Ground State Pair Research Articles

Spin squeezing and Schrödinger-cat-state generation in atomic samples with Rydberg blockade

A scheme is proposed to prepare squeezed states and Schr\"{o}dinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser fields, we can suppress non-adiabatic transfer under the time varying Hamiltonian and significantly speed up the evolution towards a maximally squeezed, J_z=0, collective spin state.

Magnetism and structure of graphene nanodots with interiors modified by boron, nitrogen, and charge

The properties (geometry, spin, and charge distribution) of a series of flat hexagonal zigzag edged graphene nanodots (GNDs), with interiors modified by centrally located substituent atoms boron and nitrogen and by positive and negative charge, have been calculated using ab initio density functional theory. The doped series X-GND has the stoichiometry C(6m(2)-1)XH(6m), zigzag size index m = 2, 4, 6, 8, 10 and substituent X = B or N. The undoped parents C(6m(2))H(6m) with m ≤ 8 have spin paired ground states and the parent m = 10 has a spin polarized singlet ground state with edges that alternate α- and β-spin. The spin on the substituent atom decreases to zero with size index m and magnetization builds on the edges of all the X-GND. This demonstrates translocation of substituent spin and a proximity or directional effect for small m as the edges show different degrees of magnetization. For the largest X-GND (m = 10) the magnetization on edges resembles the calculated triplet S = 1(a) configuration of the parent (four edge spins up and two down) and has a higher apparent symmetry than the C(2v) point group of X-GND. For charged (m = 10) GNDs the edge magnetization has strength comparable to the parent on two parallel edges and weak on the other four in a perimeter pattern that resembles the triplet S = 1(b) configuration of the undoped parent and not the ground configuration of the isoelectronic X-GND molecule. Many of the results can be interpreted by simple Kekulé valence bond structures for an unpaired spin on a network where the substituent site group symmetry is not compatible with the perimeter. A deeper understanding is provided by the properties of the Kohn-Sham orbitals. The calculations of the X-doped GNDs reveal limitations in the use of the hex-radical hypothesis of the parent ground state to systems where foreign atoms lower symmetry and perturb the π- and σ-bond manifolds.

Correction method for obtaining the variationally best ground-state pair density

We present a correction method for the pair density (PD) to get close to the ground-state one. The PD is corrected to be a variationally best PD within the search region that is extended by adding the uniformly scaled PDs to its elements. The corrected PD is kept $N$-representable and satisfies the virial relation rigorously. The validity of the present method is confirmed by numerical calculations of neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which is a good benchmark for the error of the PD, is reduced by 69.7% without additional heavy calculations.

Orientationally ordered phase produced by fully antinematic interactions: A simulation study

We consider here a classical model, consisting of D(2h) symmetric particles, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. Two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be written as a linear combination involving the squares of the scalar products between corresponding unit vectors only, thus depending on three parameters, and making the interaction model rather versatile. A coupling constant with negative sign tends to keep the two interacting unit vectors parallel to each other, whereas a positive sign tends to keep them mutually orthogonal (antinematic coupling). We address here a special, extreme case of the above family, involving only antinematic couplings: more precisely, three antinematic terms whose coefficients are set to a common positive value (hence the name PPP model). The model under investigation produces a doubly degenerate pair ground state; the nearest-neighbor range of the interaction and the bipartite character of the lattice can propagate the pair ground state and increase the overall degeneracy, but without producing frustration. The model was investigated by a simplified molecular field treatment as well as by Monte Carlo simulation, whose results suggested a second-order transition to a low-temperature biaxially ordered phase; ground-state configurations producing orientational order have been selected by thermal fluctuations. The molecular field treatment also predicted a continuous transition, and was found to overestimate the transition temperature by a factor 2.

