Energies and structures of ${}^4\mathrm{He}_N\text{−}\mathrm{I}\mathrm{Cl}\left(X\right)$ complexes, $N⩽30$, are determined within the framework of a recently developed Hartree-like approach [Phys. Rev. A 71, 033203 (2005)], in which the He atoms play the role of the electrons and the I and Cl atoms play the role of the nuclei. The potential energy of the system is represented as a sum of the He-ICl triatomic and He-He pair interactions fitted to results of ab initio calculations. The validity of the approach is evaluated through comparisons with the results of “exact” variational calculations performed for the cases of $N=1$ and 2. The procedure, which furnishes also the wavefunctions, allows for simulation of the infrared spectra of the ICl molecule embedded in the bath of ${\mathrm{He}}_N$ clusters. Similarly to the case of the “bare” ICl, when the clusters are formed from bosonic He atoms the absorption selection rules lead only to the $P$ and $R$ branches of the spectra (the $Q$ branches are missing). The spectra exhibit a monotonically increasing blueshift, albeit with a decreasing rate, as the cluster size increases.

We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized $S=1$ chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.

We present a unique theoretical description of the physics of the spherically trapped $N$-atom degenerate Fermi gas at zero temperature based on an ordinary Schrödinger equation with a microscopic, two-body interaction potential. With a careful choice of coordinates and a variational wave function, the many-body Schrödinger equation can be accurately described by a linear, one-dimensional effective Schrödinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius, and peak density of the ground-state energy are made to those predicted by Hartree-Fock (HF) theory. Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.

We describe a procedure for splitting quantum information into two or more parts so that if and only if the recipients cooperate, the original qubit can be reconstructed. Our scheme uses W-type entangled states as the quantum channel and thus the scheme is robust against decoherence. We illustrate the procedure in the ion-trap system, but the idea can also be realized in other systems.

We provide a scheme for quantum computation in lattice systems via global but periodic manipulation, in which only effective periodic magnetic fields and global nearest-neighbor interactions are required. All operations in our scheme are attainable in optical-lattice or solid-state systems. We also investigate universal quantum operations and quantum simulation of two-dimensional lattices. We find that global manipulations are superior in simulating some nontrivial many-body Hamiltonians.

Density-functional theory (DFT) is shown to provide a conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground-state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean-field approximations for realistic models of many-body systems.

The present study deals with the calculation of differential, elastic integral, momentum transfer, and excitation cross sections for electron-${\mathrm{F}}_2\mathrm{O}$ collision in a 16-state $R$-matrix method. Configuration interation (CI) wave functions are used to represent the target states. The CI model gave an adequate description of the vertical excitation spectrum from the equilibrium geometry of the ground state $X^1{A}_1$ of the ${\mathrm{F}}_2\mathrm{O}$ molecule that spans the energy range $4.21–10.21\mathrm{eV}$. Our calculated dipole moment of $0.224\mathrm{D}$ is in good agreement with the experimental value $0.297\mathrm{D}$. We also found two broad shape resonances in ${}^{2}A_1$ and ${}^{2}B_2$ scattering symmetries and both resonances support dissociative electron attachment. A born correction is applied for the elastic and dipole allowed transitions to account for higher partial waves $(l>4)$ excluded in the $R$-matrix calculation. All cross sections are presented for incident electron energies up to $15\mathrm{eV}$. Our results are compared with cross sections of ${\mathrm{Cl}}_2\mathrm{O}$ calculated at the same level of complexity using the $R$-matrix method.

Absolute $K$-shell ionization cross sections of Sb, Au, and Bi have been measured in collisions with highly charged C, O, and S ions having energies between 2 and $6.25\mathrm{MeV}∕u$. The data are presented along with the earlier results with F and Si ions as projectiles. The measured data have been compared with theoretical models based on the semiclassical approximation including relativistic effect and perturbed stationary state approximation including the corrections for energy loss, Coulomb deflection, and relativistic effects. The data were analyzed in term of relativistic effect on $K$-ionization: its dependence on the projectile atomic number, target atomic number and projectile energy. The present data set along with our recently measured similar data for F and Si ions show that the relativistic effect increases with projectile atomic number and decreases with projectile velocity. A comparison of the experimental data and relativistic calculations, both normalized to nonrelativistic model, show the inadequacy of the theoretical models in describing the relativistic correction on $K$-shell ionization. For example, the theoretical predictions agree with experimental findings for O ions on Bi while the same theoretical predictions deviate from the experimental results by about a factor of 2 for Si and S on Bi, the theory being higher.

In order to explore a universal feature of atomic Fermi gases loaded on optical lattices, we make a systematic study of the particle density profile for one- and two-dimensional attractive Hubbard models with harmonic potential wells. Using the exact diagonalization scheme and the density-matrix renormalization group technique, we show that fine inhomogeneous zigzag patterns universally emerge in the above models. Theoretical and numerical analyses suggest that these structures originate from an effective repulsive interaction between tightly bound pairs and a breakdown of translational invariance. Furthermore, it is emphasized that the pattern obtained numerically in the two-dimensional model is the checkerboard type, which is very similar to results recently observed in a vortex core of high-$T_c$ cuprate superconductor.

