High-precision Hylleraas-configuration-interaction (Hy-CI) method variational calculations are reported for the $2{}^{2}S$ ground state of neutral lithium. The nonrelativistic energy is calculated to be $-7.4780603234519\text{hartree}$, demonstrating that the Hy-CI technique is capable of sub-nanohartree accuracy for three-electron systems. A Hylleraas expansion without linked products of odd powers of $r_{ij}$ gives $-7.478060323452\text{hartree}$, showing the relative unimportance of such terms for lithium at the nanohartree level of accuracy. Hy-CI calculations are also reported for the $3{}^{2}S$, $4{}^{2}S$, $5{}^{2}S$, $6{}^{2}S$, and $7{}^{2}S$ lithium excited states.

In this paper, we report on total electron tetrahydrofuran $\left({\text{C}}_4{\text{H}}_8\text{O}\right)$ scattering cross-section measurements for energies in the range from 50 to 5000 eV with experimental errors of about 5%. In addition, integral elastic and inelastic cross sections have been calculated over a broad energy range $\left(1–10000\text{eV}\right)$, with an optical potential method assuming a screening-corrected independent atom representation. Partial and total ionization cross sections have been also obtained by combining simultaneous electron and ion measurements with a time-of-flight analysis of the ionic induced fragmentation. Finally, an average energy distribution of secondary electrons has been derived from these measurements in order to provide data for modeling electron-induced damage in biomolecular systems.

In this paper, the phase diagrams of a polar spin-1 Bose gas in a three-dimensional optical lattice with linear and quadratic Zeeman effects both at zero and finite temperatures are obtained within mean-field theory. The phase diagrams can be regrouped to two different parameter regimes depending on the magnitude of the quadratic Zeeman effect $Q$. For large $Q$, only a first-order phase transition from the nematic (NM) phase to the fully magnetic (FM) phase is found, while in the case of small $Q$, a first-order phase transition from the nematic phase to the partially magnetic (PM) phase, plus a second-order phase transition from the PM phase to the FM phase is obtained. If a net magnetization in the system exists, the first-order phase transition causes a coexistence of two phases and phase separation: for large $Q$, NM and FM phases and for small $Q$, NM and PM phases. The phase diagrams in terms of net magnetization are also obtained.

We derive a $1/c$ expansion for the single-particle density matrix of a strongly interacting time-dependent one-dimensional Bose gas, described by the Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism is derived by expanding Gaudin’s Fermi-Bose mapping operator up to $1/c$ terms. We derive an efficient numerical algorithm for calculating the density matrix for time-dependent states in the strong coupling limit, which evolve from a family of initial conditions in the absence of an external potential. We have applied the formalism to study contraction dynamics of a localized wave packet upon which a parabolic phase is imprinted initially.

We calculate the reduced single-particle density matrix (RSPDM), momentum distribution, natural orbitals and their occupancies, for a strongly repulsive one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. We assume that all particles have the same mass, and fermions are spin polarized. For mesoscopic systems, we find that the ground-state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.

We consider ultracold matter of spin-two atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian in an on-site Hilbert space taking into account spin-dependent interactions and exchange between different sites. We obtain phase diagrams and quantum phase transitions between various magnetic phases.

We show that interactions result in the emergence of a definite relative phase between two initially incoherent Bose-Einstein condensates. The many-realization interference fringe visibility is universal at $g_{12}^{\left(1\right)}\sim 1/3$ throughout the Josephson interaction regime as evident from a semiclassical picture. Other types of incoherent preparation yield qualitatively different coherence dynamics.

We have measured the evolution of the intensity emitted by a random laser during a pump pulse that is comparable in duration to the spontaneous emission decay time. The time traces of our random laser, consisting of titanium dioxide particles and sulforhodamine B dye, show clear relaxation oscillations. We compare our experimental results to an analytic, conventional model based on the four-level rate equations for a single-mode laser. The measured frequency of well-resolved fluctuation oscillations suggests an effective mode lifetime of 5 ps.

Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large. In addition, we show that the probability distributions over transition times have unusual asymmetric form in cases of unstable trajectories. We investigate in detail three types of processes related to unstable semiclassical dynamics. First, we analyze recently proposed mechanism of multidimensional tunneling where transitions proceed by formation and subsequent decay of classically unstable “states.” The second class of processes includes one-dimensional activation transitions due to energy dispersion. In this case the semiclassical transition-time distributions have universal form. Third, we investigate long-time asymptotics of transition-time distributions in the case of overbarrier wave packet transmissions. We show that behavior of these asymptotics is controlled by unstable semiclassical trajectories which linger near the barrier top.