Solubility of Metal Atoms in Helium Droplets: Exploring the Effect of the Well Depth Using the Coinage Metals Cu and Ag

We report a theoretical investigation of the solution properties of Cu and Ag atoms dissolved in He clusters. Employing our recent ab initio ground state pair potential for Me-He (Me = Ag, Cu), we simulated the species Me@He (n) (n = 2-100) by means of diffusion Monte Carlo (DMC) obtaining exact information on their energetics and the structural properties. In particular, we investigated the sensitivity of structural details on the well depth of the two interaction potentials. Whereas Ag structures the first He solvation layer similarly, to some extent, to a positive ion such as Na(+), Cu appears to require the onset of a second solvation shell for a similar dense structure to be formed despite an interaction well of 28.4 μhartree. An additional signature of the different solution behavior between Ag and Cu appears also in the dependence of the energy required to evaporate a single He atom on the size of the MeHe(n) clusters. The absorption spectrum for the (2)P ← (2)S excitation of the metals was also simulated employing the semi-classical Lax approximation to further characterize Me@He(n) (n = 2-100) using novel accurate interaction potentials between He and the lowest (2)P state of Ag and Cu in conjunction with the Diatomic-in-Molecules approach. The results indicated that Ag exciplexes should not form via a direct vertical excitation into an attractive region of the excited manifolds and that there is an interesting dependence of the shape of the Cu excitation bands on the local structure of the first solvation shell.

Coboson formalism for Cooper pairs and its application to Richardson’s equations

We propose a many-body formalism for Cooper pairs which has similarities to the one we recently developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences that $N$ Cooper pairs differ from $N$ single pairs through electron exchange only: no direct coupling exists due to the very peculiar form of the BCS potential. As a first application, we here use this formalism to derive Richardson's equations for the exact eigenstates of $N$ Cooper pairs. This gives hints on why the $N(N-1)$ dependence of the $N$-pair ground state energy we recently obtained by solving Richardson's equations analytically in the low density limit, stays valid up to the dense regime, no higher order dependence exists even under large overlap, a surprising result hard to accept at first. We also briefly question the BCS wave function ansatz compared to Richardson's exact form, in the light of our understanding of coboson many-body effects.

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha)$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha|J)$ is supported on a single ground state pair.

Correlation dynamics after short-pulse photoassociation

Two atoms in an ultracold gas are correlated at short interatomic distances due to threshold effects in which the potential energy of their interaction dominates the kinetic energy. The correlations manifest themselves in a distinct nodal structure of the density matrix at short interatomic distances. Pump-probe spectroscopy has recently been suggested [Phys. Rev. Lett. 103, 260401 (2009)] to probe these pair correlations: A suitably chosen, short photoassociation laser pulse depletes the ground-state pair density within the photoassociation window, creating a nonstationary wave packet in the electronic ground state. The dynamics of this nonstationary wave packet is monitored by time-delayed probe and ionization pulses. Here we discuss how the choice of the pulse parameters affects the experimental feasibility of this pump-probe spectroscopy of two-body correlations.

DISTRIBUTION OF PURE STATES IN SHORT-RANGE SPIN GLASSES

We review the structure of the spin glass phase in the infinite-range Sherrington–Kirkpatrick model and the short-range Edwards–Anderson (EA) model. While the former is now believed to be understood, the nature of the latter remains unresolved. However, considerable insight can be gained through the use of the metastate, a mathematical construct that provides a probability measure on the space of all thermodynamic states. Using tools provided by the metastate construct, possibilities for the nature of the organization of pure states in short-range spin glasses can be considerably narrowed. We review the concept of the "ordinary" metastate, and also newer ideas on the excitation metastate, which has been recently used to prove existence of only a single pair of ground states in the EA Ising model in the half-plane. We close by presenting a new result, using metastate methods, on the number of mixed states allowed in the EA model.

Neutron-12C elastic scattering at 96 MeV

Recent neutron elastic scattering differential cross section data for 12C at 96 MeV have been analysed within the framework of the Glauber model, suitably modified to enlarge the angular range of validity. The ground-state pair correlation correction has been considered. The effects of the medium-modified nucleon–nucleon (NN) total cross section and the phase variation of the NN scattering amplitude on the calculated cross sections have also been studied. The neutron differential cross sections have been calculated using the phenomenological target density. We find that our method of analysis gives a better description of experimental data than those with the optical model potential.

