Two-dimensional Atom Research Articles

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.

Atom Localization Using a Rydberg State

A theoretical study is presented for two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level atomic system involving a Rydberg state. The scheme is based on a mixture of two well-known V- and ladder-type systems illuminated by a weak probe field as well as control and switching laser beams of larger intensity, which could be standing waves. As a result of space-dependent atom− light interaction and due to the effect of Rydberg electromagnetically induced transparency or Rydberg electromagnetically induced absorption, various 2D and 3D localization structures appear. Specifically, the detecting probability and precision of 2D and 3D atom localization can be remarkably enhanced through suitable adjusting the controlling parameters of the system. The proposed scheme may provide a promising approach to achieve high precision and perfect resolution 2D and 3D atom localization.

Two-dimensional atom localization based on coherent field controlling in a five-level M-type atomic system.

We study two-dimensional sub-wavelength atom localization based on the microwave coupling field controlling and spontaneously generated coherence (SGC) effect. For a five-level M-type atom, introducing a microwave coupling field between two upper levels and considering the quantum interference between two transitions from two upper levels to lower levels, the analytical expression of conditional position probability (CPP) distribution is obtained using the iterative method. The influence of the detuning of a spontaneously emitted photon, Rabi frequency of the microwave field, and the SGC effect on the CPP are discussed. The two-dimensional sub-half-wavelength atom localization with high-precision and high spatial resolution is achieved by adjusting the detuning and the Rabi frequency, where the atom can be localized in a region smaller thanλ/10×λ/10. The spatial resolution is improved significantly compared with the case without the microwave field.

On the Energy of a “Two-Dimensional” Two-Electron Atom

With the use of the known solution of the Schrodinger equation for an electron in the nucleus field in the polar coordinates, the energy of a “two-dimensional” two-electron atom in the ground state, as well as its single ionization energy, has been calculated both in perturbation theory and with an almost century-old method of variation of the parameter Z in a trial wavefunction of the ground state. Since such two-dimensional atoms, e.g., helium atoms, can in principle be implemented in experiments by “freezing” of one degree of freedom in the phase of Bose–Einstein condensate, the conclusions made in this work can be tested. Fundamental features of the calculation of the energy of “one-dimensional” two-electron atoms and the formation of their Bose–Einstein condensate have also been discussed. The results obtained in this work coincide in a number of particular cases with the results obtained in a previous work, where some results were absent.

Evolution of the stimulated resonance of a channeling electron beam

The motion of channeled particles in the co-moving coordinate system can be considered as a onedimensional oscillator (in the case of planar channeling) or as a two-dimensional atom (in the case of axial channeling). The transverse motion of channeled particles is characterized by the discrete spectrum; in this case, the probability of occupation of transverse-motion levels depends on the entrance angle of the charged particle with respect to the crystallographic axes of a single crystal. A charged channeled particle passing through a single crystal experiences the periodic action of lattice atoms. If the frequency of the external periodic action of the crystal lattice coincides with that of the transition of the channeled particle from one quantum state of transverse motion to another, then resonance excitation of the channeled particle can occur; it is similar to the excitation of atomic electrons by the periodic field of a monochromatic electromagnetic wave. In this paper, the resonance conditions are discussed and the dependence of the probability of the occupation of transverse-motion levels of channeled particles (electrons) on the single-crystal thickness is analyzed.

Raman scattering of photons by the channeling electrons

The motion of channeling particles in the accompanying coordinate system can be considered as a two-dimensional atom in the case of axial channeling. The transversal motion of the channeling particles is characterized by discrete spectrum. The occupation probability of the transversal motion levels depends on the entrance angle of the charged particles relative to the crystallographic axis. In the scattering of a photon by the “quasi-bound” electron moving in the axial channeling regime would appear the frequencies ω which are a combination of the incident photon frequency ω0 and the frequency ωNM (ωNM is the transition frequency in transverse quantized motion of the channeling electron: ω=ω0±ωMN, where ℏωMN=2γ2ΔE⊥NM for the relativistic electron, γ2=E/(mc2) is the Lorentz factor of the channeling electron). In the article are discussed the criteria for choosing an adequate continuous potential of the crystallographic axis and the quantum characteristics of a transversal motion of the channeling electron. The peculiarities of the Raman scattering spectrum of photons by electrons in the axial channeling regime are analyzed and the differential cross section of this process is found.

Time-dependent density functional theory for strong-field ionization by circularly polarized pulses

By applying time-dependent density functional theory to a two-dimensional multielectron atom subject to strong circularly polarized light pulses, we confirm that the ionization of p orbitals with defined angular momentum depends on the sense of rotation of the applied field. A simple ad-hoc modification of the adiabatic local-density exchange-correlation functional is proposed to remedy its unphysical behavior under orbital depletion.

