A diagrammatic formalism for taking functional derivatives from the ab initio optimized effective potential, many-body perturbation theory (OEP-MBPT), exchange-correlation potentials is developed. Using this technique the frequency-independent (adiabatic approximation) kernel, corresponding to the second-order approximation OEP-MBPT(2) exchange-correlation potential is derived. The structure of the kernel is discussed and some initial numerical tests presented. The complexity of the computational procedure raises the question of what is warranted for a rigorous, ab initio approach that retains the one-particle structure of density functional theory compared to wave function approaches for excited states.

The unexpected higher intensity at low momentum region in $(e,2e)$ ionization cross sections, as called turn-up effect, was observed recently. This work systemically investigated this effect for the highest occupied molecular orbital of oxygen at various impact energies of 400, 600, 800, 1200, 1800, and $2400\mathrm{eV}$ by electron momentum spectroscopy. This turn-up became higher as the impact energy declined, which can be qualitatively predicted by the distorted wave explanation. However, it may be also due to some other dynamic interaction, such as the dynamic correlation. Since the oxygen molecule is the simplest multicenter system with such effects, this experimental result could be a test-bed for the accurate calculation of this effect in the molecular system.

A single-mode laser noise model driven by quadratic pump noise and quantum noise with cross-correlation between the real and imaginary parts of the noises is proposed. The approximate Fokker-Planck equation (AFPE) of the model for the laser phase and the laser amplitude is derived. It is found that the laser phase is controlled intensively by the correlation between the real and imaginary parts of the pump noise and that of the quantum noise. The correlation between the real and imaginary parts of quantum noise ${\lambda }_q$ tends to lead the laser phase to be locked at some values and the correlation between the real and imaginary parts of the pump noise ${\lambda }_p$ tends to destroy or confine the laser phase lock. Quantitative results are presented and discussed in detail. As an important application of the above-mentioned results, we take a phase lock approximation to get a Langevin equation for the laser field amplitude and an AFPE of the laser intensity.

We propose a simple and realizable method using a two-particle interferometer for the experimental measurement of pairwise entanglement, assuming some prior knowledge about the quantum state. The basic idea is that the properties of the density matrix can be revealed by the single- and two-particle interference patterns. The scheme can easily be implemented with polarized entangled photons.

A scheme of atom localization based on the interference of resonance of double-dark states is proposed, in which the atom interacts with a classical standing-wave field. It is found that the localization property is significantly improved due to the interaction of double-dark resonances. It is realized that the atom is localized just at the nodes of the standing-wave field with higher precision. Moreover, an improvement by a factor of 2 in the detecting probability of a single atom within the subwavelength domain can be achieved by adjusting the probe-field detuning. This scheme shows more advantages than other schemes of atom localization.

A simple scheme of population and detection of low-lying electronic quadrupole modes in free small deformed metal clusters is proposed. The scheme is analyzed in terms of the time-dependent local density approximation calculations. As a test case, the deformed cluster $\mathrm{Na}_{11}{}^{+}$ is considered. Long-living quadrupole oscillations are generated via resonant two-photon (two-dipole) excitation and then detected through the appearance of satellites in the photoelectron spectra generated by a probe pulse. Femtosecond pump and probe pulses with intensities $I=2\times {10}^{10}–2\times {10}^{11}\mathrm{W}∕{\mathrm{cm}}^2$ and pulse duration $T=200–500\mathrm{fs}$ are found to be optimal. The modes of interest are dominated by a single electron-hole pair and so their energies, being combined with the photoelectron data for hole states, allow us to gather full mean-field spectra of valence electrons near the Fermi energy. Besides, the scheme allows us to estimate the lifetime of electron-hole pairs and hence the relaxation time of electronic energy into ionic heat.

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proven very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrödinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.

