The temporal profile of the amplification gain of the neonlike manganese x-ray laser in the transient collisional excitation scheme was measured by the use of the 29th-order harmonic light at a wavelength of $26.9\mathrm{nm}$ as a probe beam. The raise-up time of the gain was delayed by $20\mathrm{ps}$ from the peak of the pumping laser pulse, and the duration of the gain was $50\mathrm{ps}$. This method is a promising powerful tool to realize the highly coherent x-ray laser beam by using a combination of an x-ray seeder and an x-ray amplifier.

For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generating rate is shown with a heralded single-photon source (HSPS) [Phys. Rev. A. 73, 032331 (2006)]. In this paper, the performance of the Scarani-Acin-Ribordy-Gisim (SARG) protocol utilizing the HSPS sources is considered and the numerical simulation turns out that still a significant improvement in secret key generating rate can also be observed. It is shown that the security distance for $\mathrm{HSPS}+\mathrm{SARG}$ is $120\mathrm{km}$. However, compared with the $\mathrm{HSPS}+\mathrm{BB}84$ protocols, the $\mathrm{HSPS}+\mathrm{SARG}$ protocol has a lower secret key rate and a shorter distance. Thus we show the $\mathrm{HSPS}+\mathrm{BB}84$ implementation is a preferable protocol for long distance transmittance.

We introduce the notion of entanglement of subspaces as a measure that quantifies the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces it is additive. Furthermore, we show that maximally entangled subspaces can play an important role in the study of quantum error-correction codes. We discuss both degenerate and nondegenerate codes and show that the subspace spanned by the logical code words of a nondegenerate code is a $k$-totally- (maximally) entangled subspace. As for non-degenerate codes, we provide a mathematical definition in terms of subspaces and, as an example, we analyze Shor’s 9-qubit code in terms of 22 mutually orthogonal subspaces.

Dephasing is a ubiquitous phenomenon that leads to the loss of coherence in quantum systems and the corruption of quantum information. We present a universal dynamical control approach to combat dephasing during all stages of quantum computation, namely, storage and single- and two-qubit operators. We show that (a) tailoring multifrequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropriate control fields; (c) counterintuitively and contrary to previous schemes, one can increase the gate duration, while simultaneously increasing the total gate fidelity.

A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding error-detection capability. Photons are assumed to be subjected to both photon loss and depolarization, and the threshold region of their strengths for scalable quantum computation is obtained, together with the amount of physical resources consumed. Compared to currently known results, the present scheme reduces the resource requirement, while yielding a comparable threshold region.

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock–common energy denominator Green’s function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Görling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term can be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as $1∕r^4$ for large $r$.

Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the $7s$, $7p$, $6d$, and $5f$ states of Fr-like ions with nuclear charges $Z=87–100$ are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for $7s\text{−}7p$, $7p\text{−}6d$, and $6d\text{−}5f$ electric-dipole transitions; and $7s\text{−}6d$, $7s\text{−}5f$, and $5f_{5∕2}\text{−}5f_{7∕2}$ multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions $Z=87–92$ calculations are also carried out using the relativistic all-order single-double method, in which single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. With the aid of the single-double wave functions, we obtain accurate values of energies, transition rates, oscillator strengths, and the lifetimes of these six ions. Ground state scalar polarizabilities in $\mathrm{Fr}\mathrm{I}$, $\mathrm{Ra}\mathrm{II}$, $\mathrm{Ac}\mathrm{III}$, and $\mathrm{Th}\mathrm{IV}$ are calculated using relativistic third-order and all-order methods. Ground state scalar polarizabilities for other Fr-like ions are calculated using a relativistic second-order method. These calculations provide a theoretical benchmark for comparison with experiment and theory.

We report electric quadrupole $\left(E2\right)$ and magnetic dipole $\left(M1\right)$ transition amplitudes of the first few low-lying states of quadruply ionized vanadium $\left({\mathrm{V}}^{4+}\right)$, which are important in various experimental applications and astrophysics. To our knowledge, most of these presented results are determined for the first time in the literature. A relativistic multireference Fock-space coupled-cluster theory with single $\left(S\right)$, double $\left(D\right)$, and partial triple $\left(T\right)$ excitations is employed to compute the forbidden transition probabilities and lifetimes of the low-lying states in ${\mathrm{V}}^{4+}$. Estimations of different correlation effects arising through the above formalism have been highlighted by investigating core and valence electron excitations. A long lifetime is found for the first excited $3d{}^{2}D_{5∕2}$ state, which suggests that ${\mathrm{V}}^{4+}$ may be one of the useful candidates for many important studies.

Accurate knowledge of the electron-impact ionization of the B atom is urgently needed in current fusion plasma experiments to help design ITER wall components. Since no atomic measurements exist, nonperturbative time-dependent close-coupling (TDCC) calculations are carried out to accurately determine the direct ionization cross sections of the outer two subshells of B. Perturbative distorted-wave and semiempirical binary encounter calculations are found to yield cross sections from 26% lower to an order of magnitude higher than the current TDCC results. Unlike almost all neutral atoms, large excitation-autoionization contributions are found for the B atom. Nonperturbative $R$ matrix with pseudostates (RMPS) calculations are also carried out to accurately determine the total ionization cross section of B. Previous 60 LS-term RMPS calculations are found to yield cross sections up to 40% higher than the current more extensive 476 LS-term RMPS results.

