Numerical solutions of the time-dependent Schrödinger equation for a three-dimensional H atom and an efficient genetic algorithm are used to optimize short intense excitation laser pulses in order to generate high-order harmonics from which we synthesize single attosecond pulses. It is shown that chirping of excitation pulses at intensities $\sim {10}^{14}\mathrm{W}∕{\text{cm}}^2$ and duration of up to $\sim 16\text{fs}$ can lead to synthesis of single attosecond pulses. The optimal excitation pulses and the phases of the generated harmonics are compared with the nonoptimized ones, showing thus the usefulness of genetic algorithm schemes in the search of optimal conditions for synthesizing single attosecond pulses.

We have derived a Lyapunov functional for a degenerate open atomic system. This functional develops monotonically towards its stationary state. The open system is described by a Lindblad-type master equation. For the construction of the variational functional it is necessary that the Lindblad operator can be diagonalized. Since the generator of motion is non-Hermitian, diagonalization is, in general, only possible if the eigenvalues are nondegenerate. In this paper, we propose that in a physical system the biorthogonal eigenbasis of the Lindblad operator remains complete even when degeneracy is present. Thus diagonalization of the Lindblad operator, and consequently the construction of the variational functional, is still possible. We discuss the reasons and illustrate the theory of the variational functional for a driven $\Lambda$-type three-level atom with degenerate ground state. The degeneracy has interesting effects on the variational functional in the steady state with respect to its interpretation as an entropic quantity. In case of the driven three-level atom, the dark state turns out to be an isentropic state.

We derive optimal cloning limits for finite Gaussian distributions of coherent states and describe techniques for achieving them. We discuss the relation of these limits to state estimation and the no-cloning limit in teleportation. A qualitatively different cloning limit is derived for a single-quadrature Gaussian quantum cloner.

A quantum circuit implementing 5-qubit quantum-error correction on a linear-nearest-neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations allowing the circuit to achieve the same depth as the current least depth circuit. Simulations of the circuit’s performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced decoherence that results in quantum information dissipating into the environment. For the inherent qubit-qubit interaction that is untunable in the quantum system, BB control plus DFSs encoding will eliminate its undesired effect which spoils quantum information in qubits. We show how this quantum system can be used to implement universal quantum computation.

We present a theory that describes the interaction of hydrogen atoms with antihydrogen at subkelvin temperatures. The formalism includes a nonlocal complex optical potential, whose imaginary component describes the breakup of the $\text{H-}\overline{\mathrm{H}}$ complex into positronium and protonium fragments. Using ab inito methods, we construct the imaginary part of the optical potential and calculate the cross sections for fragmentation in ultracold collisions of $\mathrm{H}$ and $\overline{\mathrm{H}}$. We find a $35\%$ reduction in the value of the scattering length from that obtained in the Born-Oppenheimer approximation. We estimate the lifetimes for quasibound states of this complex to fragment into a protonium-positronium pair.

We review the shift and broadening of hyperfine resonance lines of alkali-metal atoms in buffer gases. We present a simple theory both for the shift and the broadening induced by He gas. The theory is parametrized by the scattering length of slow electrons on He atoms and by the measured hyperfine intervals and binding energies of the $S$ states of alkali-metal atoms. The calculated shifts and their temperature dependence are in good agreement with the published experimental data. The calculated broadening is 1.6 times smaller than the recent measurements, and more than 20 times smaller than the earlier measurements. We attribute much of the linewidth in the earlier experiments to possible small temperature gradients and the resulting inhomogeneous line broadening from the temperature dependence of hyperfine frequency shift at constant buffer-gas pressure.