High-dimensional atom localization via spontaneously generated coherence in a microwave-driven atomic system

We investigate the two-dimensional (2D) and three-dimensional (3D) atom localization behaviors via spontaneously generated coherence in a microwave-driven four-level atomic system. Owing to the space-dependent atom-field interaction, it is found that the detecting probability and precision of 2D and 3D atom localization behaviors can be significantly improved via adjusting the system parameters, the phase, amplitude, and initial population distribution. Interestingly, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength. Our scheme opens a promising way to achieve high-precision and high-efficiency atom localization, which provides some potential applications in high-dimensional atom nanolithography.

Two-dimensional Talbot self-imaging via Electromagnetically induced lattice

We propose a lensless optical method for imaging two-dimensional ultra-cold atoms (or molecules) in which the image can be non-locally observed by coincidence recording of entangled photon pairs. In particular, we focus on the transverse and longitudinal resolutions of images under various scanning methods. In addition, the role of the induced nonmaterial lattice on the image contrast is investigated. Our work shows a non-destructive and lensless way to image ultra-cold atoms or molecules that can be further used for two-dimensional atomic super-resolution optical testing and sub-wavelength lithography.

Accidental Degeneracy of Hydrogen Atom Revisited

We examine accidental symmetry of hydrogen-like atoms analytically in spherical coordinates. Some unfamiliar but notable functional relations of the radial eigenfunctions of system’s Hamiltonian are constructed, for both discrete and continuous energy eigenvalues. Analytical similarity of the symmetry between two-dimensional and threedimensional hydrogen atoms are therefore demonstrated.

Two-dimensional Sub-wavelength Atom Localization of a Four-Level $$\varLambda$$ Λ -type Atomic System with two Adjacent Lower Levels Via Probe Absorption

Two-dimensional atom localization of a four-level \(\varLambda\)-shaped atom with two adjacent lower levels interacting with two orthogonal standing wave fields is considered. By measuring the probe field absorption, spatial information of position of a moving atom is obtained in \(x - y\) plane. The position of atom through two-dimensional standing wave field strongly depends on the intensity of standing waves, detuning of the probe and standing wave fields. Choosing the appropriate controlling parameters, the two-dimensional atom localization through the standing wave fields in a sub-wavelength domain will be achieved.

Two-dimensional atom localization induced by a squeezed vacuum**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574179 and 11204099) and the Natural Science Foundation of Hubei Province, China (Grant No. 2014CFC1148).

A scheme of two-dimensional (2D) atom localization induced by a squeezed vacuum is proposed, in which the three-level V-type atoms interact with two classical standing-wave fields. It is found that when the environment is changed from an ordinary vacuum to a squeezed vacuum, the 2D atom localization is realized by detecting the position-dependent resonance fluorescence spectrum. For comparison, we demonstrate that the atom localization originating from the quantum interference effect is distinct from that induced by a squeezed vacuum. Furthermore, the combined effects of the squeezed vacuum and quantum interference are also discussed under appropriate conditions. The internal physical mechanism is analyzed in terms of dressed-state representation.

Nature of the Insulating Ground State of the Two-Dimensional Sn Atom Lattice on SiC(0001).

Semiconductor surfaces with narrow surface bands provide unique playgrounds to search for Mott-insulating state. Recently, a combined experimental and theoretical study of the two-dimensional (2D) Sn atom lattice on a wide-gap SiC(0001) substrate proposed a Mott-type insulator driven by strong on-site Coulomb repulsion U within a single-band Hubbard model. However, our systematic density-functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals shows that the Sn dangling-bond state largely hybridizes with the substrate Si 3p and C 2p states to split into three surface bands due to the crystal field. Such a hybridization gives rise to the stabilization of the antiferromagnetic order via superexchange interactions. The band gap and the density of states predicted by the hybrid DFT calculation agree well with photoemission data. Our findings not only suggest that the Sn/SiC(0001) system can be represented as a Slater-type insulator driven by long-range magnetism, but also have an implication that taking into account long-range interactions beyond the on-site interaction would be of importance for properly describing the insulating nature of Sn/SiC(0001).

Atom localization with double-cascade configuration

We investigate the one-dimensional (1D) and two-dimensional (2D) atom localization of a four-level system in a double-cascade configuration. We demonstrate the possibility of 1D localization in the field of a standing wave, 2D localization in the field of two standing waves and 2D localization only in the field of running waves by using different configurations of driven waves on transitions. In addition, for each configuration we reached a high-precision atom localization in one of the states at scales much smaller than the wavelength of the incident optical radiation.