A method to prepare nonclassical states of the motion of a trapped ion that interacts with a traveling wave light field has been proposed, which is based on modulation of the frequency of the traveling wave field. In the end, an experiment configuration about its preparation is proposed and discussed.

A system of coupled nonlinear Schrödinger equations describes pulse propagation in weakly birefringent optical fibers. Soliton solutions of this system are found numerically through the shooting method. We employ Poincaré surface of section plots—a standard dynamical systems approach—to analyze the phase space behavior of these solutions and neighboring trajectories. Chaotic behavior around the solitons is apparent and suggests dynamical instability. A Lyapunov stability analysis confirms this result. Thus, solitons exist in the midst of chaos.

Soliton dynamics under the action of higher-order dispersion and the Raman effect is analyzed. Though we consider a wide variety of parameters, a particularly interesting phenomenon occurs when the presence of cubic and quartic dispersion results in two regions of anomalous group velocity dispersion (GVD) separated by a region of normal dispersion. In this case a sharp switching of the soliton frequency from one anomalous GVD region to the other may exist. During such a transformation, the center of the soliton spectrum passes through the normal GVD region. We show that this switching occurs due to the phase matching between the soliton and the resonance frequency in the two anomalous GVD regions.

Entanglement sudden death (ESD), the complete loss of entanglement in finite time, is demonstrated to occur in a class of bipartite states of qudit pairs of any finite dimension $d>2$, when prepared in so-called “isotropic states” and subject to multilocal dephasing noise alone. This extends previous results for qubit pairs [T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006)] to all qudit pairs with $d>2$.

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the “standard criterion” for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic theorem and the adiabatic approximation, two quite different, although closely related, ideas.

A different way to realize nonadiabatic geometric quantum computation is proposed by varying parameters in the Hamiltonian for nuclear-magnetic resonance, where the dynamical and geometric phases are implemented separately without the usual operational process. Therefore the phase accumulated in the geometric gate is a pure geometric phase for any input state. In comparison with the conventional geometric gates by rotating operations, our approach simplifies experimental implementations making them robust to certain experimental errors. In contrast to the unconventional geometric gates, our approach distinguishes the total and geometric phases and offers a wide choice of the relations between the dynamical and geometric phases.

The Dicke model describes $N$ two-level atoms interacting with a single-mode bosonic field and exhibits a second-order phase transition from the normal to the superradiant phase. The energy levels are not degenerate in the normal phase but have degeneracy in the superradiant phase, where quantum tunneling occurs. By means of the Born-Oppenheimer approximation and the instanton method in quantum field theory, the tunneling splitting, inversely proportional to the tunneling rate for the adiabatic Dicke model, in the superradiant phase can be evaluated explicitly. It is shown that the tunneling splitting vanishes as $\exp (-N)$ for large $N$, whereas for small $N$ it disappears as $\sqrt{N}∕\exp \left(N\right)$. The dependence of the tunneling splitting on the relevant parameters, especially on the atom-field coupling strength, is also discussed.

The transmission of fermions of mass $m$ and energy $E$ through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height $U>E+m{c}^2$—due to the many-body nature of the Dirac equation evidentiated by the Klein paradox—has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle—the latter circumstance being hardly escapable in most realistic cases.

Most approximation algorithms for #$\mathit{P}$-complete problems (e.g., evaluating the partition function of a monomer-dimer or ferromagnetic Ising system) work by reduction to the problem of approximate sampling from a distribution $\pi$ over a large set $\mathcal{S}$. This problem is solved using the Markov chain Monte Carlo method: a sparse, reversible Markov chain $P$ on $\mathcal{S}$ with stationary distribution $\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called mixing time of $P$, is $O\left({\delta }^{-1}\text{log}1∕{\pi }_{\ast }\right)$ as shown by Aldous, where $\delta$ is the spectral gap of $P$ and ${\pi }_{\ast }$ is the minimum value of $\pi$. A natural question is whether a speedup of this classical method to $O\left(\sqrt{{\delta }^{-1}}\text{log}1∕{\pi }_{\ast }\right)$ is possible using quantum walks. We provide evidence for this possibility using quantum walks that decohere under repeated randomized measurements. We show that (i) decoherent quantum walks always mix, just like their classical counterparts, (ii) the mixing time is a robust quantity, essentially invariant under any smooth form of decoherence, and (iii) the mixing time of the decoherent quantum walk on a periodic lattice ${\mathbb{Z}}_n^d$ is $O\left(nd\text{log}d\right)$, which is indeed $O\left(\sqrt{{\delta }^{-1}}\text{log}1∕{\pi }_{\ast }\right)$ and is asymptotically no worse than the diameter of ${\mathbb{Z}}_n^d$ (the obvious lower bound) up to at most a logarithmic factor.

We consider experimentally feasible chains of trapped ions with pseudospin $1∕2$ and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the error resistance of the system is achieved by encoding the qubits distributed over the whole system. We therefore call our system a quantum neural network and present a quantum neural network model of quantum computation. Qubits are encoded in a few quasi degenerated low-energy levels of the whole system, separated by a large gap from the excited states and large energy barriers between themselves. We investigate protocols for implementing a universal set of quantum logic gates in the system by adiabatic passage of a few low-lying energy levels of the whole system. Naturally appearing and potentially dangerous distributed noise in the system leaves the fidelity of the computation virtually unchanged, if it is not too strong. The computation is also naturally resilient to local perturbations of the spins.