Vision of a fully laser-driven ${\sf n\gamma}{-}{\sf m\gamma}$ collider

The use is suggested of a laser-accelerated dense electron sheet with an energy of ( $E=\tilde{\gamma} mc^2$ ) as a relativistic mirror to reflect coherently a second laser with photon energy ħω, generating by the Doppler boost high-energy γ photons with $$ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega $$ and short duration [A. Einstein, Annalen der Physik 17, 891 (1905); D. Habs et al., Appl. Phys. B 93, 349 (2008)]. Two of these counter-propagating γ beams are focused by the parabolically shaped electron sheets into the interaction region with small, close to diffraction-limited, spot size. Comparing the new nγ-mγ collider with former proposed γγ collider schemes we achieve the conversion of many photon-pairs in a small space-time volume to matter-antimatter particles, while in the other discussed setups only two isolated, much more high-energetic photons will be converted, reaching in the new approach much higher energy densities and temperatures. With a γ-field strength somewhat below the Schwinger limit we can reach this complete conversion of the γ bunch energy into e+e- or quark-antiquark $q\bar{q}$ -plasmas. For a Bose-Einstein condensate (BEC) [A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 261 (1924); A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 3 (1925); A. Griffin, D.W. Snoke, S. Stringari, Bose-Einstein Condensation (Cambridge University Press, 1995)] final state or for the Cooper pair ground state at higher densities [A.J. Leggett, Quantum Liquids, Oxford Graduate Texts (Oxford University Press, 2006)] the strong induced transition into this coherent state is of special interest for single-cycle γ pulses. Due to annihilation these cold coherent states are very short-lived. For γ beams with photon energies of 1–10 keV the rather cold e+e--plasma or e+e--BEC expands to a cold dense aggregate of positronium (Ps) atoms, where the production of Ps molecules is discussed. For photon energies of 1–10 MeV we discuss the production of a cold induced π0-BEC followed by the formation of molecules. For the direct population of higher $q\bar{q}$ densities we can study condensates of color-neutral mesons with enhanced population. For a γγ collider with several-cycle laser pulses the following cycles heat up the fermion-antifermion $f\bar{f}$ system to a certain temperature. Thus we can reach high energy densities and temperatures of an e+e-γ plasma, where the production of hadrons in general or the quark-gluon phase transition can be observed. Within the long-term goal of very high photon energies of about 1 GeV in the nγ-mγ-collider, even the electro-weak phase transition or SUSY phase transition could be reached.

A pair density functional theory utilizing the correlated wave function

We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme[Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

Boson and fermion many-body assemblies: fingerprints of excitations in the ground-state wave functions, with examples of superfluid 4He and the homogeneous correlated electron liquid

After a brief summary of some basic properties of ideal gases of bosons and of fermions, two many-body Hamiltonians are cited for which ground-state wave functions allow the generation of excited states. Because of the complexity of ground-state many-body wave functions, we then consider properties of reduced density matrices, and in particular, the diagonal element of the second-order density matrix. For both the homogeneous correlated electron liquid and for an assembly of charged bosons, the ground-state pair correlation function g(r) has fingerprints of the zero-point energy of the plasmon modes. These affect crucially the static structure factor, S(k), in the long wavelength limit. This is best understood by means of the Ornstein–Zernike direct correlation function c(r), which plays an important role throughout this article. Turning from such charged liquids, both boson and fermion, to superfluid 4He, the elevated temperature (T) structure factor S(k, T) is related, albeit approximately, to its zero-temperature counterpart, via the velocity of sound, reflecting the collective phonon excitations and the superfluid density. Finally, some future directions are pointed.

