Real-space Theory Research Articles

Atomic-type photonic crystals with adjustable band gaps

If the electromagnetic waves are scattered by the periodic structure of media with different refractive indexes, a band gap in the transmitted spectrum can be generated. This is the photonic crystal whose band gap is usually uncontrollable as its structure parameters are fixed after the fabrication. Alternatively, based on the quantum theory in real space for single photons transporting along a one-dimensional waveguide embed by a series of two-level atoms, we propose here a quantum mechanical configuration to implement the photonic crystal with adjustable band gap. It is shown that if the scattering two-level atoms are arranged as a periodic array, the desirable band gap in the photonic transmission spectrum can be formed. This is the atomic-type photonic crystal, in which the center frequency of the gap can be controlled by adjusting the eigenfrequencies of the atoms. The possible physical implementations of our proposal with the voltage-biased superconducting qubits for the centimeter waves and the voltage-biased electrons on liquid helium for the millimeter waves are also discussed.

Controllable photon extraction based on a single-photon Raman interaction

A target whispering-gallery-mode microresonator (WGMM) directly coupled to a waveguide with an auxiliary side-coupled WGMM is proposed to deterministically extract both the resonant and non-resonant single incident photons from a waveguide. Based on the single-photon Raman interaction (SPRINT) between an Λ-type three-level atom and the target WGMM, a full quantum theory in real space is adopted to calculate the extraction efficiencies at the single-photon level. The results show that the extraction efficiencies can be significantly improved by appropriately tuning the frequencies of the auxiliary WGMM and the coupling strength between the two WGMMs, even when the atom and WGMMs have dissipations. Since mode redistribution is only externally imposed on the auxiliary WGMM, the population and phase of the atom are not directly affected. The nonlocal control, which ensures that the SPRINT takes place, results in high extraction efficiencies. We also find that the transmission probabilities of both the resonant and non-resonant incident photons can be controlled in a range from 0 to 100%, so that the proposed double-WGMM system has the potential to be used as a single-photon switch.

Spatial behavior in a Mott insulator near the voltage-driven resistive transition

We develop a real space theory of the voltage bias driven transition from a Mott insulator to a correlated metal. Within our Keldysh mean field approach the problem reduces to a self-consistency scheme for the charge and spin profiles in this open system. We solve this problem for a two dimensional antiferromagnetic Mott insulator at zero temperature. The charge and spin magnitude is uniform over the system at zero bias, but a bias $V$ leads to spatial modulation over a lengthscale $\xi(V)$ near the edges. $\xi(V)$ grows rapidly and becomes comparable to system size as $V$ increases towards a threshold scale $V_c$. The linear response conductance of the insulator is zero with the current being exponentially small for $V \ll V_c$. The current increases rapidly as $V \rightarrow V_c$. Beyond $V_c$, we observe an inhomogeneous low moment antiferromagnetic metal, and at even larger bias a current saturated paramagnetic metal. We suggest an approximate scheme for the spectral features of this nonequilibrium system.

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities.

Covariance of the galaxy angular power spectrum with the halo model

As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxyCℓ, with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limber’s approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equalitykeq. A short self-contained summary of the equations is provided in Sect. 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.

Designing Fano-Like Quantum Routing via Atomic Dipole-Dipole Interactions**Supported by the National Natural Science Foundation of China under Grant No 11247032, the Natural Science Foundation of Jiangxi Province under Grant Nos 20151BAB202012 and 20151BAB212004, and the Scientific Research Foundation of the Jiangxi Provincial Education Department under Grant No GJJ160633.

Fano-like quantum routing of single photons in a system with two waveguides coupled to two collocated atoms is investigated theoretically. Using a full quantum theory in real space, photonic scattering amplitudes along four ports of the waveguide network are analytically obtained. It is shown that, by adjusting the atomic dipole-dipole interaction, an evident Fano-line shape emerges in the scattering spectra of the single-dot configuration system. Moreover, Fano resonance can also be achieved by varying the atom-waveguide coupling strength and atomic detuning, in the presence of the atomic dipole-dipole interaction. Therefore, the atomic dipole-dipole interaction may be utilized as a possible way to control spectral Fano-like resonance. The feasibility with the experimental waveguide channels is also discussed.

