The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting $N$-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting $N$-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle ($p$-$p$) and hole-hole ($h$-$h$) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion.

A version of the $J$-matrix method for solving numerically the three-body Faddeev-Merkuriev differential equations is proposed. This version allows one to take into account the full spectrum of the two-body Coulomb subsystem. As a result, a discrete analog of the Lippmann-Schwinger equation is obtained which allows one to interpret correctly the three-body wave function in two-body domains. The scheme is applied to calculations of the fully resolved absolute differential cross sections for the $\mathrm{He}(e,2e){\mathrm{He}}^{+}$ reactions leaving the residual ion in an excited state, at small energy and momentum transfer. The results are in good agreement with the experiment both in shape and in absolute value.

As part of an ongoing investigation of cold-molecule collisions involving nitric oxide (NO), we here theoretically assess the first- and second-order perturbation-theory approximations to the Stark shifts; such approximations have been used almost exclusively in previous published research on NO in external electric fields. We perform this assessment by comparison to Stark shifts from the corresponding nonperturbative two-state model, considering field strengths from zero to values typical of current experimental studies of cold molecules. To facilitate the future use of this model, we give expressions for the Stark energies in a generic form that can trivially be applied to any molecules in the class under consideration. To provide insight into the validity of the two-state model, we also experimentally assess the two-state Stark shifts for NO.

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

We theoretically and experimentally investigate the mutual collapse dynamics of two spatially separated optical beams in a Kerr medium. Depending on the initial power, beam separation, and the relative phase, we observe repulsion or attraction, which in the latter case reveals a sharp transition to a single collapsing beam. This transition to fusion of the beams is accompanied by an increase in the collapse distance, indicating the effect of the nonlinear coupling on the individual collapse dynamics. Our results shed light on the basic nonlinear interaction between self-focused beams and provide a mechanism to control the collapse dynamics of such beams.

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schrödinger Hamiltonian $H=-\Delta +V$ with a potential $V\left(x\right)$ converging to different limits $V_{\ell }$ and $V_r$ as $x\to -\infty$ and $+\infty$, respectively. Due to the anisotropy, they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V\left(x\right)$ vanishes as $\mid x\mid \to \infty$ $(V_{\ell }=V_r)$. We show that it remains true in the anisotropic case $V_{\ell }\ne V_r$, i.e., we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally, we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression, which is commonly used for time delay in the literature.

Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of four-qubit entangled pure states. Apart from the expected degenerate classes, we show that there exist eight inequivalent ways to entangle four qubits. In this respect, permutation symmetry is taken into account and states with a structure differing only by parameters inside a continuous set are considered to belong to the same class.

We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)] for two such measurements can in fact be tight for up to $\sqrt{d}$ measurements in mutually unbiased bases. We then show that using more mutually unbiased bases does not always lead to a better locking effect. We prove that the optimal bound for the accessible information using up to $\sqrt{d}$ specific mutually unbiased bases is $\log d∕2$, which is the same as can be achieved by using only two bases. Our result indicates that merely using mutually unbiased bases is not sufficient to achieve a strong locking effect and we need to look for additional properties.

We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located in the Dicke limit. Although our proposal is general to any system of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV) centers in diamond as an experimental context for our theoretical results.

We generalize an already proposed protocol for quantum state transfer to spin chains of arbitrary spin. An arbitrary unknown $d$-level state is transferred through a chain with rather good fidelity by the natural dynamics of the chain. We compare the performance of this protocol for various values of $d$. A by-product of our study is a much simpler method for picking up the state at the destination as compared with the one proposed previously. We also discuss entanglement distribution through such chains and show that the quality of entanglement transition increases with the number of levels $d$.

It is known that any positive-energy state of a free Dirac particle that is initially highly localized evolves in time by spreading at speeds close to the speed of light. As recently indicated by Strauch, this general phenomenon, and the resulting “two-horned” distributions of position probability along any axis through the point of initial localization, can be interpreted in terms of a quantum random walk, in which the roles of “coin” and “walker” are naturally associated with the spin and translational degrees of freedom in a discretized version of Dirac’s equation. We investigate the relationship between these two evolutions analytically and show how the evolved probability density on the $x$ axis for the Dirac particle at any time $t$ can be obtained from the asymptotic form of the probability distribution for the position of a “quantum walker.” The case of a highly localized initial state is discussed as an example.

Recently, we have shown that for conditions under which the so-called light-shift imbalance induced blockade occurs, the collective excitation of an ensemble of a multilevel atom can be treated as a closed two-level system. In this paper, we describe how such a system can be used as a quantum bit (qubit) for quantum communication and quantum computing. Specifically, we show how to realize a controlled-NOT gate using the collective qubit and an easily accessible ring cavity, via an extension of the so-called Pellizzari scheme. We also describe how multiple, small-scale quantum computers realized using these qubits can be linked effectively for implementing a quantum internet. We describe the details of the energy levels and transitions in an ${}^{87}\mathrm{Rb}$ atom that could be used for implementing these schemes.

The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value $Z\approx 170$, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.

We propose a model for description of the process of nuclear excitation by electron transition (NEET) near the $K$-shell ionization threshold of an atom. We explain the experimental results for the ${}^{197}\mathrm{Au}$ excitation cross-section ${\sigma }_N$-obtained by Kishimoto et al. [Phys. Rev. C 74, 031301(R) (2006)], using synchrotron radiation near the Au $K$ edge. We predict the behavior of ${\sigma }_N$-as a function of the incident photon energy for the nuclei ${}^{193}\mathrm{Ir}$ and ${}^{189}\mathrm{Os}$. We reveal that ${}^{189}\mathrm{Os}$ excitation begins when the energy of incident photons is below the $K$-shell ionization threshold in Os.

A fully relativistic restricted active space configuration interaction method is employed to compute the $P,T$-odd interaction constant $W_s$ for the ground $\left({}^2\Sigma _{1∕2}\right)$ state of $\mathrm{YbF}$ and $\mathrm{BaF}$ molecules, which yield the results $W_s=-41.2\mathrm{kHz}$ and $-9.7\mathrm{kHz}$ for $\mathrm{YbF}$ and $\mathrm{BaF}$, respectively. Our present estimated results of the $P,T$-odd interaction constant $W_s$ is in reasonable agreement with previous calculations.

We report three types of nonplanar conformations, $\alpha$, $\beta$, and $\gamma$, for a neutral isolated oligoaniline molecule as well as for an oligoaniline with Au and Pd atoms attached at its ends. Each type of conformation has several conformers of nearly equal energies. An applied external voltage can be used to switch between conformations, producing in the process a sharp decrease of their energies. These bias voltage-induced conformational changes are a potential switching mechanism for two terminal molecular devices at the nanoscale domain. They cause the conductivity of the molecule to alternate between high and low states, compensating for the behavior of typical three-terminal devices, needed for the development of a gate-less electronics.

We have measured differential double capture cross sections for 15 to $150\mathrm{keV}$ $p+\mathrm{He}$ collisions. We also analyzed differential double to single capture ratios, where we find pronounced peak structures. An explanation of these structures probably requires a quantum-mechanical description of elastic scattering between the projectile and the target nucleus. Strong final-state correlations have a large effect on the magnitude of the double capture cross sections.

We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.

We develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.