Ground-state Atoms Research Articles

Photoassociation spectra of cesium 31D<sub>5/2</sub>+6S<sub>1/2</sub>(<i>F</i> = 4) ultralong-range Rydberg molecules

In this paper, we conduct the experiment and simulation on 31D<sub>5/2</sub>+6S<sub>1/2</sub>(<i>F</i> = 4) Cs<sub>2</sub> ultralong-range Rydberg molecules (ULRMs). These molecules are prepared by employing a two-photon photoassociation scheme. Two distinct ultralong-range Rydberg molecular signals are observed at the detuning –162.8 MHz and –66.6 MHz of 31D<sub>5/2</sub> atomic resonant line, which are bound by the pure triplet potential and mixed singlet-triplet potential, respectively. We use the model of scattering interaction between the Rydberg electron and ground-state atom to perform the simulation. The molecular potential-energy curves are obtained by solving the Hamiltonian on a grid of intermolecular distances <i>R</i>. The calculations of the binding energy of pure triplet and mixed singlet-triplet <i>v</i> = 0 vibrational states are compared with the experimental measurements. The calculated and measured values of the binding energy are in good agreement. The s-wave pure triplet and singlet zero-energy scattering length are obtained to be <inline-formula><tex-math id="M3">\begin{document}${a}_{{\rm{s}}}^{{\rm{T}}}({0})=-{19.16}{a}_{0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ {a}_{{\rm{s}}}^{{\rm{S}}}(0)=-{1.92}{a}_{0} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230520_M4.png"/></alternatives></inline-formula>, respectively. This kind of molecule with large size, abundant vibrational states and large permanent electric dipole moment is an excellent candidate for studying low-energy collision dynamics. The study of these molecules will further deepen and enrich the understanding of the special binding mechanism and exotic properties of the ULRMs.

Preparation of ultra-cold (36D<sub>5/2</sub>+ 6S<sub>1/2</sub>) Rydberg molecule and measurement of its permanent electric dipole moment

<sec>Ultra-cold long-range Rydberg molecules, consisting of a Rydberg atom and a ground-state atom or another Rydberg atom or ion, have attracted considerable attention due to their exaggerated properties, such as huge size, long chemical bond, large polarization and electric dipole moment, abundant vibrational states and exotic adiabatic potentials. The binding mechanism of Rydberg molecules is a low-energy scattering interaction between the Rydberg electron and the ground state atom for ground-Rydberg molecules or long-range multipole interaction for Rydberg-atom macrodimers and Rydberg-ion molecules, in contrast to covalent bonds, ionic bonds of normal and van der Waals interaction. Owing to its huge size, the dynamic evolution becomes slow compared with normal diatomic molecules and the ultra-long chemical bonds allow being imaged directly by high resolution imaging technology, which makes it convenient to observe the molecular dynamics process chemical reaction process in real time. The investigation of Rydberg molecules will be significant for understanding the mechanism of molecular collision and quantum chemical reaction.</sec><sec>In this work, we study the ultra-cold Rydberg-ground state molecules theoretically and experimentally. Theoretically, we calculate the adiabatic potential energy curve of cesium (36D<sub>5/2</sub>+ 6S<sub>1/2</sub>) Rydberg molecule based on the Fermi model of low energy electron scattering by numerically solving the Hamiltonian of Rydberg molecules. And also, we obtain its characteristic parameters, such as the potential depth, binding energy and equilibrium nuclear distance of Rydberg molecule. Experimentally, the Rydberg-ground molecules are investigated by a photoassociation spectroscopy, where two laser pulses are used to achieve a two-photon transition, and their spectra are obtained by ion detection technology. We successfully observe the Rydberg-ground state molecular spectra that correspond to a scattering triplet and a scattering single-triplet mixture (<sup>S,T</sup>Σ). The measured binding energy of Rydberg-ground state molecules is in good agreement with the theoretical result. In addition, taking the Rydberg-ground state molecules formed by scattering triplet (<sup>T</sup>Σ) for example, we demonstrate the spectrum broadening of Rydberg molecules in a weak electric field, from which we obtain the permanent electric dipole moments <inline-formula><tex-math id="M2">\begin{document}$|\bar{d}|$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M2.png"/></alternatives></inline-formula> of polar Rydberg-ground state molecules about (12.10<inline-formula><tex-math id="M3">\begin{document}$ \pm $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M3.png"/></alternatives></inline-formula>1.65) Debye ((4.76<inline-formula><tex-math id="M4">\begin{document}$ \pm $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M4.png"/></alternatives></inline-formula>0.65) <i>ea</i><sub>0</sub>). The results are consistent with the theoretical calculations. Our study provides a feasible scheme for the experimental preparation of D-type Rydberg-ground molecules, which is of great significance in studying the binding mechanism and the spectral characteristics of polar Rydberg molecules.</sec>

