Two-dimensional Atom Research Articles

Rydberg-Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array.

We demonstrate high fidelity two-qubit Rydberg blockade and entanglement on a pair of sites in a large two-dimensional qubit array. The qubit array is defined by a grid of blue detuned lines of light with 121 sites for trapping atomic qubits. Improved experimental methods have increased the observed Bell state fidelity to F_{Bell}=0.86(2). Accounting for errors in state preparation and measurement we infer a fidelity of F_{Bell}^{-SPAM}=0.88. Accounting for errors in single qubit operations we infer that a Bell state created with the Rydberg mediated C_{Z} gate has a fidelity of F_{Bell}^{C_{Z}}=0.89. Comparison with a detailed error model based on quantum process matrices indicates that finite atom temperature and laser noise are the dominant error sources contributing to the observed gate infidelity.

Complex conductivity-dependent two-dimensional atom microscopy

A two-dimensional atom microscopy is investigated using the absorption spectrum under the effect of complex conductivity in a four-level inverted N-type atomic system. Sharp localized peaks are noticed in one wavelength domain in 2D inverse space $ -\pi\leq kx\leq\pi$ and $ -\pi\leq ky\leq\pi$. Four, three, two and even single localized peaks having high precise position, minimum uncertainty and significant probability are measured in the proposed model. The localized probability is enhanced or degraded with the application of complex conductivity. The phase and amplitude of complex conductivity significantly influence the atom microscopy for useful technological applications. The results may be helpful to advance laser cooling and trapping.

Graphene oxide reduction using green chemistry

Graphene, a very attractive two-dimensional single atom thick carbon nanomaterial with excellent mechanical flexibility, superior electrical conductivity, high thermal and chemical stability has attracted scientific researchers from all across the world. Synthesis of graphene can be done by epitaxial growth, exfoliating graphite mechanically, chemical vapour deposition, and by reducing graphene oxide (GO). Here we report Graphene Oxide’s synthesis using Improved Hummer’s method by overcoming the flaws of Hummer’s method. A crucial step in synthesizing and exercising GO is the reduction, which helps in restoring its structure and attributes. Popular method of GO reduction is by treatment with hydrazine hydrate which is not environment friendly. Hence we report a green method to reduce GO using fresh ginger and garlic extracts. Different reduction procedures give rise to different attributes of reduced GO (rGO), ultimately affecting the outcome of the devices or materials constituting rGO. The prepared reduced GO is characterized by X-ray Diffraction, Fourier Transform Infrared Spectroscopy, Raman Spectroscopy and UV–Visible Spectroscopy. The results confirmed that GO was reduced by using green chemistry.

Two-dimensional hydrogen-like atom in a constant magnetic field

The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective attraction between the nucleus and the electron and one for which it causes an effective repulsion. Each of the two problems has three separate cases depending on the sign of a shifted energy eigenvalue. For two of the six possibilities (shifted energy eigenvalue that is negative) it is shown that the first four solutions can be obtained exactly. For another two of the six possibilities (shifted energy eigenvalue that is positive) it is shown that the first eight solutions can be obtained exactly. For higher order states the energy eigenvalue is the root of a fifth or higher order polynomial, hence, the eigenvalue must be obtained numerically. Once the energy eigenvalue is known the solution to the radial wave equation is also known. Exact solutions for the radial wave equation, for the remaining two possibilities (shifted energy eigenvalue that is zero), are given to any desired order by means of a recursion relation.

Correlation-Driven Charge Order in a Frustrated Two-Dimensional Atom Lattice.

We thoroughly examine the ground state of the triangular lattice of Pb on Si(111) using scanning tunneling microscopy and spectroscopy. We detect electronic charge order, and disentangle this contribution from the atomic configuration which we find to be 1-down-2-up, contrary to previous predictions from density functional theory. Applying an extended variational cluster approach we map out the phase diagram as a function of local and nonlocal Coulomb interactions. Comparing the experimental data with the theoretical modeling leads us to conclude that electron correlations are the driving force of the charge-ordered state in Pb/Si(111). These results resolve the discussion about the origin of the well-known 3×3 reconstruction. By exploiting the tunability of correlation strength, hopping parameters, and band filling, this material class represents a promising platform to search for exotic states of matter, in particular, for chiral topological superconductivity.