Periodically modulated single-photon transport in one-dimensional waveguide

Single-photon transport along a one-dimension waveguide interacting with a quantum system (e.g., two-level atom) is a very useful and meaningful simplified model of the waveguide-based optical quantum devices. Thus, how to modulate the transport of the photons in the waveguide structures by adjusting certain external parameters should be particularly important. In this paper, we discuss how such a modulation could be implemented by periodically driving the energy splitting of the interacting atom and the atom–photon coupling strength. By generalizing the well developed time-independent full quantum mechanical theory in real space to the time-dependent one, we show that various sideband-transmission phenomena could be observed. This means that, with these modulations the photon has certain probabilities to transmit through the scattering atom in the other energy sidebands. Inversely, by controlling the sideband transmission the periodic modulations of the single photon waveguide devices could be designed for the future optical quantum information processing applications.

A multipolar approach to the interatomic covalent interaction energy.

Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities ρA(r) and ρB(r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1-2 pairs) albeit it works reasonably well most times for 1- n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l1+l2=2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.

Lattice dynamics calculations based on density-functional perturbation theory in real space

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

Attractive Hofstadter-Hubbard model with imbalanced chemical and vector potentials

We study the interplay between the Hofstadter butterfly, strong interactions and Zeeman field within the mean-field Bogoliubov-de Gennes theory in real space, and explore the ground states of the attractive single-band Hofstadter-Hubbard Hamiltonian on a square lattice, including the exotic possibility of imbalanced vector potentials. We find that the cooperation between the vector potential and superfluid order breaks the spatial symmetry of the system, and flourish stripe-ordered Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like superfluid and supersolid phases that can be distinguished and characterized according to their coexisting pair-density (PDW), charge-density (CDW) and spin-density (SDW) wave orders. We also discuss confined systems and comment on the likelihood of observing such stripe-ordered phases by loading neutral atomic Fermi gases on laser-induced optical lattices under laser-generated artificial gauge fields.

One-electron images in real space: natural adaptive orbitals.

We introduce a general procedure to construct a set of one-electron functions in chemical bonding theory, which remain physically sound both for correlated and noncorrelated electronic structure descriptions. These functions, which we call natural adaptive orbitals, decompose the n-center bonding indices used in real space theories of the chemical bond into one-electron contributions. For the n = 1 case, they coincide with the domain natural orbitals used in domain-averaged Fermi hole analyses. We examine their interpretation in the two-center case, and show how they behave and evolve in simple cases. Orbital pictures obtained through this technique converge onto the chemist's molecular orbital toolbox if electron correlation may be ignored, and provide new insight if it may not.

Controlling single-photon transport with three-level quantum dots in photonic crystals

We investigate how to control single-photon transport along the photonic crystal waveguide with the recent experimentally demonstrated artificial atoms [i.e., $\ensuremath{\Lambda}$-type quantum dots (QDs)] [S. G. Carter et al., Nat. Photon. 7, 329 (2013)] in an all-optical way. Adopting full quantum theory in real space, we analytically calculate the transport coefficients of single photons scattered by a $\ensuremath{\Lambda}$-type QD embedded in single- and two-mode photonic crystal cavities (PCCs), respectively. Our numerical results clearly show that the photonic transmission properties can be exactly manipulated by adjusting the coupling strengths of waveguide-cavity and QD-cavity interactions. Specifically, for the PCC with two degenerate orthogonal polarization modes coupled to a $\ensuremath{\Lambda}$-type QD with two degenerate ground states, we find that the photonic transmission spectra show three Rabi-splitting dips and the present system could serve as single-photon polarization beam splitters. The feasibility of our proposal with the current photonic crystal technique is also discussed.

Pseudopotential calculation of the bulk modulus and phonon dispersion of the bcc and hcp structures of titanium

The structural stability of Ti in the hexagonal-closed-packed and body-centered cubic structures was studied by means of the full potential linearized augmented plane wave method. The effect of pressure on the bulk modulus of the crystal structures was investigated. In this study, the plane wave ultrasoft pseudopotential method was used to calculate the elastic constants, bulk modulus and phonon frequency of Ti. Phonon calculations were performed by employing the density functional perturbation theory in real space, using the calculated lattice dynamical force constants. All calculations were based on the density functional theory with the generalized gradient approximation and local density approximation, which well describe the properties of the above-mentioned metal.