Электромагнитно-индуцированная прозрачность в ячейках конечных размеров с антирелаксационным покрытием стенок

In this paper, we propose an approach that makes it possible to obtain an analytical expression of the spectral dependence of the resonance of electromagnetically induced transparency detected by bichromatic radiation in a cell of finite size in the longitudinal direction of the laser beam. Specular and diffuse reflections of atoms from walls are considered. It was found that a significant difference between these types of reflections takes place only for cells of small longitudinal dimensions compared to the splitting wavelength of the ground state of atoms. A physical explanation is proposed for the difference between the Stokes and anti-Stokes scattering channels of probe radiation in terms of dressed states.

DC slice ion imaging of the ultraviolet photodissociation of 2-bromohexane

The ultraviolet photodissociation dynamics of 2‑bromohexane around 234 nm has been investigated using the DC slice velocity map imaging technique. Relative quantum yield of the ground state bromine atom is measured to be 0.961. By analyzing the slice images, we can obtain the speed and angular distributions of the ground state and excited state bromine atoms. The speed distribution contains two Gaussian components, which are attributed to two dissociation channels. The high translational energy component is formed via the direct dissociation along the C–Br bond. Nevertheless, the low translational energy component is formed via the multidimensional dissociation along the C–Br bond coupling with the bending modes. The alkyl radical branching promotes the multidimensional dissociation. What’s more, the contribution of the electric-dipole allowed3Q1, 3Q0 and 1Q1 states to the product formation is also discussed. The nonadiabatic 1Q1←3Q0 transition plays a significant role in the dissociation process.

Ion-loss events in a hybrid trap of cold Rb-Ca+ : Photodissociation, blackbody radiation, and nonradiative charge exchange

We theoretically investigate the collisional dynamics of laser-cooled $^{87}$Rb ground-state atoms and $^{40}$Ca$^+$ ground-state ions in the context of the hybrid trap experiment of Ref. [Phys. Rev. Lett. 107, 243202 (2011)], leading to ion losses. Cold $^{87}$Rb$^{40}$Ca$^+$ ground-state molecular ions are created by radiative association, and we demonstrate that they are protected against photodissociation by black-body radiation and by the $^{40}$Ca$^+$ cooling laser at 397~nm. This study yields an interpretation of the direct observation of $^{87}$Rb$^{40}$Ca$^+$ ions in the experiment, in contrast to other hybrid trap experiments using other species. Based on novel molecular data for the spin-orbit interaction, we also confirm that the non-radiative charge-exchange is the dominant loss process for Ca$^+$ and obtain rates in agreement with experimental observations and a previous calculation.

A novel tetrahedral spectral element method for Kohn-Sham model

High order computational approach for the electronic structure calculation is a long-standing research area. Among all the discretization methods, spectral element method stands out for its flexibility to capture the singularity and high accuracy from the spectral perspective. In this work, we propose a tetrahedral spectral element method for full-potential electronic structure calculation. In the method, a C0 space is constructed for the numerical solution, based on a modification of basis functions proposed in [L. Jia et al. (2022) [48]] with the aid of generalized Koornwider polynomials, and a special designed tetrahedral mesh. Moreover, the interpolation and visualization are developed to provide numerical insights of our method. To demonstrate its potential towards practical simulations, we apply our method for calculating ground states of given electronic structures using the Kohn-Sham model. The method consists of a combination of an imaginary time propagation method and a self-consistent field iteration. For accelerating the simulation, a p-multigrid solver is developed which takes the advantage of the high order property of our method. A number of numerical experiments validate the effectiveness of our method, i.e., the expected spectral accuracy can be observed from results, and convincing ground states of various atoms and molecules are obtained.

