Alkaline-earth Atoms Research Articles

Tight-binding Kondo model and spin-exchange collision rate of alkaline-earth-metal atoms in a mixed-dimensional optical lattice

We study the two-body problem of the ultracold fermionic alkaline-earth (like) atoms in the electronic $^1$S$_0$ state ($g$-state) and $^3$P$_0$ state ($e$-state), which are confined in a quasi-one-dimensional (quasi-1D) tube. In addition, in the axial direction, the $g$-atom experience a 1D optical lattice and the $e$-atom is localized by a harmonic potential. In this work, we propose two appropriate tight-binding models, which are applicable for the cases that the odd-wave scattering between the $g$- and $e$-atom is negligible or not, respectively. We further give a microscopic derivation for the inter-atomic interaction parameters of these tight-binding models, by exactly calculating the low-energy inter-atomic scattering amplitude. Our results show that, as one can predict, these interaction parameters can be efficiently controlled by the confinement potentials. We further exam the simple "projection approximation" with which one derives the interaction parameters by directly projecting the 3D Huang-Yang pseudopotential on the ground state of the confinement and the lowest band of the optical lattice. We find that one should be very careful about determining the interaction parameters in the tight-binding models. Furthermore, we calculate the spin-exchanging rate, which dependents on the incident quasi-momentum $k$ of the $g$-atom, for the recent experiment (L. Riegger, {\it et. al.,} Phys. Rev. Lett. {\bf 120}, 143601 (2018)) of $^{173}$Yb atoms in this quasi-(1+0)D system, and study finite-momentum effect in this experiment. Our results show that in this system the finite-momentum effect of the $g$-atom is very significant, and the momentum of the $g$-atoms in this experiment may be pretty high (already in the second Brillouin zone of the optical lattice)

Rashba and Weyl spin-orbit coupling in an optical lattice clock

Recent experimental realization of one-dimensional (1D) spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin textures of such topological bands for 2D Rashba and 3D Weyl SOC can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb.

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

Transition‐Metal Chemistry of Alkaline‐Earth Elements: The Trisbenzene Complexes M(Bz)3(M=Sr, Ba)

AbstractWe report the synthesis and spectroscopic identification of the trisbenzene complexes of strontium and barium M(Bz)3(M=Sr, Ba) in low‐temperature Ne matrix. Both complexes are characterized by aD3symmetric structure involving three equivalent η6‐bound benzene ligands and a closed‐shell singlet electronic ground state. The analysis of the electronic structure shows that the complexes exhibit metal–ligand bonds that are typical for transition metal compounds. The chemical bonds can be explained in terms of weak donation from the π MOs of benzene ligands into the vacant (n−1)d AOs of M and strong backdonation from the occupied (n−1)d AO of M into vacant π* MOs of benzene ligands. The metals in these 20‐electron complexes have 18 effective valence electrons, and, thus, fulfill the 18‐electron rule if only the metal–ligand bonding electrons are counted. The results suggest that the heavier alkaline earth atoms exhibit the full bonding scenario of transition metals.

Transition-Metal Chemistry of Alkaline-Earth Elements: The Trisbenzene Complexes M(Bz)3 (M=Sr, Ba).

We report the synthesis and spectroscopic identification of the trisbenzene complexes of strontium and barium M(Bz)3 (M=Sr, Ba) in low‐temperature Ne matrix. Both complexes are characterized by a D 3 symmetric structure involving three equivalent η6‐bound benzene ligands and a closed‐shell singlet electronic ground state. The analysis of the electronic structure shows that the complexes exhibit metal–ligand bonds that are typical for transition metal compounds. The chemical bonds can be explained in terms of weak donation from the π MOs of benzene ligands into the vacant (n−1)d AOs of M and strong backdonation from the occupied (n−1)d AO of M into vacant π* MOs of benzene ligands. The metals in these 20‐electron complexes have 18 effective valence electrons, and, thus, fulfill the 18‐electron rule if only the metal–ligand bonding electrons are counted. The results suggest that the heavier alkaline earth atoms exhibit the full bonding scenario of transition metals.