Atomic polarization can have a profound effect on the generation of the high-order harmonics during the interaction of the polarized atom with intense field. In this work, the atomic polarization effect is investigated for the specific case of the $2{}^{1}P$ helium subject to infrared radiation. The strong coupling between the $2{}^{1}P$ and $2{}^{1}S$ states of helium is taken into account using a multichannel version of the strong-field approximation of Lewenstein and co-workers [Lewenstein et al., Phys. Rev. A 49, 2117 (1994); Antoine et al., Phys. Rev. A 53, 1725 (1996)]. The analysis reveals a strong dependence of the high-order harmonic generation efficiency on the atomic polarization. While the occurrence of the predicted effect can be explained in terms of the recollision model, its magnitude is deeply affected by the fast population oscillations between the excited bound states. Moreover, the induced bound-bound transitions bring about the interesting double-maximum structure in the ellipticity dependences of the emitted harmonics, both maxima occurring for nonzero field ellipticities. This unusual structure shows up even for the high-energy harmonics generated solely by the bound-continuum mechanism.

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, which is derived from this scheme, and we investigate the temperature effects on molecular dynamics.

Classical, quantum-mechanical, and semiclassical expressions for the transition probability in one-dimensional Rydberg atom irradiated by short half-cycle pulse are derived and compared. The simple formulas obtained for excitation of Rydberg atom by two time delayed weak half-cycle pulses reproduce well the experimental data and the solutions of time-dependent Schrödinger equation. When the transferred momenta are stronger and positive, the transition probabilities exhibit fast oscillations with time delay between the pulses. The classical transition probability is constant in time. For negative transferred momenta a focusing phenomenon is observed, and there is a region in time delay, where the transition probabilities oscillate with the Kepler period.

The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve $T=0$ and all of the particles must be evaporated.

We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, when the resonance is crossed slowly the no-transition probability is directly proportional to the rate at which the resonance is crossed.

Using constrained-search approach, we obtain orbitals and the corresponding local potentials of noninteracting systems that lead to a given exact ground-state or excited-state density with a configuration of our choice. Thus on the basis of constrained-search formulation we demonstrate that all densities, irrespective of whether they belong to the ground state or an excited state, can be treated on equal footing. This has direct relevance to the time-independent excited-state density-functional theory, which makes excited-state calculations as easy as they are for the ground states. We make a comparison of the exact potentials generated by us with the approximate ones obtained using the local-density approximation and show the latter to be as good an approximation for the excited states as it is for the ground state.

For crucial tests between theory and experiment, ab initio close-coupling calculations are carried out for photoionization of several oxygen ions: O II, O III, O IV, and O V. The relativistic fine-structure and resonance effects are studied using the $R$ matrix and its relativistic variant, the Breit-Pauli $R$-matrix (BPRM) approximations. Extremely detailed comparison is made with high-resolution experimental measurements carried out in three different setups: Advanced Light Source at Berkeley, synchrotron radiation experiment with a new modulator at University of Aarhüs, and synchrotron radiation experiment at University of Paris-Sud. The comparisons illustrate physical effects in photoionization such as (i) fine structure, (ii) resolution, and (iii) metastable components. Photoionization cross sections ${\sigma }_{PI}$ of the ground and a few low-lying excited states of these ions obtained in the experimental spectrum include combined features of these states. The general features of the measured ${\sigma }_{PI}$ were predicted in the earlier calculations in $LS$ coupling. However, due to higher-resolution achievement in the recent experiments, the theoretically calculated resonances need to be resolved with much finer energy mesh for precise comparison. In addition, prominent resonant features are observed in the measured spectra that can form from transitions allowed with relativistic fine structure, but not in $LS$ coupling. Present results include calculations from both $LS$ coupling and the relativistic BPRM method to decipher the features in photoionization spectra. ${\sigma }_{PI}$ are obtained for ground and metastable (i) $2s^{2}2p^3\left({}^{4}S^o,{}^{2}D^o,{}^{2}P^o\right)$ states of O II, (ii) $2s^{2}2p^2\left({}^{3}P,{}^{1}D,{}^{1}S\right)$ and $2s2p^3\left({}^{5}S^o\right)$ states of O III, (iii) $2s^{2}2p\left({}^{2}P_J^o\right)$ and $2s2p^2\left({}^{4}P_J\right)$ levels of O IV, and (iv) $2s^2\left({}^{1}S\right)$ and $2s2p\left({}^{3}P^o,{}^{1}P^o\right)$ states of O V. Most of the computed theoretical resonance structures are seen experimentally, although there are some discrepancies. One of the main conclusions of the present study is that resonances in photoionization cross sections of the ground and metastable states can be a diagnostic of experimental beam composition, with potential applications to astrophysical and laboratory plasma environments.