Cold atom traps and certain neutron star layers may contain fermions with separation much larger than the range of pairwise potentials yet much shorter than the scattering length. Such systems can display universal characteristics independent of the details of the short range interactions. Our main result is that for space dimensions $D$ smaller than two and larger than four a specific extension of this problem is amenable to exact results. In particular, the energy per particle at the BCS-BEC crossover point is equal to the energy of the free fermion system in all $D⩽2$ whereas this energy is rigorously nonpositive (and potentially vanishing) in all $D⩾4$. We discuss the $D=3$ case. A particular unjustified recipe suggests $\xi =1∕2$ in $D=3$.

We study the condensation of a homogeneous interacting Bose gas in the presence of a superimposed weak periodic potential. In contrast to, e.g., a harmonic trap, the periodic potential does not reduce the significance of long-wavelength fluctuations and thus influences the phase transition in a more profound way. We present general thermodynamic descriptions of the system above condensation in terms of mean-field as well as renormalization-group theory. Our approaches are based on describing the interplay between the effects of the interactions and the potential by means of a renormalization of the potential amplitude. These theories are then used to study the critical chemical potential and particle density and their dependence on the properties of the applied potential. A main result of our investigations concerns the characteristic nonperturbative momentum scale $k_c$ of the critical interacting Bose gas. It is shown that the existence of this momentum scale becomes macroscopically manifest in the behavior of the critical thermodynamic properties.

We report the observation of normal-mode splitting of the atom-cavity dressed states in both the fluorescence and transmission spectra for large atom number and observe subnatural linewidths in this regime. We also implement a method of utilizing the normal-mode splitting to observe Rabi oscillations on the ${}^{87}\mathrm{Rb}$ ground state hyperfine clock transition. We demonstrate a large collective cooperativity, $C=1.2\times {10}^4$, which, in combination with large atom number, $N\sim 2\times {10}^5$, offers the potential to realize an absolute phase sensitivity better than that achieved by state-of-the-art atomic fountain clocks or inertial sensors operating near the quantum projection noise limit.

Using the Dawson-March transformation of two-level wave functions in terms of density amplitude and phase, a differential equation is constructed relating the single-particle kinetic energy to the fermion density. Employing then the differential form of the virial theorem derived by March and Young [Nucl. Phys. 12, 237 (1959)], a nonlinear electron-density–one-body potential relation emerges. Application to the Be-like atomic ions is briefly considered.

We have measured the lifetimes of ${}^{1}P^e$ $(n=9–12)$ doubly excited states in static electric fields $(1–6\mathrm{kV}∕\mathrm{cm})$ by observing the decay of the fluorescence signal as a function of time. The effects of the field on these helium states below the second ionization threshold are twofold: their excitation becomes possible due to the Stark mixing with the optically allowed ${}^{1}P^o$ series, and their lifetime is strongly modified by the opening of the autoionization channel, not accessible in zero field. Although the electric field represents only a tiny perturbation of the atomic potential, a substantial shortening of the lifetimes below $100\mathrm{ps}$ is observed. This is the simplest quantum system where the ratio of autoionization to fluorescence decay probability can be effectively controlled by an electric field of moderate strength.

We propose a genuine multiparty correlation measure for a multiparty quantum system as the trace norm of the cumulant of the state. The legitimacy of our multiparty correlation measure is explicitly demonstrated by proving it satisfies the five basic conditions required for a correlation measure. As an application we construct an efficient algorithm for the calculation of our measures for all stabilizer states.

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more Hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the $XY$ model, that of the Heisenberg antiferromagnet, a state in Shor’s factoring algorithm, and a state in Grover’s quantum search algorithm. Although the visualization function can take negative values, it becomes nonnegative (hence, becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.

The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature $T$, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.

We give a further investigation of the range criterion and low-to-high rank generating mode introduced in Chen and Chen [Phys. Rev. A 73, 052310 (2006)], which can be used for the classification of $2\times M\times N$ states under reversible local filtering operations. By using these techniques, we entirely classify the family of $2\times 4\times 4$ states, which actually contains infinitely many kinds of states. The classifications of true entanglement of $2\times (M+3)\times (2M+3)$ and $2\times (M+4)\times (2M+4)$ systems are briefly listed, respectively.

We find a universal lower bound on locally accessible information for arbitrary bipartite quantum ensembles, when one of the parties is two dimensional. In higher dimensions and in a higher number of parties, the bound is on accessible information by separable operations. We show that for any given density matrix (of an arbitrary number of parties and dimensions), there exists an ensemble, which averages to the given density matrix and whose locally accessible information saturates the lower bound. Moreover, we give a general method to obtain bounds on the yield of singlets in distillation protocols that involves local distinguishing, by using lower and upper bounds on locally accessible information. We then illustrate it by using our lower bound, along with a previously obtained upper bound, on locally accessible information.