Wavelength-dependent nonsequential double ionization of magnesium by intense femtosecond laser pulses

We report on a systematic investigation of wavelength scaling strong-field double ionization of Mg in intense laser fields. A significant decrease of nonsequential double ionization (NSDI) yield with increasing wavelength from 800--2000 nm is observed. Our data is well reproduced by a three-dimensional Monte Carlo simulation considering recollision impact excitation cross section. We demonstrate that the NSDI of Mg mainly occurs via the first ionic excited state ${\mathrm{Mg}}^{+*}(3p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2,1/2})$ pumped by returning electron impact process. The recollision impact direct ionization pathway plays a minor role here. The wavelength dependence of the NSDI ratio is due to the recollision energy-dependent excitation cross section as well as the electron wave packet diffusion effects, both sensitively depending on the wavelength. Our work represents a step towards strong-field double ionization experiments on Mg in the long wavelength limit and sheds light on the NSDI mechanism of alkaline-earth metal atoms.

Topological superfluidity with repulsive alkaline-earth atoms in optical lattices

We discuss a realization of topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the other itinerant, and show how quantum fluctuations of the localized fermions give rise to an attraction and spin–orbit coupling in the itinerant band. At low temperature, these effects stabilize a topological superfluid of mobile atoms even if their bare interactions are repulsive. This emergent state can be engineered with alkaline-earth atoms in a superlattice with a dimerized unit cell. To probe its unique properties we describe protocols that use high spectral resolution and controllability of a narrow clock transition, such as momentum-resolved spectroscopy and supercurrent response to a synthetic (laser-induced) magnetic field.

Quantum Beat Spectroscopy in a System of N Identical, Closely Spaced Atoms. I. N = 2

Using the example of two closely spaced localized alkaline-earth atoms, we consider the possibilities of the quantum beat method (a version of the level-crossing spectroscopy in a magnetic field) in finding two parameters characterizing the system, namely, the direction from one atom to another and the distance between them. The applicability of the method to the nanoscopy of systems of closely spaced quantum dots, vacancy centers (NV centers, etc.), and impurity atoms (molecules) in crystals is discussed.

Novel Metallic Clathrates of Group-IV Elements and Their Compounds in a Dense Hexagonal Lattice

Further, to recently introduced metallic NaSi6 and Si6 clathrate structures, we show that not only Si but also other group-IV elements, such as C, Ge, and Sn, can form stable and metallic clathrate structures with open channels at the corners of hexagons. These elemental clathrates of Si, Ge, and Sn can be viewed as if they are a combination of 2D metallic planes and perpendicular 1D metallic chains, the interplay of which can give rise to interesting physical effects. When free-standing, these atomic planes transform to 2D semiconducting, single-layer structures. The clathrate structure of C, which consists of weakly interacting, vertical hexagonal tubes situated at the corners of a 2D hexagonal lattice, is insulating in the plane but 1D metallic perpendicular to the planes. We also show that stable compound clathrate structures can form by hosting different alkali, alkaline earth, and light transition metal atoms in the open channels of elemental clathrates. These new metallic allotropes of group-IV ele...

Driven-dissipative quantum dynamics in ultra-long-lived dipoles in an optical cavity

We study the quantum dynamics of many-body arrays of two-level atoms in a driven cavity subject to collective decay and interactions mediated by the cavity field. We work in the bad cavity limit accessible, for example, using long-lived electronic clock states of alkaline-earth atoms, for which the bare atomic linewidth is much less than the cavity linewidth. In the absence of interactions, our system reduces to previously studied models of collective fluorescence. We show that while interactions do not qualitatively change the steady-state properties they lead to a drastic change in the dynamical properties. We find that, for some intervals of driving strengths, the system shows two very distinct types of transient behaviors that depend on the initial state of the system. In particular, there is a parameter regime where the system features oscillatory dynamics with a period of oscillation that becomes much shorter than the duration of the overall transient dynamics as the atom number increases. We use both mean-field and exact numerical calculations of the quantum system to investigate the dynamics.

