The speedup provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speedup are not yet completely understood and deserve further attention. In this context, the classical simulation of quantum algorithms is a useful tool that can help us in gaining insight. Starting from the study of general conditions for classical simulation, we highlight several important differences between two nonequivalent classes of quantum algorithms. We investigate their performance under realistic conditions by quantitatively studying their resilience with respect to static noise. This latter refers to errors affecting the initial preparation of the register used to run an algorithm. We also compare the evolution of the entanglement involved in the different computational processes.

The indirect controllability of an arbitrary finite-dimensional quantum system ($N$-dimensional qudit) through a quantum accessor is investigated. Here, the qudit is coupled to a quantum accessor, which is modeled as a fully controllable spin chain with nearest-neighbor (anisotropic) $XY$ coupling. The complete controllability of such an indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two- and three-dimensional quantum systems. For two- and three-dimensional systems, a simpler indirect control scheme is also presented.

The optimized structure and electronic properties of neutral, singly, and doubly charged strontium clusters have been investigated using ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly, and doubly charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, the gap between the highest occupied and the lowest unoccupied molecular orbitals, and spectra of the density of electronic states (DOS). It is demonstrated that the size evolution of structural and electronic properties of strontium clusters is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. It is shown that the excessive charge essentially affects the optimized geometry of strontium clusters. Ionization of small strontium clusters results in the alteration of the magic numbers. The strong dependence of the DOS spectra on details of ionic structure allows one to perform a reliable geometry identification of strontium clusters.

We introduce a set of effective Maxwell-Bloch equations for broad area semiconductor lasers, and study the long-wavelength instability of the homogeneous solution. Unlike in two-level lasers, the presence of the semiconductor $\alpha$ factor allows us to observe this pattern forming instability even in the frequency domain where the homogeneous solution emission has the lower threshold.

We study the excitation of electromagnetic surface waves in a slab of a left-handed metamaterial separating a one-dimensional periodic photonic crystal and a homogeneous dielectric medium, the so-called surface Tamm states. We show that such a layered structure can exhibit a giant lateral Goos-Hänchen shift of the scattered beam accompanied by a splitting of the reflected and transmitted beams due to the resonant excitation of surface waves at the interfaces between the left-handed metamaterial and photonic crystal. The beam shift can be either positive or negative, depending on the type of the surface Tamm states excited by the incoming beam.

Encouraged by the experiments on production of antihydrogen atoms in high Rydberg states we have calculated the effect of deexcitation towards lower states by a chirped train of identical unidirectional half-cycle pulses. The calculations exploit both the one-dimensional and impulse approximations providing convenient analytical formulas for the Rydberg-to-Rydberg transition amplitudes. The calculated deexcitation is shown in terms of the mean value of localization of the Rydberg wave packet in the coordinate space, the Rydberg-state population distribution, the Husimi phase-space distribution function, and the probability density distribution, each of these measures vs the length of the applied train of half-cycle pulses. The results for chirped trains are compared with those for periodic trains and examples of higher deexcitation efficiency of the chirped trains are given.

Laser cooling is theoretically investigated in a cascade three-level scheme, where the excited state of a laser-driven transition is coupled by a second laser to a top, more stable level, as for alkaline-earth-metal atoms. The second laser action modifies the atomic scattering cross section and produces temperatures lower than those reached by Doppler cooling on the lower transition. When multiphoton processes due to the second laser are relevant, an electromagnetic-induced transparency modifies the absorption of the first laser, and the final temperature is controlled by the second laser parameters. When the intermediate state is only virtually excited, the dynamics is dominated by the two-photon process and the final temperature is determined by the spontaneous decay rate of the top state.

We derive explicit expressions for the Wigner function of wave functions in $D$ dimensions which depend on the hyperradius—that is, of $s$ waves. They are based either on the position or the momentum representation of the $s$ wave. The corresponding Wigner function depends on three variables: the absolute value of the $D$-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary $s$ wave and the energy eigenfunction of a free particle.

We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green’s functions. Therefore, all operators describing interaction of $M$ valence electrons and $N\text{−}M$ core electrons [the core part of the Hartree-Fock Hamiltonian $V^{N\text{−}M}$, the correlation potential ${\widehat{\Sigma }}_1(\mathbf{r},{\mathbf{r}}^{\prime },E)$, and the screening of interaction between valence electrons by the core electrons ${\widehat{\Sigma }}_2$] may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^N$ potential (the mean field produced by all electrons); ${\widehat{\Sigma }}_1+{\widehat{\Sigma }}_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate ${\widehat{\Sigma }}_1$ and ${\widehat{\Sigma }}_2$ using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral $\mathrm{Xe}\mathrm{I}$ and all positive ions up to $\mathrm{Xe}\mathrm{VIII}$ as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same ${\widehat{\Sigma }}_1$ and ${\widehat{\Sigma }}_2$ to build the CI Hamiltonian in all these systems $(M=1,2,3,4,5,6,7,8)$. Good agreement with experiment for energy levels and Landé factors is demonstrated for all cases from $\mathrm{Xe}\mathrm{I}$ to $\mathrm{Xe}\mathrm{VIII}$.

Measurements of cross sections for electron-impact excitation out of the $J=0$ and $J=2$ $3p^{5}4s$ metastable levels of argon into nine of the ten levels of the $3p^{5}5p$ manifold are presented in the energy range from threshold to $10\mathrm{eV}$. A mixed target of atoms in both metastable levels was created by a hollow cathode discharge. Laser quenching was used to depopulate either one of the metastable levels, allowing separate measurements of the cross sections from each of the two metastable levels. Unlike the metastable excitation cross sections into $3p^{5}4p$ levels, the cross sections into the $3p^{5}5p$ levels are not found to be proportional to optical oscillator strengths.