Correlation Renormalized and Induced Spin-Orbit Coupling

Interplay of spin-orbit coupling (SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators and topological transitions. We find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using the Hartree–Fock mean field theory, phase diagrams of px /py orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of strength of SOC δ λ ∝ (Uʹ–J). Due to breaking down of rotation symmetry, form of SOC on multi-orbital materials is also changed under correlation. If a non-interacting system is close to fermionic instability, spontaneous generalized SOC can also be found. Using renormalization group, SOC is leading instability close to quadratic band-crossing point. Mean fields at quadratic band-crossing point are also studied.

Correlation renormalized and induced spin-orbit coupling

Abstract Interplay of spin-orbit coupling (SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators (TI) and topological transitions. In this work, we find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using Hartree-Fock mean field theory, phase diagrams of $p_{x}/p_{y}$ orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of strength of SOC $\delta \lambda \propto (U'-J)$. Due to breaking down of rotation symmetry, form of SOC on multi-orbital materials are also changed under correlation. If non-interacting system is close to fermionic instability, spontaneous generalized SOC can also be found. Using renormalization group, SOC is leading instability close to quadratic band-crossing point. Mean fields at quadratic band-crossing point are also studied.

Extended reaction kinetics model for non-thermal argon plasmas and its test against experimental data

An extended reaction kinetics model (RKM) suitable for the analysis of weakly ionised, non-thermal argon plasmas with gas temperatures around 300 K at sub-atmospheric and atmospheric pressures is presented. It considers 23 different species including electrons as well as the ground state atom, an atomic and molecular ion, four excited molecular states, and 15 excited atomic states of argon, where all individual 1s and 2p states (in Paschen notation) are included as a separate species. This 23-species RKM involves 409 collision processes and radiative transitions and recent electron collision cross section data. It is evaluated by means of results of time- and space-dependent fluid modelling of argon discharges and their comparison with measured data for two different dielectric barrier discharge configurations as well as a micro-scaled atmospheric-pressure plasma jet setup. The results are also compared with those obtained by use of a previously established 15-species RKM involving only the two lumped 2p states 2p10…5 and . It is found that the 23-species RKM shows generally better agreement with experimental data and provides more options for direct comparison with measurements than the frequently used 15-species RKM.

Quantum thermal field fluctuation induced corrections to the interaction between two ground-state atoms

We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) in the fourth order for two atoms in interaction with scalar fields in vacuum to a thermal bath at finite temperature T, and then calculate the interatomic interaction energy of two ground-state atoms separately in terms of the contributions of thermal fluctuations and the radiation reaction of the atoms and analyze in detail the thermal corrections to the van der Waals and Casimir–Polder interactions. We discover a particular region, i.e. with L, β and λ denoting the interatomic separation, the wavelength of thermal photons and the transition wavelength of the atoms respectively, where the thermal corrections remarkably render the van der Waals force, which is usually attractive, repulsive, leading to an interesting crossover phenomenon of the interatomic interaction from attractive to repulsive as the temperature increases. We also find that the thermal corrections cause significant changes to the Casimir–Polder force when the temperature is sufficiently high, resulting in an attractive force proportional to TL −3 in the λ ≪ β ≪ L region, and a force that can be either attractive or repulsive and even vanishing in the β ≪ λ ≪ L region depending on the interatomic separation.

Observation of oscillatory Raman gain associated with two-photon Rabi oscillations of nanofiber-coupled atoms

Quantum emitters with a Λ-type level structure enable numerous protocols and applications in quantum science and technology. Understanding and controlling their dynamics is, therefore, one of the central research topics in quantum optics. Here, we drive two-photon Rabi oscillations between the two ground states of cesium atoms and observe the associated oscillatory Raman gain and absorption that stems from the atom-mediated coherent photon exchange between the two drive fields. The atoms are efficiently and homogeneously coupled with the probe field by means of a nanofiber-based optical interface. We study the dependence of the two-photon Rabi frequency on the system parameters and observe Autler–Townes splitting in the probe transmission spectrum. Beyond shedding light on the fundamental processes underlying two-photon Rabi oscillations, our method could also be used to investigate (quantum) correlations between the two drive fields as well as the dynamical establishment of electromagnetically induced transparency.