Monolayer GaN functionalized with alkali metal and alkaline earth metal atoms: A first-principles study

Abstract Based on first-principles calculations, we have carried out a systematic study on the geometric, electronic and magnetic properties of free-standing monolayer GaN (ML GaN) functionalized with Lithium (Li), Sodium (Na), Beryllium (Be) or Calcium (Ca) atoms. We consider three different levels of concentrations i.e. θ = 1 / 8 , 1 / 18 and 1 / 32 . Within the tested θ , metallization of ML GaN only occurs with the adsorption of Li or Na atoms. The adsorption of Be or Ca atoms preserves the semiconducting characteristics of ML GaN. The ML GaN remains non-magnetic with the adsorption of Be or Ca atom. In contrast, the total magnetization of the Li-adsorbed ML GaN decreases as Li atoms concentration increases. For the case of Na adsorption, the ML GaN exhibits ferromagnetism only at θ = 1 / 18 . In addition, we found the work function of the functionalized ML GaN can be controlled by varying the concentrations of the adatoms. Our findings here suggest that by selective adsorption of Group I and Group II element, ML GaN is a promising material for the development of spintronic and field emission devices.

A theoretical study of alkaline-earthides Li(NH3)4M (M = Be, Mg, Ca) with large first hyperpolarizability.

With the aid of ab initio calculations at the MP2 level of theory, a novel type of alkaline-earthides, namely Li(NH3)4M (M = Be, Mg, Ca), has been theoretically designed and investigated. These compounds possess a similar geometric structure, in which the alkali-metal cation Li+ lies near the center of the cagelike (NH3)4 complexant and the alkaline-earth anion M- is located outside. All the proposed alkaline-earthides exhibit extremely large static first hyperpolarizability (β0) up to 8.01 × 106 au, indicating that they can be considered as novel NLO molecules with high performance. The calculated results reveal that the alkaline-earth atom is more suitable to serve as excess electron acceptor in excess electron compounds for increasing the β0 value. We hope that our study can attract more research interest in alkaline-earthides and further experimental research.

Electrochemical Method for Graphene Preparation from Multi-Walled Carbon Nanotubes

There are the numerous methods of graphene synthesis from multi-walled carbon nanotubes (MWCNTs): redox reaction, modification via incorporation of nitrogen and alkaline earth atoms; plasma sputtering; unzipping by microwave radiation, ultrasonic and electrical treatment, treatment with metallic catalytic particles, treatment with laser irradiation and scanning tunnelling microscope tip hydrogenation in high-temperature conditions, as well as unrolling by electrochemical methods [1]. Among these technologically advanced methods, the electrochemical process seems to be most promising since it can be easily controlled by selection of three parameters, namely current, voltage and time. As it is known from the literature, it is possible to carry out the electrochemical reduction of graphene oxide (GO) to electrochemical reduced graphene oxide (ERGO) in different media by a two-step electrochemical approach. Some investigators the processes of oxidation and reduction of graphene carried out in dilute sulfuric acid first at the anodic and then at cathodic polarization without changing the electrolyte. In our opinion, for more complete unzipping of nanotubes during their oxidation, more concentrated sulfuric acid should be used. The reduction process is preferably carried out in concentrated alkaline medium to neutralize the acid intercalated during oxidation. Additional cathode treatment in an alkaline medium will lead to an increase in the specific surface area and a more complete reducing to graphene. Therefore, the aim of our study was to develop a simple electrochemical method to produce ERGO as the catalyst carrier for oxygen electrodes for fuel cells using anodic oxidation of MWCNTs in an acidic medium and subsequent reduction in an alkaline medium. MWCNT diameter was 10-30 nm, and the specific surface area was 230 m2g-1. The number of walls ranged from 8 to 15. The anodic oxidation in sulphuric acid and the electrochemical reduction in alkaline electrolyte carried out in a galvanostatic. The materials synthesized via the electrochemical oxidation of MWCNTs with subsequent reduction were characterized using an electron microscopy (JEM-100 CXII), and X-ray diffraction (XRD) (DRON-4, CuKα radiation), Raman spectra and XPS spectra. Molecular species were analysed with FTIR spectroscopy. The obtained materials were investigated as cathode material for the oxygen electrodes of power sources in alkaline electrolyte. We have studied electrochemical characteristics of the oxygen electrodes produced by oxidation of the carbon nanotubes over different time. The MWCNT anodic oxidation was carried out under +3 V over 1.5, 4, and 5 hours. We found that in over conditions the more suitable time for the obtained electrochemical parameters (current density) of the oxygen electrodes is 4-hour oxidation duration. We have also studied the MWCNTs oxidation at various potentials for 4 hours. The potentials were chosen in the range +1.8–+4.5 V. Anodic oxidation during 4 hours at +3.0 V creates an extremely active catalytic material, which best suits for oxygen electrodes compared to those made of electrochemically oxidized MWCNTs at other potentials. The materials obtained by anodic oxidation of the carbon nanotubes were subsequently reduced in the alkaline solution at -1.4 V potential over 4 hours. The Raman spectra of all three measured samples show the presence of the Raman marker bands characteristic of the graphite structure, namely, D, G and 2D modes. Based on the analysis of the shape and position of these bands one can assume that after the anodic oxidation, the MWCNT crystallinity becomes worse while it improves after subsequent electrochemical reduction. This observation is also confirmed by corresponding XRD data. The frequencies for the D mode, G mode, and 2D mode suggest well-crystallized graphene structure. Closely positioned tags of C atoms in the XRD rings suggest that the synthesized sample consists of flat wavy sheets. As follows from the analysis of the Raman and IR spectra, XPS and XRD data, in the result of the MWCNT electrochemically treatment we obtained graphene nanoplatelets (Fig1), which contains carbon oxide groups on its surface. Electrodes based on electrochemically reduced graphene nanoplatelets produced from oxidized MWCNTs have the electrocatalytic characteristics close to those of the electrodes from MWCNTs containing deposited platinum. Obtained graphene nanoplatelets were stable over six months subject to testing in the fuel cell mock-up galvanostatic mode. The electrochemical synthesis of graphene nanoplatelets via anodic oxidation of MWCNTs and it reduction has been confirmed by electron microscopy, XRD, X-ray fluorescence, IR and Raman spectroscopy. Electrochemical studies have shown that the obtained graphene are promising materials as a catalyst carrier for fuel cells oxygen electrodes. M.O. Danilov, et al., Graphene Science Handbook. Fabrication Methods, (Eds. M. Aliofkhazraei, et al.), CRC Press/Taylor & Francis, 2016, pp. 205. Figure 1