In this paper, we investigate the effects of spontaneously generated coherence (SGC) on the conditions for exhibiting lasing without inversion (LWI) in the presence of a weak probe and a strong-coupling field. We find that owing to the effect of SGC, LWI can be realized without the incoherent pumping or the decay between two upper levels. However, in the region where LWI can be exhibited, the effect of SGC term on the exhibition of LWI is not always positive, sometimes it can even cumber the realization of LWI for some values of SGC. These values are given in this paper. In addition, we also analyze the essence of the generation of the probe field.

We quantify the entanglement generated between an atom and a laser pulse in free space. We find that the entanglement calculated using a simple closed-system Jaynes-Cummings Hamiltonian is in remarkable agreement with a full open-system calculation, even though the free-space geometry is far from the strong-coupling regime of cavity QED. We explain this result using a simple model in which the atom couples weakly to the laser, while coupling strongly to the vacuum. Additionally we place an upper bound on the total entanglement between the atom and all paraxial modes using a quantum trajectories unravelling. This upper bound provides a benchmark for atom-laser coupling.

Using a geometric approach, we derive the minimum number of applications needed for an arbitrary controlled-unitary gate to construct a universal quantum circuit. An analytic construction procedure is presented and shown to be either optimal or close to optimal. This result can be extended to improve the efficiency of universal quantum circuit construction from any entangling gate. In addition, for both the controlled-NOT (CNOT) and double-CNOT gates, we develop simple analytic ways to construct universal quantum circuits with three applications, which is the least possible for these gates.

The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be reached by using the conjecture that the set of states visited by a quantum algorithm can be replaced by the uniform (Haar) ensemble. These general results are tested numerically against quantum computer simulations of two particular periodically driven quantum systems.

We present a systematic analysis of how one can improve performance of probabilistic programmable quantum processors. We generalize a simple Vidal-Masanes-Cirac processor that realizes U(1) rotations on a qubit with the phase of the rotation encoded in a state of the program register. We show how the probability of success of the probabilistic processor can be enhanced by using the processor in loops. In addition we show that the same strategy can be utilized for a probabilistic implementation of nonunitary transformations on qubits. In addition, we show that an arbitrary SU(2) transformation of qubits can be encoded in program state of a universal programmable probabilistic quantum processor. The probability of success of this processor can be enhanced by a systematic correction of errors via conditional loops. Finally, we show that all our results can be generalized also for qudits. In particular, we show how to implement SU(N) rotations of qudits via programmable quantum processor and how the performance of the processor can be enhanced when it is used in loops.

We investigate analytically a star network of spins, in which all spins interact exclusively and continuously with a central spin through Heisenberg $XX$ couplings of equal strength. We find that the central spin correlates and entangles the other spins at zero temperature to a degree that depends on the total number of spins. We find that the entanglement mediating capability of the central spin depends on the evenness or oddness of this number. In the limit of an infinite collection of spins, the difference between entanglement and correlations in terms of divisibility among multiple parties is clearly demonstrated. We also show that with a significant probability one can maximally entangle any two noncentral spins by measuring all the other spins (a process related to the recently introduced notion of localizable entanglement). This probability depends on the evenness and oddness of the total number of spins and remains substantial even for an infinite collection of spins. We show how symmetric multiparty states for optimal sharing and splitting of entanglement can be obtained as ground states of this system using a magnetic field. These states can then be mapped on to flying qubits for transmission to distant parties. We discuss a number of advantages of this mode of generation and distribution of entanglement over other standard methods.