Experimental Determination of a Single Atom Ground State Orbital through Hyperfine Anisotropy.

Historically, electron spin resonance (ESR) has provided excellent insight into the electronic, magnetic, and chemical structure of samples hosting spin centers. In particular, the hyperfine interaction between the electron and the nuclear spins yields valuable structural information about these centers. In recent years, the combination of ESR and scanning tunneling microscopy (ESR-STM) has allowed to acquire such information about individual spin centers of magnetic atoms bound atop a surface, while additionally providing spatial information about the binding site. Here, we conduct a full angle-dependent investigation of the hyperfine splitting for individual hydrogenated titanium atoms on MgO/Ag(001) by measurements in a vector magnetic field. We observe strong anisotropy in both the g factor and the hyperfine tensor. Combining the results of the hyperfine splitting with the symmetry properties of the binding site obtained from STM images and a basic point charge model allows us to predict the shape of the electronic ground state configuration of the titanium atom. Relying on experimental values only, this method paves the way for a new protocol for electronic structure analysis for spin centers on surfaces.

A quantum-mechanical investigation of O(3P) + CO scattering cross sections at superthermal collision energies

ABSTRACT The kinetics and energetic relaxation associated with collisions between fast and thermal atoms are of fundamental interest for escape and therefore also for the evolution of the Mars atmosphere. The total and differential cross sections of fast O(3P) atom collisions with CO have been calculated from quantum mechanical calculations. The cross sections are computed at collision energies from 0.4 to 5 eV in the centre-of-mass frame relevant to the planetary science and astrophysics. All the three potential energy surfaces (3A′, 3A″, and 2 3A″ symmetry) of O(3P) + CO collisions separating to the atomic ground state have been included in calculations of cross sections. The cross sections are computed for all three isotopes of energetic O(3P) atoms collisions with CO. The isotope dependence of the cross sections are compared. Our newly calculated data on the energy relaxation of O atoms and their isotopes with CO molecules will be very useful to improve the modelling of escape and energy transfer processes in the Mars’ upper atmosphere.

Hawking radiation and entropy of a BTZ black hole with minimum length

In this paper we consider a BTZ black hole with minimum length which has been introduced through the probability density of the ground state of the hydrogen atom. We analyzed the effect of the minimum length by calculating the thermodynamic quantities such as temperature and entropy and verified the stability of the black hole by computing the specific heat capacity.

Preparation of 87Rb and 133Cs in the motional ground state of a single optical tweezer

We report simultaneous Raman sideband cooling of a single 87Rb atom and a single 133Cs atom held in separate optical tweezers at 814 nm and 938 nm, respectively. Starting from outside the Lamb-Dicke regime, after 45 ms of cooling we measure probabilities to occupy the three-dimensional motional ground state of for Rb and for Cs. Our setup overlaps the Raman laser beams used to cool Rb and Cs, reducing hardware requirements by sharing equipment along the same beam path. The cooling protocol is scalable, and we demonstrate cooling of single Rb atoms in an array of four tweezers. After motional ground-state cooling, a 938 nm tweezer is translated to overlap with a 814 nm tweezer so that a single Rb and a single Cs atom can be transferred into a common 1064 nm trap. By minimising the heating during the merging and transfer, we prepare the atoms in the relative motional ground state with an efficiency of . This is a crucial step towards the formation of single RbCs molecules confined in optical tweezer arrays.

Atomic isotropic hyperfine properties for second row elements (Al-Cl).

Isotropic hyperfine properties have been obtained for the second row elements Al-Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are -1.80 27Al (2Po 1/2), -24.31 29Si (3P0), 63.70 31P (4So 3/2), 20.77 33S (3P2), and 35.42 35Cl (2Po 3/2). We find a large K shell contribution to the spin density at the nucleus that is almost canceled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to the atomic number.