Controlled Electrochemical Synthesis of the Partially Unzipped Multi-Wall Carbon Nanotubes

Graphene is a two-dimensional monolayer of sp2-hybridized carbon atoms with a cellular structure. By the chemical methods, graphene is obtained in the form of a mixture of mono-, bi- and multilayer (3-10 monolayers) of irregular structured flakes or flat sheets. Multi-walled carbon nanotubes (MWCNT) are several graphene layers rolled into a tube. Using any oxidative effects, you can unzip such MWCNT. Currently, there are the following methods for obtaining graphene from MWCNT [1]: redox reaction, modification via incorporation of nitrogen and alkaline earth atoms; plasma sputtering; unzipping by microwave radiation, ultrasonic and electrical treatment, treatment with metallic catalytic particles, tip hydrogenation in high-temperature conditions, as well as unrolling by electrochemical methods. One of the promising technological methods is the electrochemical method of unzipping nanotubes. Changing the voltage, current and time, it is possible to control the process of unzipping. The aim of our work was to check the possibility of controlled unzipping of MWCNT under the influence of electrochemical anodic oxidation. As a result we obtain etched carbon nanotubes, partially unzipped, fully unzipped and nanocomposite fragments of graphene nano-plates. Due to its properties, graphene materials are used as catalysts carriers for electrodes of chemical power sources. The study of the electrocatalytic properties of such materials as an oxygen electrode can indirectly confirm the degree of unzipping of MWCNT, since the catalytic properties depend on the structure and specific surface of the electrode material. MWCNT were subjected to electrochemical anodic oxidation. The outer diameter of the MWCNT was ~ 10–30 nm, the specific surface area was 230 m2 / g. The bulk density is 25–30 g / dm3, the number of walls is from 8 to 15. Samples of unzipped nanotubes were examined using electron microscope, X-ray phase analysis, Raman spectra. From the obtained materials, by pressing, two-layer oxygen electrodes were made. Studies were carried out in the mock up of the fuel cell. The zinc electrode was used as anode. The dependence of the electrochemical characteristics of oxygen electrodes on the time of the oxidation of MWCNTs was investigated. Anodic oxidation of MWCNTs was carried out in concentrated sulfuric acid at a potential of +3 V. Oxidation was carried out for 0.5, 1.5, 4, and 5 hours. It was found that with an anodic oxidation time increasing to 4 hours, the electrochemical characteristics of oxygen electrodes (current density at one and the same potential) increase. With further increase in oxidation time (≥ 5 hours), the characteristics do not change much. This is due to the production of etched carbon nanotubes (Figure 1a), with a further increase in the oxidation time (≤ 1.5 hours), partially unzipped nanotubes are obtained (Figure 1b). Next, we obtain fully unzipped nanotubes (Fig. 1c) and fragments of graphene nanoplates (Fig. 1d). We carried out the oxidation of MWCNTs for 4 h at various potentials (from 1.8 V to 4.5 V). In this case, a similar dependency was also found. With increasing potential up to 3 V, an increase in the electrochemical characteristics of the electrodes was observed. As the potential increased to 4.5 V, the electrode characteristics deteriorated. This dependence confirms the fact that the gradual unzipping of the nanotubes, depended on the applied oxidative effects. By controlling the treatment process, we obtained unzipped nanotubes with a controlled level of unzipping, a modified surface, the number of defects and functional groups on the surface. That is, Raman spectra, confirm that the anodic oxidation of MWCNTs results in partially unzipped nanotubes, fully unzipped nanotubes and fragments of graphene nanoplates. These materials are obtained by changing the oxidation time or the applied potential. The material contains all marker bands characterizing graphite structures, namely, D-, G- and 2D-bands. The position, intensity, and half-width of the bands are a reflection of the changes that occur in the samples as a result of the applied effects. Oxygen electrodes, based on electrochemically obtained samples, were stable in galvanostatic mode at current densities of 200 mA / cm2 for the six months. Thus, by oxidizing multi-walled carbon nanotubes at different anodic potentials, as well as by changing the processing time, we obtain controlled unzipping of MWCNT. The resulting materials are the good catalyst carrier for electrodes of chemical power sources. By applying various catalysts to them, it is possible to obtain hybrid nanocomposites with predetermined characteristics. O. Danilov, I.A. Slobodyanyuk, I.A. Rusetskii, et al.Graphene Science Handbook. Fabrication Methods, (Eds. M. Aliofkhazraei, et al.), CRC Press, 2016, pp. 205. Figure 1