Structures and absorption spectra of sulfur cluster S9 via first-principles calculations

We have applied a finite-difference pseudopotential density-functional theory in real space with Langevin molecular dynamics annealing technique to determine the ground state structure of S 9 cluster, and a linear response method within the adiabatic time-dependent density-functional theory (TDDFT) with the local density approximation (TDLDA) to calculate the optical absorption spectra . It is found that the ground state structure of sulfur cluster S 9 belongs to C 2 symmetry structure. It seems that our ground state structures of S 9 are more stable than other theoretical results. Our results show that the calculated ground state structures of S 9 cluster are hardly dependent on the initial structure of S 9 cluster. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.

Raman Spectroscopy of Graphene Edges

Graphene edges are of particular interest since their orientation determines the electronic properties. Here we present a detailed Raman investigation of graphene flakes with edges oriented at different crystallographic directions. We also develop a real space theory for Raman scattering to analyze the general case of disordered edges. The position, width, and intensity of G and D peaks are studied as a function of the incident light polarization. The D-band is strongest for polarization parallel to the edge and minimum for perpendicular. Raman mapping shows that the D peak is localized in proximity of the edge. For ideal edges, the D peak is zero for zigzag orientation and large for armchair, allowing in principle the use of Raman spectroscopy as a sensitive tool for edge orientation. However, for real samples, the D to G ratio does not always show a significant dependence on edge orientation. Thus, even though edges can appear macroscopically smooth and oriented at well-defined angles, they are not necessarily microscopically ordered.

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Nonlinearity and Redshift-Space Distortion Effects

Abstract An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several ongoing and/or future galaxy surveys aim to detect and precisely determine the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices for the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007, ApJ, 657, 51) indeed shows very small shifts ($\lesssim$1%) relative to the prediction in linear theory in real space. The shifts can be predicted accurately for scales where perturbation theory is reliable.

Effective medium super-cell approximation for interacting disordered systems: analternative real-space derivation of generalized dynamical cluster approximation

We develop a generalized real-space effective medium super-cell approximation (EMSCA)method to treat the electronic states of interacting disordered systems. This method isgeneral and allows randomness both in the on-site energies and in the hopping integrals.For a non-interacting disordered system, in the special case of randomness in theon-site energies, this method is equivalent to the non-local coherent potentialapproximation (NLCPA) derived previously. Also, for an interacting system the EMSCAmethod leads to the real-space derivation of the generalized dynamical clusterapproximation (DCA) for a general lattice structure. We found that the originalDCA and the NLCPA are two simple cases of this technique, so the EMSCAis equivalent to the generalized DCA where there is included interaction andrandomness in the on-site energies and in the hopping integrals. All of the equations ofthis formalism are derived by using the effective medium theory in real space.

Density-functional calculations of structures and absorption spectra of sulfur cluster S6

A finite-difference pseudopotential density-functional theory in real space and the Langevin molecular dynamics annealing technique as well as the adiabatic time-dependent density functional theory within the time-dependent local density approximation (TDLDA) are applied to the descriptions of structures and optical absorption spectra of sulfur cluster S6. It is found that the ground-state structure of S6 belongs to either a boat-shaped C2v or chair-shaped D3d symmetry structure and the calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations. PACS Nos.: 31.15.Ew, 31.15.Qg, 36.40.–c

First-principles calculations for structures and absorption optical spectra of sulfur cluster S 7

A finite-difference pseudopotential density-functional theory in real space and Langevin molecular dynamics annealing technique are applied to determine the ground state structure of sulfur cluster S 7 and the corresponding optical absorption spectra from a linear response method within the adiabatic time-dependent local density approximation. It is found that the ground state structure of sulfur cluster S 7 belongs to a chair structure with C s symmetry and the calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations.

Pseudopotential Density-Functional Calculations for Structures of Small Carbon Clusters CN (N = 2 ~ 8)**The project supported by National Natural Science Foundation of China under Grant No. 10274055 and the Research Fund for the Doctoral Program of High Education of China under Grant No. 20020610001

We introduce a first-principles density-functional theory, i.e. the finite-difference pseudopotential density-functional theory in real space and the Langevin molecular dynamics annealing technique, to the descriptions of structures and some properties of small carbon clusters CN (N = 2 ~ 8). It is shown that the odd-numbered clusters have linear structures and most of the even-numbered clusters prefer cyclic structures.