Two-dimensional Atom Research Articles

High-precision two-dimensional atom localization via probe absorption in an M-scheme atomic system

In the present paper, we investigate the behavior of two-dimensional atom localization in a five-level M-scheme atomic system driven by two orthogonal standing-wave fields. We find that the precision and resolution of the atom localization depends on the probe field detuning significantly. And because of the effect of the microwave field, an atom can be located at a particular position via adjusting the system parameters.

Magnetic order in a frustrated two-dimensional atom lattice at a semiconductor surface

Two-dimensional electron systems, as exploited for device applications, can lose their conducting properties because of local Coulomb repulsion, leading to a Mott-insulating state. In triangular geometries, any concomitant antiferromagnetic spin ordering can be prevented by geometric frustration, spurring speculations about 'melted' phases, known as spin liquid. Here we show that for a realization of a triangular electron system by epitaxial atom adsorption on a semiconductor, such spin disorder, however, does not appear. Our study compares the electron excitation spectra obtained from theoretical simulations of the correlated electron lattice with data from high-resolution photoemission. We find that an unusual row-wise antiferromagnetic spin alignment occurs that is reflected in the photoemission spectra as characteristic 'shadow bands' induced by the spin pattern. The magnetic order in a frustrated lattice of otherwise non-magnetic components emerges from longer-range electron hopping between the atoms. This finding can offer new ways of controlling magnetism on surfaces.

On the Maximal Excess Charge of the Chandrasekhar–Coulomb Hamiltonian in Two Dimension

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|\bx| T(\bp) + T(\bp) |\bx| $$ which -- in two dimensions -- is false for the non-relativistic case $T(\bp) = \bp^2$, but is proven in this paper for $T(\bp) = |\bp|$, i.e., the ultra-relativistic kinetic energy.

Two-Dimensional Atom Localization via Spontaneous Emission in an Inverted-Y System

We investigate the behavior of two-dimensional atom localization in an inverted-Y system driven by one coherent field and two standing-wave fields. The position probability distribution of the atom passing through the spatial-position-dependent standing-wave fields can be determined by measuring the spontaneously emitted photon. It is found that high-precision two-dimensional atom localization can be obtained by choosing appropriate system parameters.

Roton Instability and Phonon Collapse of Two-dimensional Tilted Dipoles

Bose-Einstein condensed gas of two-dimensional tilted dipoles in a thin layer is under consideration. The problem of stability is resolved. Phase diagram for system of two-dimensional dipole atoms in a thin layer is obtained. A formation of density waves and their orientation control possibility via polarizing field are considered. These effects can be experimentally observed for magnetically dipolar atoms at the Feshbach resonance or polar molecules in one-dimensional optical lattices.

Origin of the first Hund rule and the structure of Fermi holes in two-dimensional He-like atoms and two-electron quantum dots

The lowest singlet–triplet pair of states of the two-electron two-dimensional quantum dots and the corresponding pair of states of the two-dimensional helium-like systems have been studied by the full configuration interaction method focusing on the origin of the first Hund rule. The one- and two-electron components of the singlet–triplet energy gap show distinct trends for the systems studied in the regime of small nuclear charge Zn or of small confinement strength ω. The (0σg)(1πu) singlet state in quantum dots is characterized by a larger electron repulsion than its counterpart triplet state for all values of ω, while this relationship gets inverted for the corresponding (1s)(2p) singlet–triplet pair of He-like systems for small values of Zn, such as Zn = 2 or 3. The internal part of the full configuration interaction wavefunctions has been extracted and visualized in the three-dimensional internal space (r1, r2, ϕ−) to rationalize the observed trends. The singlet probability density of He-like systems located originally near the Fermi holes is shown to migrate into regions where either r1 or r2 are large while the corresponding singlet probability of quantum dots stays close to the Fermi holes. Their differences and their observed trends are rationalized on the basis of the structure of the genuine and conjugate Fermi holes.

Indirect Coulomb energy for two-dimensional atoms

In this paper we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.

Multipeak envelope of the above-threshold-ionization energy spectrum in a strong circularly polarized laser field

We develop a well-known strong-field approximation in the length gauge for a two-dimensional model atom in a strong circularly polarized laser field. For excited initial states (with the principal quantum number $n=2$) outgoing photoelectrons usually show energy spectra with an envelope having two or three peaks: one always below and one always above the ponderomotive energy ${U}_{P}$. In contrast, for the ground state (with $n=1$) there is always a single peak near ${U}_{P}$. Our numerical calculations show that the multipeak effect appears for sufficiently high laser intensities $I$ and is more pronounced for higher laser frequencies $\ensuremath{\omega}$. We believe that the field parameters $\ensuremath{\omega}$ and $I$, for which the multipeak envelope in the energy spectrum of above-threshold ionization exists, will enable its experimental observation in the near future.

Nonlinear optical properties of graphene-based materials

Graphene, a two-dimensional carbon atom sheet, has attracted tremendous attention and research interest because of its exceptional physical properties. Graphene has high mobility and optical transparency, in addition to flexibility, robustness and environmental stability. The main focus so far has been on fundamental physics and electronic devices. However, because the linear dispersion of the Dirac electrons enables ultrawideband tunability, we believe its true potential lies in photonics and optoelectronics. In this review, we introduce recent advances in the nonlinear optical properties of graphene-based materials. The rise of graphene in nonlinear optics is shown by several recent results, ranging from saturable absorbers and the four-wave mixing effect to giant two-photon absorption, reverse saturable absorption and optical limiting. The relevant forms of the graphene-based materials include pure graphene, graphene oxide and graphene hybrids.