Atom localization in five-level atomic system driven by an additional incoherent pump

We propose a new scheme for two-dimensional (2D) and three-dimensional (3D) atom localization via spatial quantum interference in a five-level atomic system driven by an additional incoherent pump. Because of the position-dependent atom–field interaction, the position information of the atom can be obtained by the measurement of the probe absorption. We find that the 3D atom localization is obtained with high precision by adjusting the incoherent pump. In particular, we show that adjusting the incoherent pump can lead to a redistribution of the atoms and a significant change in the visibility of the interference pattern. As a result, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength.

Efficient two-dimensional sub-wavelength atom localisation via probe absorption in a four-level Λ-shaped atomic system

Two-dimensional (2D) atom localisation of a four-level Λ-shaped atomic system with a nearly hyper-fine doublet interacting with two orthogonal standing-wave fields is investigated. The spatial information of a moving atom in xy plane is obtained by measuring the probe field absorption. The effect of quantum interference on two-dimensional atom localisation is described. The intensity of standing-waves and the detuning of the probe and standing-wave fields are found to strongly affect the two-dimensional atom localisation that lead to different spatial distribution patterns.

Regarding the Main Spectral Lines of a Two-dimensional Two-Electron Atom

The energy of a two-dimensional two-electron atom is calculated in its lowest excited states; together with the previously calculated energy in the ground state, this makes it possible to find the screening constant σ in the lowest excited state and the fundamental frequencies of radiation of such atoms (for example, Не), which can, in principle, be obtained in the Bose condensate phase as has already been done with Na atoms. The possibility of experimental verification of the results is indicated. Errors incurred by other authors in their calculations of σ in the excited state of the two-dimensional He atom are also pointed out.

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are carried out with the use of the Sturmian expansion of the two-dimensional generalized radial Dirac–Coulomb Green function derived in the paper. It is found that, in contrast to the case of the three-dimensional atom (Stefańska, 2015), in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities) are expressible in terms of elementary algebraic functions of a nuclear charge and electron quantum numbers. The problem considered here is related to the Coulomb impurity problem for graphene in a weak magnetic field.

Energy of a Two-Dimensional Helium Atom in an Excited State

Using perturbation theory methods and a variational method, we have calculated the energy of a twodimensional helium atom in its lower excited states, this energy showing itself to be practically independent of the specific characteristics of these excited states; this, together with the known value of the energy in the ground state, found earlier by one of the authors, presents the fundamental possibility of determining the frequencies of the main spectral lines of such an atom, which can be checked experimentally.

Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

The well-known hypervirial perturbation method (HPM), based on hypervirial relations and the Hellmann-Feynman theorem, is suitable for the calculation of perturbation corrections of large order for the non-relativistic, spinless, two-dimensional hydrogen-like atom in a uniform magnetic field. We show analytical results in terms of the quantum numbers and large-order corrections for particular states. This approach appears to be simpler and more efficient than the recently proposed one based on the Green’s functions for this particular model.

On the Question of the Existence of Two-Dimensional Multi-Electron Atoms

The semiclassical Thomas–Fermi method is extended to the case of two-dimensional (planar) multi-electron atoms. It is shown that within the framework of this model a two-dimensional multi-electron atom cannot exist, due to the impossibility of fulfilling the physical asymptotic limit φ(r)|r→0 → (Ze)/r of the solution of the corresponding two-dimensional Thomas–Fermi equation.

Lasing and Amplification from Two-Dimensional Atom Arrays.

We explore the ability of two-dimensional periodic atom arrays to produce light amplification and generate laser emission when gain is introduced through external optical pumping. Specifically, we predict that lasing can take place for arbitrarily weak atomic scatterers assisted by cooperative interaction among atoms in a 2D lattice. We base this conclusion on analytical theory for three-level scatterers, which additionally reveals a rich interplay between lattice and atomic resonances. Our results provide a general background to understand light amplification and lasing in periodic atomic arrays, with promising applications in the generation, manipulation, and control of coherent photon states at the nanoscale.

Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state

The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_{3}F_{2}$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\leqslant Z\leqslant68$ are provided in a tabular form. A simple formula for the polarizability of a nonrelativistic two-dimensional hydrogenic atom, reported previously by several other authors, is recovered from our result in the nonrelativistic limit.

Two-dimensional hydrogen-like atom in a weak magnetic field

.We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schrödinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth order in the strength of the perturbing magnetic field. In the case of the ground state, we correct an expression for the fourth-order correction to energy available in the literature.