In this paper we derive the evolution equation for the reduced propagator, an object that evolves vectors of the Hilbert space of a system $\mathcal{S}$ interacting with an environment $\mathcal{B}$ in a non-Markovian way. This evolution is conditioned to certain initial and final states of the environment. Once an average over these environmental states is made, reduced propagators permit the evaluation of multiple-time correlation functions of system observables. When this average is done stochastically the reduced propagator evolves according to a stochastic Schrödinger equation. In addition, it is possible to obtain the evolution equations of the multiple-time correlation functions which generalize the well-known quantum regression theorem to the non-Markovian case. Here, both methods, stochastic and evolution equations, are described by assuming a weak coupling between system and environment. Finally, we show that reduced propagators can be used to obtain a master equation with general initial conditions, and not necessarily an initial vacuum state for the environment. We illustrate the theory with several examples.

In the course of slow, nearly adiabatic motion of a system, relative changes in the slowness can cause abrupt and high magnitude phase changes, “phase avalanches,” superimposed on the ordinary geometric phases. The generality of this effect is examined for arbitrary Hamiltonians and multicomponent $(>2)$ wave packets and is found to be connected (through the Blaschke term in the theory of analytic signals) to amplitude zeros in the lower half of the complex time plane. Motion on a nonmaximal circle on the Poincaré-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes.

We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states.

We present a protocol to construct an arbitrary quantum circuit. The quantum bits (qubits) are encoded in polarization states of single photons. They are stored in spatially separated dense media deposed in an optical cavity. Specific sequences of pulses address individually the storage media to encode the qubits and to implement a universal set of gates. The proposed protocol is decoherence-free in the sense that spontaneous emission and cavity damping are avoided. We discuss a coupling scheme for experimental implementation in neon atoms.

A three-qubit ${}^{13}\mathrm{C}$ solid-state nuclear magnetic resonance (NMR) system for quantum-information processing, based on the malonic acid molecule, is used to demonstrate high-fidelity universal quantum control via strongly modulating radio-frequency pulses. This control is achieved in the strong-coupling regime, in which the time scales of selective qubit addressing and of two-qubit interactions are comparable. State evolutions under the internal Hamiltonian in this regime are significantly more complex, in general, than those of typical liquid-state NMR systems. Moreover, the transformations generated by the strongly modulating pulses are shown to be robust against the types of ensemble inhomogeneity that dominate in the employed molecular crystal system. The secondary focus of the paper is upon detailed characterization of the malonic acid system. The internal Hamiltonian of the qubits is determined through spectral simulation. A pseudopure state preparation protocol is extended to make a precise measurement of the dephasing rate of a three-quantum coherence state under residual dipolar interactions. The spectrum of intermolecular ${}^{13}\mathrm{C}–{}^{13}\mathrm{C}$ dipolar fields in the crystal is simulated, and the results compared with single-quantum dephasing data obtained using appropriate refocusing sequences. We conclude that solid-state NMR systems tailored for quantum-information processing have excellent potential for extending the investigations begun in the liquid-state systems to a greater number of qubits.

We present a direct algebraic decoupling approach to generate arbitrary single-qubit operations in the presence of a constant interaction by application of local control signals. To overcome the difficulty of undesirable entanglement generated by the untunable interaction, we use an algebraic approach to decouple the two-qubit Hamiltonian into two single-qubit Hamiltonians and the desired single-qubit operations are then generated by steering on the single-qubit operation spaces. Specifically, we derive local control fields that are designed to drive the qubit systems back to unentangled states at the end of the time interval over which the desired single-qubit operation is completed. As a result of the decoupling, optimal control strategies may be carried out on single qubit subspaces rather than on the full coupled qubit Hilbert space. This approach is seen to be particularly relevant for the physical implementation of solid-state quantum computation.

We give the time evolution solution of simultaneous amplitude and phase damping for any continuous variable state. For the simultaneous amplitude and phase damping of two-mode $x\text{−}p$ symmetric entangled Gaussian states, two analytical conditions of the separability are given. One is the sufficient condition of separability. The other is the condition of positive partial transpose (PPT) separability where the Peres-Horodecki criterion is applied. Between the two conditions there may exist bound entanglement. The simplest example is the simultaneous amplitude and phase damping of a two-mode squeezed vacuum state. The damped state is non-Gaussian.

