O in the Rydberg 4p(2), 5p(0) and 5s(0) complex region. The measurements show that the quantum yields of electronically excited C atoms in the photodissociation of 13C16O are dramatically different from those of 12C16O, revealing strong isotope effect. This isotope effect strongly depends on specific quantum states of CO being excited, which implies that such effect must be considered in the photochemical models on a state by state basis., Carbon monoxide is the main C and O reservoir in interstellar media, where it undergoes photochemistry. The authors show that isotopic substitution affects not only its absorption. spectrum and photodissociation rates but also the branching ratio, key to understand isotopic. fractionation in the solar system

In this work, a review of six functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Rydberg potential, followed by functions by Hulburt-Hirschfelder, Murrell-Sorbie, Thakkar, Hua and finalizing with the potential for diatomic systems by Aguado and Paniagua. The mathematical behavior of these functions for the short- and long-range regions is discussed. A comparison highlighting the positive and negative aspects of each representation is also presented. As study cases, three diatomic systems O2, N2 and SO in their respective ground electronic states were selected. To obtain spectroscopic parameters, ab initio energies were first calculated at multi-reference configuration interaction (MRCI) with the Davidson modification (MRCI+Q) level of theory, using aug-cc-pVXZ (X = T,Q,5,6) Dunning basis sets. Such energies were then fitted to respective functional forms. The so-obtained spectroscopic constants are compared also with available literature data.

The latest molecular constant potential energy curves used for the electronic ground states of I2, F2 and CO molecules are constructed by the Rydberg–Klein–Rees–Vanderslice (RKRV) method. The Morse, Rydberg, Hulbert–Hirschfelder and extended Rydberg potential functions compare each other and have good agreement with RKRV curves for these molecules. The percentage deviations from RKRV curves are drawn at the same abscissa scale. These curves show that the extended Rydberg potential energy curve deviation is $$< 0.5{-}2\%$$ error to dissociation limit.