Biaxial and uniaxial phases produced by partly repulsive mesogenic models involvingD2hmolecular symmetries

The present paper considers biaxial nematogenic lattice models, involving particles of D2h symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice. The pair potential is isotropic in orientation space and restricted to nearest neighbors. Let two orthonormal triads define orientations of a pair of interacting particles. The investigated potential models are quadratic with respect to the nine scalar products between the two sets of unit vectors. Actually, based on available geometric identities, these expressions can be reduced to diagonal form containing only the scalar products between corresponding unit vectors and depending on three parameters. Over the years, this comparatively simple functional form has also proven to be rather versatile. By now, various sets of potential parameters capable of producing mesogenic behavior of some kind have been proposed and studied in the literature. A new and simplified form was recently proposed and investigated by Sonnet, Virga, Durand, and De Matteis [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003); G. De Matteis and E. G. Virga, Phys. Rev. E 71, 061703 (2005)] and is known to support a biaxial phase at sufficiently low temperature. Following the idea of the above authors, we have studied a more extended range of parameters, including cases where biaxiality cannot be sustained in the pair ground state. In cases where a biaxial phase survives, an appropriate mean-field analysis may predict the existence of a direct second-order transition to the isotropic phase as well as a second-order sequence isotropic-to-uniaxial-to-biaxial. A second-order phase transition is also predicted, which involves isotropic and uniaxial phases only. Monte Carlo simulations have been carried out as well, for a few points in the parameter space, and found to produce results which partly confirm mean-field predictions.

Ferromagnetic pairing states on two-coupled chains

We propose a concrete model which exhibits ferromagnetism and electron-pair condensation simultaneously. The model is defined on two chains and consists of the electron hopping term, the on-site Coulomb repulsion and a ferromagnetic interaction which describes ferromagnetic coupling between two electrons, one on a bond in a chain and the other on a site in the other chain. It is rigorously shown that the model has fully-polarized ferromagnetic pairing ground states. The higher dimensional version of the model is also presented.

Pore Size Effect on the Dynamics of Excimer Formation for Chemically Attached Pyrene on Various Silica Surfaces

Excimer formation by pyrene is a well-known process in solution and on solid surfaces. In solution, excimer formation is highly dependent on the concentration of pyrene. When adsorbed on solid surfaces (i.e., silica surfaces), pyrene has been shown to form ground-state pairs which lead to static excimer emission even at very low surface coverages as a result of a solvent pooling effect induced during solvent removal from the surface. Ground-state pairing on silica surfaces results from a π−π interaction between two adjacent pyrene molecules and can not be avoided even by slow evaporation of the solvent from the surface as the molecules diffuse toward one another during the process. One possible method to alleviate the pairing of pyrene molecules and hence the formation of excimer is to chemically attach pyrene molecules to the silica surface. Chemical attachment, however, does not allow effective control over the spacing between the pyrene molecules to avoid ground-state pairing. To circumvent this, spacer molecules can be incorporated onto the surface by chemical attachment to control the spacing between two adjacent pyrene molecules. Furthermore, by using surfaces that provide various pore sizes, it is possible to control the number of pyrene molecules that can be grafted onto and confined to the pore surface, as well as the steric environment in which the molecules can rotate. Cabosil (fumed silica with no pores) and mesoporous silica surfaces with various pore diameters (i.e., MCM-41) are ideal candidates to examine the feasibility of controlling the spacing between pyrene molecules on a flat surface and confined inside the pores using a cografted spacer molecule (i.e., biphenyl). We have now used such an approach to examine the extent of excimer formation as the ratio of spacer/pyrene molecules is varied on nonporous silica surfaces as well as mesoporous silica surfaces with various pore diameters. Our results show that a decrease in the ratio of spacer/pyrene is accompanied by an increase in the excimer emission on both nonporous and porous silicas. Furthermore, as the pore diameter is increased, an increase in the excimer emission is observed at similar spacer:pyrene grafting ratio. This suggests that a decrease in the separation of pyrene molecules on the surface, as the concentration of biphenyl spacer is decreased relative to pyrene, results in closer proximity of the neighboring pyrene molecules leading to the excimer emission. It is also observed that the alkyl side chain length (i.e., four carbon chain) bearing the pyrene fluorescent probe provides a more facile path for excimer formation by providing the flexibility needed for two pyrenes to reach and interact. When the alkyl side chain is removed and pyrene is directly attached to the surface, the contribution of excimer emission is diminished.