Characteristics of a Two-Dimensional Hydrogen-like Atom

Using the customary and well-known representation of the radiation probability of a hydrogen-like atom in the three-dimensional case, a general expression for the probability of single-photon emission of a twodimensional atom has been obtained along with an expression for the particular case of the transition from the first excited state to the ground state, in the latter case in comparison with corresponding expressions for the three-dimensional atom and the one-dimensional atom. Arguments are presented in support of the claim that this method of calculation gives a value of the probability that is identical to the value given by exact methods of QED extended to the subspace {0, 1, 2}. Relativistic corrections ~ (Zα)4 to the usual Schrodinger value of the energy (~ (Zα)2) are also discussed.

High-precision two- and three-dimensional atom localization via spatial dependent probe absorption in a closed-loop M-type atomic system

We propose a scheme for high-precision two- and three-dimensional atom localization in a coherently driven closed-loop five-level M-type atomic system by using a density matrix formalism. Our system consists of not only strong and probe fields but also a microwave field to form a closed loop in the atomic system. Due to position-dependent interaction of the atom in the standing-wave field, the absorption spectra of the probe field provide the precise information about atom localization in a subspace of one wavelength. While numerically solving the density matrix equations, various kinds of localization patterns are obtained, such as parallel wave-, crater-, valley-, and bell-shape-like, in the case of two-dimensional atom localization. Further, the three-dimensional atom localization case is also discussed under different parametric conditions. High precession and high resolution of atom localization are observed for our case and the localization can be tuned to the desired subspace by properly adjusting external parameters. Moreover, maximum conditional probability distribution of the atom is also achieved, i.e., 1 in both two- and three-dimensional localization cases under appropriate conditions.

High-precision two-dimensional atom localization from four-wave mixing in a double-Λ four-level atomic system

We propose a scheme for high-precision two-dimensional (2D) atom localization via the four-wave mixing (FWM) in a four-level double- atomic system. Due to the position-dependent atom-field interaction, the 2D position information of the atoms can be directly determined by the measurement of the normalized light intensity of output FWM-generated field. We further show that, when the position-dependent generated FWM field has become sufficiently intense, efficient back-coupling to the FWM generating state becomes important. This back-coupling pathway leads to competitive multiphoton destructive interference of the FWM generating state by three supplied and one internally generated fields. We find that the precision of 2D atom localization can be improved significantly by the multiphoton destructive interference and depends sensitively on the frequency detunings and the pump field intensity. Interestingly enough, we show that adjusting the frequency detunings and the pump field intensity can modify significantly the FWM efficiency, and consequently lead to a redistribution of the atoms. As a result, the atom can be localized in one of four quadrants with holding the precision of atom localization.

Two-Dimensional Hydrogen-like Atom: Photon Emission and Relativistic Energy Corrections

Using the well-known solution Ψ S of the Schrodinger equation for an electron in the field of a nucleus (Ze) in polar coordinates, via which the spin-state-dependent Dirac spinor Ψ± obtained here is expressed, and by extending the QED methods to subspace {0; 1, 2}, we have calculated the probability of single-photon emission by a two-dimensional hydrogen-like atom with allowance made for the polarization and spin states. Relativistic energy corrections ∼(Zα)4 to the energy value have also been found. We show that the so-called contact interaction typical of a three-dimensional hydrogen-like atom also takes place in the twodimensional case, while the ordinary three-dimensional spin–orbit interaction is absent altogether.

Combinatorial selection of a two-dimensional 3d-TM-tetracyanoquinodimethane (TM-TCNQ) monolayer as a high-activity nanocatalyst for CO oxidation.

The CO oxidation reaction on single 3d-transition metal catalytic sites in experimentally realized tetracyanoquinodimethane (TM-TCNQ) monolayers (TM = Sc-Zn) is systematically investigated by means of first-principles calculations. Considering the stabilities, adsorption characteristics and thermodynamics of all the ten candidates (Sc-Zn), Sc-TCNQ is found to display the lowest activation energies and yield the highest catalytic activity for room temperature CO oxidation. Exploring the Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms, we find that the rate-limiting step of CO oxidation catalyzed by Sc-TCNQ (CO + O2* → OOCO*) can follow the LH mechanism with free energy barriers as low as 0.73 eV at 300 K. The second step of CO + O* → CO2 can occur with rather small energy barriers via either LH or ER mechanisms. The high activity of Sc-TCNQ can be attributed to its unique structural and electronic features by possessing high stability, optimum adsorption energies with adsorbates, and fast reaction kinetics. These results have significant implications for the synthesis of two-dimensional single atom catalysis for CO oxidation with low-cost and high activity at low temperature.