Massive Goldstone (Higgs) mode in two-dimensional ultracold atomic lattice systems

We discuss how to reveal the massive Goldstone mode, often referred to as the Higgs amplitude mode, near the Superfluid-to-Insulator quantum critical point (QCP) in a system of two-dimensional ultracold bosonic atoms in optical lattices. The spectral function of the amplitude response is obtained by analytic continuation of the kinetic energy correlation function calculated by Monte Carlo methods. Our results enable a direct comparison with the recent experiment [M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schau{\ss}, C. Gross, E. Demler, S. Kuhr, and I. Bloch, Nature 487, 454-458 (2012)], and demonstrate a good agreement for temperature shifts induced by lattice modulation. Based on our numerical analysis, we formulate the necessary conditions in terms of homogeneity, detuning from the QCP and temperature in order to reveal the massive Goldstone resonance peak in spectral functions experimentally. We also propose to apply a local modulation at the trap center to overcome the inhomogeneous broadening caused by the parabolic trap confinement.

Atom localization in 2D for five-level atomic schemes in X-configuration

A five-level X-type atomic scheme is proposed to elucidate the two-dimensional (2D) atom localization in sub-wavelength domain by using different coupling situations of the atom with standing wave fields. The scheme is a mixture of two upper V- and lower -type usual three level systems which both are connected at a common intermediate level. The combination of the upper and lower systems can lead to different atom localization patterns as lattice-, chain-, crater-, wave-, and spike-like structures. We discuss how these structures may depend on different coupling conditions of the atom with the standing wave fields. Finally, an experimental implementation for such an atomic model is presented using the 87Rb atoms.

Triangular Spin-Orbit-Coupled Lattice with Strong Coulomb Correlations: Sn Atoms on a SiC(0001) Substrate.

Two-dimensional (2D) atom lattices provide model setups with Coulomb correlations that induce competing ground states. Here, SiC emerges as a wide-gap substrate with reduced screening. We report the first artificial high-Z atom lattice on SiC(0001) by Sn adatoms, based on experimental realization and theoretical modeling. Density-functional theory of our triangular structure model closely reproduces the scanning tunneling microscopy. Photoemission data show a deeply gapped state (∼2 eV gap), and, based on our calculations including dynamic mean-field theory, we argue that this reflects a pronounced Mott-insulating scenario. We also find indications that the system is susceptible to antiferromagnetic superstructures. Such artificial lattices on SiC(0001) thus offer a novel platform for coexisting Coulomb correlations and spin-orbit coupling, with bearing for unusual magnetic phases and proposed topological quantum states of matter.

Two-dimensional atom localization via phase-sensitive absorption-gain spectra in five-level hyper inverted-Y atomic systems

A scheme for realizing two-dimensional atom localization in the sub-wavelength domain is proposed in a microwave-driven five-level hyper inverted-Y atomic system in which the atom interacts with a weak probe field, two control fields together with two orthogonal standing-wave fields. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be extracted directly from the absorption and gain spectra of a weak probe field. It has been found that the probe detuning, the intensities of two control fields, and the relative phase of the driving fields can significantly improve the localization precision. Moreover, the maximal probability of finding the atom at an expected position in the sub-wavelength domain of the standing-wave field can reach unity via properly adjusting the system parameters.

Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models

We use a simple mathematical method to solve the problem of a two-dimensional hydrogen-like atom in the inhomogeneous magnetic fields B = (k/r)z and B = (k/r3)z. We construct a Hamiltonian that takes the same form as the Hamiltonian of a hydrogen-like atom in the homogeneous magnetic fields and obtain the energy spectrum by comparing the Hamiltonians. The results show that the whole spectrum of the atom in the magnetic field B = (k/r)z can be obtained, and the problem is exactly solvable in this case. We find analytic solutions of the Schrodinger equation for the atom in the magnetic field B = (k/r3)z for particular values of the magnetic strength k and thus present a quasi-exactly solvable model.

Two-Dimensional Atom Localization via Controlled Spontaneous Emission in a Coupled Cavity Waveguide

A scheme of atom localization based on controlled spontaneous emission is proposed, in which the atom is embedded in a coupled cavity waveguide with two orthogonal standing-wave fields. We can achieve high-precision and high-resolution atom localization by properly adjusting the system parameters. It is shown that the localization is significantly improved due to the strong coupling effect between the atom and a coupled cavity waveguide.