Absorption and emission lineshapes and ultrafast solvation dynamics of NO in parahydrogen

We perform a theoretical study on the electronic spectroscopy of dilute NO impurity embedded in parahydrogen (p-H(2)). Absorption and emission lineshapes for the A (2)Sigma(+)<--X (2)Pi Rydberg transition of NO in parahydrogen have been previously measured and simulated, which yielded results for the NO/p-H(2) ground and excited state pair potentials [L. Bonacina et al., J. Chem. Phys. 125, 054507 (2006)]. Using these potentials, we performed molecular dynamics simulation, theoretical statistical mechanical calculations of absorption and emission lineshapes, and both equilibrium and nonequilibrium solvation correlation functions for NO chromophore in parahydrogen. Theory was shown to be in good agreement with simulation. Linear response treatment of solvation dynamics was shown to break down due to a dramatic change in the solute-solvent microstructure upon solute excitation to the Rydberg state and the concomitant increase of the solute size.

Rotating Ground States of a One-Dimensional Spin-Polarized Gas of Fermionic Atoms with Attractivep-Wave Interactions on a Mesoscopic Ring

The major finding of this Letter is that a one-dimensional spin-polarized gas composed of an even number of fermionic atoms interacting via attractive p-wave interactions and confined to a mesoscopic ring has a degenerate pair of ground states that are oppositely rotating. In any realization the gas will be measured to rotate one way or the other in spite of the fact that there is no external rotation or bias fields. Our goal is to show that this counterintuitive finding is a natural consequence of the combined effects of quantum statistics, ring topology, and exchange interactions.

Chromium Aromatic Hydrocarbon Sandwich Molecules and the Eighteen-Electron Rule

Ab initio density functional theory (DFT) calculations are reported for the chromium sandwich structure CrnR2, where n = 7 and R is the aromatic hydrocarbon hexabenzocoronene (C42H18). This system is remarkable in that the structure of the chromium sites strongly resemble those in chromium bis-benzene Cr1(C6H6)2, as judged by geometry and charge density properties. The electron localization function of the sandwich shows a hexagonally arrayed set of V(C, Cr, C) valence basins about each chromium atom with modification due to local site symmetry. This system satisfies an extension of the 18-electron rule to components of a conjugated molecular system. This idea is explored further by examining the electronic and geometric properties of the series CrnR2, where n and R are given by n = 1, benzene C6H6 as reference; n = 2, biphenyl (C6H5)2; n = 3, triphenylene C18H12; n = 3, coronene C24H18; and n = 4, dibenzopyrene C24H14. On the basis of electron counting and ring isolation, all the sandwich structures in this series could satisfy the extension of the 18-electron rule, with the exception of coronene, which was deliberately included. The DFT calculations predict spin-paired ground states for some but not all of the sandwich structures, implying that the Cr-ring interactions at work require understanding at a deeper level. Thus, while sandwiches with n = 1, n = 2, n = 4 and n = 7 have spin paired singlet ground states and appear to satisfy the rule, those with n = 3 (triphenylene, coronene) have antiferromagnetic singlet ground states and do not. This is attributed to nonuniformity in the electronic charge density of the rings of the isolated hydrocarbons and to a reduction of symmetry from D3h to C2v with a concomitant spin-charge density change in the sandwiches.

Superfuid-insulator transitions at noninteger filling in optical lattices of fermionic atoms

We determine the superfluid transition temperatures ${T}_{c}$ and the ground states of the attractive Hubbard model and find unusual insulating phases associated with noninteger filling at sufficiently strong pairing attraction $\ensuremath{\mid}U\ensuremath{\mid}$. These states, distinct from the band-and Mott-insulating phases, derive from pair localization; pair hopping at large $\ensuremath{\mid}U\ensuremath{\mid}$ and high densities is impeded by intersite, interpair repulsive interactions. The best way to detect the breakdown of superfluidity is by using fermionic optical lattices, which should reveal these unusual forms of ``bosonic'' order, reflecting ground-state pairing without condensation.