2000-Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays.

We demonstrate single-atom resolved imaging with a survival probability of 0.99932(8) and a fidelity of 0.99991(1), enabling us to perform repeated high-fidelity imaging of single atoms in tweezers thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in 813.4nm tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retroreflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below 5 μK, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of 0.996(1) and average state detection fidelity of 0.981(1). Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.

Cluster State Generation with Spin-Orbit Coupled Fermionic Atoms in Optical Lattices.

Measurement-based quantum computation, an alternative paradigm for quantum information processing, uses simple measurements on qubits prepared in cluster states, a class of multiparty entangled states with useful properties. Here we propose and analyze a scheme that takes advantage of the interplay between spin-orbit coupling and superexchange interactions, in the presence of a coherent drive, to deterministically generate macroscopic arrays of cluster states in fermionic alkaline earth atoms trapped in three dimensional (3D) optical lattices. The scheme dynamically generates cluster states without the need of engineered transport, and is robust in the presence of holes, a typical imperfection in cold atom Mott insulators. The protocol is of particular relevance for the new generation of 3D optical lattice clocks with coherence times >10 s, 2 orders of magnitude larger than the cluster state generation time. We propose the use of collective measurements and time reversal of the Hamiltonian to benchmark the underlying Ising model dynamics and the generated many-body correlations.

Narrow-Line Cooling and Imaging of Ytterbium Atoms in an Optical Tweezer Array.

Engineering controllable, strongly interacting many-body quantum systems is at the frontier of quantum simulation and quantum information processing. Arrays of laser-cooled neutral atoms in optical tweezers have emerged as a promising platform because of their flexibility and the potential for strong interactions via Rydberg states. Existing neutral atom array experiments utilize alkali atoms, but alkaline-earth atoms offer many advantages in terms of coherence and control, and also open the door to new applications in precision measurement and time keeping. In this Letter, we present a technique to trap individual alkaline-earth-like ytterbium (Yb) atoms in optical tweezer arrays. The narrow ^{1}S_{0}-^{3}P_{1} intercombination line is used for both cooling and imaging in a magic-wavelength optical tweezer at 532nm. The low Doppler temperature allows for imaging near the saturation intensity, resulting in a very high atom detection fidelity. We demonstrate the imaging fidelity concretely by observing rare (<1 in 10^{4} images) spontaneous quantum jumps into and out of a metastable state. We also demonstrate stochastic loading of atoms into a two-dimensional, 144-site tweezer array. This platform will enable advances in quantum information processing, quantum simulation, and precision measurement. The demonstrated narrow-line Doppler imaging may also be applied in tweezer arrays or quantum gas microscopes using other atoms with similar transitions, such as erbium and dysprosium.