Efficient two-dimensional atom localization via spontaneous emission in a single decay channel

We investigate the two-dimensional atom localization behaviors in a four-level atomic system via controlled spontaneous emission in a single decay channel. It is found that the detecting probability and precision of atom localization behaviors can be significantly improved via adjusting the system parameters. More importantly, the two-dimensional atom localization patterns reveal that the maximal probability of finding an atom within the sub-half-wavelength domain of the standing waves can reach unity when the corresponding conditions are satisfied. As a result, our scheme may be helpful in laser cooling or the atom nano-lithography via atom localization.

High-precision atom localization via controllable spontaneous emission in a cycle-configuration atomic system

A scheme for realizing two-dimensional (2D) atom localization is proposed based on controllable spontaneous emission in a coherently driven cycle-configuration atomic system. As the spatial-position-dependent atom-field interaction, the frequency of the spontaneously emitted photon carries the information about the position of the atom. Therefore, by detecting the emitted photon one could obtain the position information available, and then we demonstrate high-precision and high-resolution 2D atom localization induced by the quantum interference between the multiple spontaneous decay channels. Moreover, we can achieve 100% probability of finding the atom at an expected position by choosing appropriate system parameters under certain conditions.

Atom localization via controlled spontaneous emission in a five-level atomic system

We investigate the one- and two-dimensional atom localization behaviors via spontaneous emission in a coherently driven five-level atomic system by means of a radio-frequency field driving a hyperfine transition. It is found that the detecting probability and precision of atom localization behaviors can be significantly improved via adjusting the system parameters. More importantly, the two-dimensional atom localization patterns reveal that the maximal probability of finding an atom within the sub-wavelength domain of the standing waves can reach unity when the corresponding conditions are satisfied. As a result, our scheme may be helpful in laser cooling or the atom nano-lithography via atom localization.

Two-dimensional sub-half-wavelength atom localization via controlled spontaneous emission

We propose a scheme for two-dimensional (2D) atom localization based on the controlled spontaneous emission, in which the atom interacts with two orthogonal standing-wave fields. Due to the spatially dependent atom-field interaction, the position probability distribution of the atom can be directly determined by measuring the resulting spontaneously emission spectrum. The phase sensitive property of the atomic system leads to quenching of the spontaneous emission in some regions of the standing-waves, which significantly reduces the uncertainty in the position measurement of the atom. We find that the frequency measurement of the emitted light localizes the atom in half-wavelength domain. Especially the probability of finding the atom at a particular position can reach 100% when a photon with certain frequency is detected. By increasing the Rabi frequencies of the driving fields, such 2D sub-half-wavelength atom localization can acquire high spatial resolution.

Two-dimensional atom localization via two standing-wave fields in a four-level atomic system

We propose a scheme for the two-dimensional (2D) localization of an atom in a four-level Y-type atomic system. By applying two orthogonal standing-wave fields, the atoms can be localized at some special positions, leading to the formation of sub-wavelength 2D periodic spatial distributions. The localization peak position and number as well as the conditional position probability can be controlled by the intensities and detunings of optical fields.

Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system

The behavior of two-dimensional (2D) atom localization is explored by monitoring the probe absorption in a microwave-driven four-level atomic medium under the action of two orthogonal standing-wave fields. Because of the position-dependent atom-field interaction, the information about the position of the atom can be obtained via the absorption measurement of the weak probe field. It is found that the localization behavior is significantly improved due to the joint quantum interference induced by the standing-wave and microwave-driven fields. Most importantly, the atom can be localized at a particular position and the maximal probability of finding the atom in one period of the standing-wave fields reaches unity by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve high-precision and high-resolution 2D atom localization.

Quantum Spectra and Classical Orbits in Artificial Atom

We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional artificial atom. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical closed orbits and the classical opened orbits from one point to another. These results give new evidence about the classical-quantum correspondence.

Relativistic two-dimensional H-like model atoms in an external magnetic field

The Klein–Gordon and Dirac equations for the two-dimensional hydrogen-like systems in the presence of an external magnetic field are solved using the power expansion method. For an arbitrary magnetic field intensity B the approximate solutions are determined by imposing asymptotic boundary conditions at finite radius ρ=R. For particular values of B, exact polynomial solutions are obtained. The dependence on the effective coupling constant γ=B/Z2 and on the atomic number Z of the energy eigenvalues for several states is studied.

Efficient two-dimensional atom localization via phase-sensitive absorption spectrum in a radio-frequency-driven four-level atomic system

A scheme of two-dimensional (2D) atom localization based on the phase-sensitive probe absorption is proposed in a four-level Λ-type atomic system with an assisting radio-frequency (rf)-driven field. The obtained 2D atom localization patterns reveal that the maximal probability of finding an atom within the sub-wavelength domain of the standing waves can arrive at unity by appropriate choice of the system parameters.

Two-dimensional noncommutative atom gas with the Anandan interaction

Landau like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the AC system and the HMW system, the torques of the system on the magnetic dipole and the electric dipole don't vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, NC space and NC phase space are obtained respectively. By using the coherent state method, some statistical properties of such free atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of $\sigma$ and revolution direction clearly, and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labelled by $\sigma$ can be related by a supersymmetry transformation on commutative space, but the phenomenon don't occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.

Asymptotics for Two-Dimensional Atoms

We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge Z > 0 and N quantum electrons of charge −1 is $${E(N,Z)=-\frac{1}{2}Z^2{\rm ln} Z+(E^{\rm TF}(\lambda)+\frac{1}{2}c^{\rm H})Z^2+o(Z^2)}$$ when Z → ∞ and N/Z → λ, where E TF(λ) is given by a Thomas–Fermi type variational problem and c H ≈ −2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z → ∞, which is contrary to the expected behavior of three-dimensional atoms.