The process of multiple electron ionization of Ne and Ar noble gases produced by impact of proton beams is studied in the framework of the independent-electron model. The role played by different mechanisms is analyzed, including intershell Auger and intrashell Coster-Kronig electron emission, which follow the production of vacancies due to direct interaction of the projectile with the target electrons. The present results, obtained with the continuum distorted wave–eikonal initial state (CDW-EIS) approximation, confirm previous predictions given by a different theoretical model. Semiempirical approximations are introduced by using analytical single-ionization probabilities with adjustable parameters determined from CDW-EIS total cross sections. The small computational time required to calculate multiple ionization cross sections with these semiempirical approximations and the good agreement found with existing experimental data and with results obtained with more elaborated theoretical models make them good candidates to study electron emission from complex targets.

We find that Bell’s inequality can be significantly violated (up to Tsirelson’s bound) with two-mode entangled coherent states using only homodyne measurements. This requires Kerr nonlinear interactions for local operations on the entangled coherent states. Our example is a demonstration of Bell-inequality violations using classical measurements. We conclude that entangled coherent states with coherent amplitudes as small as $0.842$ are sufficient to produce such violations.

We report the experimental realization and tomographic analysis of quantum light states obtained by exciting a classical thermal field by a single photon. Such states, although completely incoherent, possess a tunable degree of quantumness which is here exploited to put to a stringent experimental test some of the criteria proposed for the proof and the measurement of state nonclassicality. The quantum character of the states is also given in quantum information terms by evaluating the amount of entanglement that they can produce.

I consider the deterministic distinguishability of a set of orthogonal, bipartite states when only a single copy is available and the parties are restricted to local operations and classical communication, but with the additional requirement that entanglement must be preserved in the process. Several general theorems aimed at characterizing sets of states with which the parties can succeed in such a task are proven. These include (i) a maximum for the number of states when the Schmidt rank of every outcome must be at least a given minimum, (ii) an upper bound (equal to the dimension of Hilbert space if entanglement need not be preserved) for the sum over Schmidt ranks of the initial states when only one-way classical communication is allowed, and (iii) separately, a necessary and a sufficient condition on the states such that their original Schmidt ranks can always be preserved. Two additional theorems explicitly demonstrate a trade-off between the extent to which the set of states fill Hilbert space, as measured by their Schmidt ranks, and how refined the parties must make their measurements, an important factor in determining the Schmidt rank the state can retain after it has been identified. It is shown that our bound on the sum of Schmidt ranks can be exceeded if two-way communication is permitted, and this includes the case that entanglement need not be preserved, so that this sum can exceed the dimension of Hilbert space. Such questions, concerning how the various results are affected by the resources used by the parties (amount of classical communication and types of local operations), are addressed for each theorem. This subject is closely related to the problem of locally purifying an entangled state from a mixed state, which is of direct relevance to teleportation and dense coding using a mixed-state resource. In an appendix, I give an extremely simple and transparent proof of “nonlocality without entanglement,” a phenomenon originally discussed by Bennett and co-workers several years ago.

We propose a general description for the unambiguous discrimination of mixed states according to the system-environment coupling, and present a procedure to reduce this to a standard semidefinite programming problem. In the two-state case, we introduce the canonical vectors and partly simplify the problem to the case of discrimination between pairs of canonical vectors. By considering the positivity of the $2\times 2$ matrices, we obtain a series of new upper bounds for the total success probability, which depends on both the prior probabilities and specific state structures.

We study the suppression of reflections in the numerical simulation of the time-dependent Schrödinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electron-field coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantage of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.

A detailed study of the ground state of the $\mathrm{H}_3{}^{+}$ molecular ion in linear configuration, parallel to the magnetic field direction, and its low-lying $\Sigma$, $\Pi$, and $\Delta$ states is carried out for magnetic fields $B=0–4.414\times {10}^{13}\mathrm{G}$ in the Born-Oppenheimer approximation. The variational method is employed with a single trial function which includes electronic correlation in the form $\exp \left(\gamma r_{12}\right)$, where $\gamma$ is a variational parameter. It is shown that the quantum numbers of the state of the lowest total energy (ground state) depend on the magnetic field strength. The ground state evolves from the spin-singlet ${}^1\Sigma _g$ state for weak magnetic fields $B\lesssim 5\times {10}^8\mathrm{G}$ to a weakly bound spin-triplet ${}^3\Sigma _u$ state for intermediate fields and, eventually, to a spin-triplet ${}^3\Pi _u$ state for $5\times {10}^{10}\lesssim B\lesssim 4.414\times {10}^{13}\mathrm{G}$. Local stability of the linear parallel configuration with respect to possible small deviations is checked.

We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down-conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the biphoton state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the full entanglement.

We combine newly developed experimental and theoretical methods to explore and control the rotations of asymmetric top molecules. In the low-temperature limit, the revival spectra of laser-driven rotational wave packets exhibit a fascinating quantum-mechanical structure, which is qualitatively different for asymmetric tops compared to symmetric or linear tops. With increasing fluence, the structure gradually simplifies, illustrating a controllable transformation of the rotational dynamics. Our theoretical and experimental predictions are in qualitative agreement.

We explore consequences of a hypothetical difference between active charges, which generate electric fields, and passive charges, which respond to them. A confrontation with experiments using atoms, molecules, or macroscopic matter yields limits on their fractional difference at levels down to ${10}^{-21}$, which at the same time corresponds to an experimental confirmation of Newton’s third law.