Substituent effects at nitrogen/phosphorus atoms of dialkaline earth metal complexes: Excess electron and large second‐hyperpolarizability

AbstractA number of imido‐, amido‐, and phosphido‐bridged dialkaline earth metal (M = Be, Mg, and Ca) complexes and their alkali metal (Li and Na) derivatives have been considered to study the ground state structure and the second‐hyperpolarizability. The calculated ground state geometries contain four‐membered MN(P)MN(P) ring having either planar or butterfly‐like bent structure. The second‐hyperpolarizability has been calculated at the HF and CCSD(T) levels using Sadlej's pol and aug‐pc‐2 basis sets, respectively. The addition of second hydrogen/alkali metal atom on nitrogen/phosphorus (N/P) atom substantially reduces the charge transfer from the alkaline earth metal atoms as the high negative charge on N/P exerts stronger push effect on the outermost electron pair in the “ns” sub‐shell of M. The excess electron density on the alkaline earth metal atoms plays a crucial role in the enhancement of second‐hyperpolarizability. The sum‐over‐state method calculated two‐photon contribution of second‐hyperpolarizability has been found to be significant. The variation of second‐hyperpolarizability has been explained satisfactorily in terms of the TD‐CAMB3LYP calculated spectroscopic properties in the light of two‐state model. The calculated mean second‐hyperpolarizabilities of alkali substituted amido‐ and phosphido‐bridged complexes are in the order of 107 au.

Matrix Infrared Spectra and Electronic Structure Calculations of Linear Alkaline Earth Metal Di-isocyanides CNMNC, Ionic (NC)M(NC) Bowties, and Ionic (MNC)2 Rings.

Laser-ablated group 2 metal atoms exhibit different reactivities with (CN)2 in excess argon and neon during condensation at 4 K. UV irradiation (220-290 nm) is required to activate Be to produce the linear CNBeNC di-isocyanide molecule with a strong antisymmetric C-N stretching band at 2104.3 cm-1 and a C-N-Be-N-C stretching mode at 1265.7 cm-1. The di-isocyanide appears at lower frequency and exhibits more nitrogen and less carbon isotopic shift than the cyanide counterpart, which is confirmed by B3LYP isotopic frequency calculations. Two weak bands were observed for the cyanide NCBeCN, and three absorptions were found for the mixed ligand CNBeCN molecule, which would be difficult to synthesize and put into a bottle. Mg reacts with (CN)2 to form the CNMgNC counterpart at 2085.8 cm-1 on annealing to 25 K. Absorptions for the Ca(NC)2, Sr(NC)2, and Ba(NC)2 molecules at 2060.8, 2048.1, and 2045.9 cm-1 increase on sample annealing with these more reactive heavier alkaline earth metal atoms, which have calculated twisted bowtie side-bound (CN) structures of C2 symmetry with shorter computed M-N than M-C distances. NBO calculations for the latter molecules reveal natural charges of +1.54, 1.64, 1.71 e on the metal centers and - 0.77, 0.82, and 0.855 e on the corresponding CN subunits, with a doubly occupied sp-sp σ and two p-p π bonds on each (CN), which supports an ionic model for bonding in these molecules. A weaker band at 2056.6 cm-1 behaves nearly the same as the Ca bowtie band in the spectrum on 25 K annealing and photolysis, and it is assigned to the 6 kJ/mol higher-energy linear CNCaNC isomer. Additional similar sharp absorptions for a new Ca, Sr, and Ba reaction product at 2036.3, 2040.6, and 2036.0 cm-1 increase on annealing at the expense of adjacent broader bands: B3LYP and NBO calculations validate their assignment to ionic hexagonal C2 h (MNC)2 rings from the reaction of two M atoms with (CN)2.

Topological Devil’s staircase in atomic two-leg ladders

We show that a hierarchy of topological phases in one dimension—a topological Devil’s staircase—can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek–Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.