A generalization of the static-exchange approximation for core-electron spectroscopies to the relativistic four-component realm is presented. The initial state is a Kramers restricted Hartree-Fock state and the final state is formed as the configuration-interaction single excited state, based on the average of configurations for $(n-1)$ electrons in $n$ near-degenerate core orbitals for the reference ionic state. It is demonstrated that the static-exchange Hamiltonian can be made real by considering a set of time-reversal symmetric electron excitation operators. The static-exchange Hamiltonian is constructed at a cost that parallels a single Fock matrix construction in a quaternion framework that fully exploits time-reversal and spatial symmetries for the $D_{2h}$ point group and subgroups. The $K$- and $L$-edge absorption spectra of ${\mathrm{H}}_2\mathrm{S}$ are used to illustrate the methodology. The calculations adopt the Dirac-Coulomb Hamiltonian, but the theory is open ended toward improvements in the electron-electron interaction operator. It is demonstrated that relativistic effects are substantial for the $L$-edge spectrum of sulfur, and substantial deviations from the statistical 2:1 spin-orbit splitting of the intensity distribution are found. The average ratio in the mixed region is 1.54 at the present level of theory.

We investigate two-photon double ionization of helium by intense $(\approx {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2)$ ultrashort $(\approx 300\mathrm{as})$ soft-x-ray pulses $(\mathrm{E}=91.6\mathrm{eV})$. The time-dependent two-electron Schrödinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides insight into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the “independent-electron” peaks is close to dipolar while it acquires in the “valley” of correlated emission a significant quadrupolar component within a few hundred attoseconds.

We present a time-dependent generalized pseudospectral (TDGPS) approach in hyperspherical coordinates for fully ab initio nonperturbative treatment of multiphoton dynamics of atomic systems in intense laser fields. The procedure is applied to the investigation of high-order-harmonic generation (HHG) of helium atoms in ultrashort laser pulses at a KrF wavelength of $248.6\mathrm{nm}$. The six-dimensional coupled hyperspherical-adiabatic-channel equations are discretized and solved efficiently and accurately by means of the TDGPS method. The effects of electron correlation and doubly excited states on HHG are explored in detail. A HHG peak with Fano line profile is identified which can be attributed to a broad resonance of doubly excited states. Comparison of the HHG spectra of the ab initio two-electron and the single-active-electron model calculations is also presented.

In this paper we show that a normal total number-of-particle fluctuation can be obtained consistently from the static thermodynamic relation and dynamic compressibility sum rule. In models using the broken U(1) gauge symmetry, in order to keep the consistency between statics and dynamics, it is important to identify the equilibrium state of the system with which the density response function is calculated, so that the condensate particle number $N_0$, the number of thermal depletion particles $\tilde{N}$, and the number of noncondensate particles $N_{\mathrm{NC}}$ can be unambiguously defined. We also show that the chemical potential determined from the Hugenholtz-Pines theorem should be consistent with that determined from the equilibrium equation of state. The $N^{4∕3}$ anomalous fluctuation of the number of noncondensate particles is an intrinsic feature of the broken U(1) gauge symmetry. However, this anomalous fluctuation does not imply the instability of the system. Using the random phase approximation, which preserves the U(1) gauge symmetry, such an anomalous fluctuation of the number of noncondensate particles is completely absent.

We propose an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noises. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of $5\mathrm{dB}$, with a frequency-independent squeeze angle for frequencies below $1\mathrm{kHz}$. This squeeze source is well suited for injection into a gravitational-wave interferometer, leading to improved sensitivity from reduction in the quantum noise. Furthermore, this design provides an experimental test of quantum-limited radiation pressure effects, which have not previously been tested.

Measurements are reported for production of $\mathrm{C}{\mathrm{O}}_2$ resulting from the impact of a monoenergetic $\mathrm{O}\left({}^3\mathrm{P}\right)$ beam upon a surface cooled to $4.8\mathrm{K}$ and covered with a CO ice. Using temperature-programmed desorption and mass spectrometer detection, one clearly detects increasing amounts of $\mathrm{C}{\mathrm{O}}_2$ formation with $\mathrm{O}\left({}^3\mathrm{P}\right)$ energies of 2, 5, 10, and $14\mathrm{eV}$. This is a measurement of polyatomic molecule formation on a surface in a new regime using superthermal atoms. The chosen surface coverage, surface temperature, and superthermal atom energy simulate conditions in shock-heated circumstellar and interstellar regions.