Quantum-brachistochrone approach to the conversion from W to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits

Using the quantum-brachistochrone formalism, we address the problem of finding the fastest possible (time-optimal) deterministic conversion between $W$ and Greenberger-Horne-Zeilinger (GHZ) states in a system of three identical and equidistant neutral atoms that are acted upon by four external laser pulses. Assuming that all four pulses are close to being resonant with the same internal (atomic) transition---the one between the atomic ground state and a high-lying Rydberg state---each atom can be treated as an effective two-level system ($gr$-type qubit). Starting from an effective system Hamiltonian, which is valid in the Rydberg-blockade regime and defined on a four-state manifold, we derive the quantum-brachistochrone equations pertaining to the fastest possible $W$-to-GHZ state conversion. By numerically solving these equations, we determine the time-dependent Rabi frequencies of external laser pulses that correspond to the time-optimal state conversion. In particular, we show that the shortest possible $W$-to-GHZ state-conversion time is given by ${T}_{\text{QB}}=6.8\phantom{\rule{0.222222em}{0ex}}\ensuremath{\hbar}/E$, where $E$ is the total laser-pulse energy used, this last time being significantly shorter than the state-conversion times previously found using a dynamical-symmetry-based approach [${T}_{\text{DS}}=(1.33\ensuremath{-}1.66)\phantom{\rule{0.222222em}{0ex}}{T}_{\text{QB}}$].

Theoretical study of the enhancement of saturable absorption of Kr under x-ray free-electron laser

The generation of hollow atoms will reduce the probability of light absorption and provide a high-quality diffraction image in the experiment. In this paper, we calculated the ionization rate of the Kr atom under x-ray free-electron laser (XFEL) using Hartree–Fock–Slater model and simulated the ionization model of Kr atom using Monte–Carlo method to determine the response of the hollow atom of Kr atom to the XFEL photon energy. Calculating the correlation between the total photoionization cross-section of the ground state of Kr atom and the photon energy, we determined three particular photon energies of 1.75 keV, 1.90 keV, and 14.30 keV. The dynamics simulation under the experimental condition’s 17.50 keV photon energy was achieved by implementing the Monte–Carlo method and calibrating the photon flux modeling parameters. Consequently, our calculated data are more consistent with experimental phenomena than previous theoretical studies. The saturable absorption of Kr at 1.75 keV, 1.90 keV, 14.30 keV, and 17.50 keV energies was further investigated by using the optimized photon flux model theory. We compared the statistics on main ionization paths under those four specific photon energies and calculated the population changes of various Kr hollow atoms with different configurations. The results demonstrate that the population of hollow atoms produced at the critical ionization photon energy is high. Furthermore, the change of population with respect to position is smooth, which shows a significant difference between the generation mode of ions with low and high photon energies. The result is important for the study of medium- and high-Z element hollow atoms, which has substantial implications for the study of hollow atoms with medium and high charge states, as well as for the scaling of photon energy of free electron lasers.

Double hyperbolic cosine basis sets for LCAO calculations

Recently, we reported a new set of hyperbolic cosine type basis sets, which include the radial part of exponential type functions. In this study, it is show that the double hyperbolic cosine basis sets with non-integer Slater type orbitals give extremely accurate results, with the accuracy superior to that of the previous similar calculations. Total energy differences and comparison between double hyperbolic cosine and other similar basis sets suggested in literature are presented. Using double hyperbolic cosine orbitals, combined Hartree–Fock-Roothaan calculations have been carried out on the ground states of atoms and their ions within the minimal basis sets framework to compare the performance of the basis sets. The basis sets achieved the accuracy far beyond the double-zeta quality. Proposed basis sets can also play an effective role in ion-atom collisions problems and semi-empirical methods.

Nonreciprocity with Structured Light Using Optical Pumping in Hot Atoms

Nonreciprocal transmission of structured light has possible applications in high-capacity optical communication and high-dimensional signal processing. Here, we demonstrate the magnet-free and cavity-free optical nonreciprocity of an orbital-angular-momentum (OAM) beam using optical-pumping technology with the assistance of the Doppler effect in hot atoms. By using optical pumping to induce a direction-dependent population transfer of the ground-state atoms, we realize optical nonreciprocity for the signal laser that is carrying OAM. Interestingly, an isolation ratio close to 30 dB and maximum transmission over 0.86 can be achieved simultaneously without the use of an optical cavity. Due to the unique amplitude and helical phase profile of the structured light, our proposal may open an avenue for exploring the singularity characteristics of optical nonreciprocity using structured light.