We discuss the state tomography of a fixed qubit (a spin-1/2 target particle), which is in general in a mixed state, through one-dimensional scattering of a probe qubit off the target. Two strategies are presented by making use of different degrees of freedom of the probe, i.e. spin and momentum. Remarkably, the spatial degree of freedom of the probe can be utilized for optimizing the tomographic schemes.

Using a simple model potential, we study the effects of weak Markovian dissipation on the quantum arrival time. The interaction with the environment is incorporated into the dynamics through a Markovian master equation of Lindblad type, which allows us to compare time-of-arrival distributions and approximate crossing probabilities for different dissipation strengths and temperatures. We also establish a connection to an earlier study where quantum tunneling with dissipation was investigated, which leads us to some conclusions concerning the formulation of the continuity equation in the Lindblad theory.

We discuss how to characterize entanglement sources with finite sets of measurements. The measurements do not have to be tomographically complete and may consist of POVMs rather than von Neumann measurements. Our method yields a probability that the source generates an entangled state as well as estimates of any desired calculable entanglement measures, including their error bars. We apply two criteria, namely, Akaike's information criterion and the Bayesian information criterion, to compare and assess different models (with different numbers of parameters) describing entanglement-generating devices. We discuss differences between standard entanglement-verification methods and our present method of characterizing an entanglement source.

We consider electron capture in fast collisions between a proton and hydrogen in the presence of an intense x-ray laser whose angular frequency $\omega$ is close to $v^2/2$, where $v$ is the collision velocity. We show that in such a case laser-induced capture becomes possible and that the latter proceeds via both induced photon emission and photon absorption channels and can, in principle, compete with kinematic and radiative electron capture.

We report on the extension of the recently formulated relativistic convergent close-coupling (RCCC) method to include the Breit and Møller interactions. The inclusion of these relativistic effects ensures that the RCCC method is now capable of calculating electron scattering excitation and ionization cross sections for highly charged ions. We have calculated the polarization of the Lyman-${\alpha }_1$ x-ray line emitted by hydrogenlike ${\text{Ti}}^{21+}$, ${\text{Ar}}^{17+}$, and ${\text{Fe}}^{25+}$ ions excited by electron impact. We find that account of Breit relativistic corrections is important to resolve the discrepancy between experiment and theoretical calculations. For the much heavier hydrogenlike ${\text{U}}^{91+}$ ion where the Møller interaction becomes important we present the estimate of the polarization of the Lyman-${\alpha }_1$ x-ray line and performed a calculation of the total ionization cross section.

We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum accelerator modes can be created by exposing a Bose-Einstein condensate to a pulsed standing light wave. We show that constructive interference between momentum states populated by the pulsed light determines the stability island’s existence in the underlying pseudoclassical phase space. We generalize this interference model to incorporate higher-order accelerator modes, showing that they are generated if the rephasing occurs after multiple pulses. The model is extended to predict the momentum structure of the quantum accelerator modes close to higher-order quantum resonances. These predictions are in good agreement with our experimental observations.

We analyzed the discrepancy of the angular dependence of strong-field ionization for ${\text{CO}}_2$ among the different theoretical calculations and experiments. Using a more accurate ground-state wave function of ${\text{CO}}_2$ in the asymptotic region, we showed that the accuracy in the earlier tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)] is much improved. We also concluded that the angular dependence deduced from the experiment of Pavičić et al. [Phys. Rev. Lett. 98, 243001 (2007)] appears to be too narrowly distributed.

We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a nonsingular static surface in ordinary three-dimensional space in the presence of arbitrary configurations of time independent electric currents. Starting from the canonical action in the embedding space we show that a charged particle with charge $q$ couples to a term linear in $q{A}^{3}M$, where $A^3$ is the transverse component of the electromagnetic vector potential and $M$ is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion nonseparable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally nonseparable independently of the coupling to the geometry and the boundary constraints.

We investigate a state discrimination problem which interpolates minimum error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.

The ${}^{19}\text{F}$ spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multipulse control, the nuclear-spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analytical methods, we explore the effects of long-range intrachain couplings, cross-chain couplings, as well as couplings to a spin environment, all of which tend to damp the oscillations of the multiple quantum coherence signal at sufficiently long times. Our analysis characterizes the extent to which fluorapatite can faithfully simulate a one-dimensional quantum wire.

Freeman resonance is one of the most important phenomena in strong-field laser physics. The previous calculations to determine peak laser intensities were mainly based on solving the entire time-dependent Schrödinger equation, which requires tedious theoretical and numerical work. The newly obtained exact solutions to a driven two-level atom made accurate calculations of quasienergies and the Bloch-Siegert shifts with an arbitrary laser-beam intensity possible and practical. With the recent progress in the numerical calculations of driven two-level atom, we find a direct theoretical method, without solving the entire time-dependent Schrödinger equation, to calculate the peak laser intensities which can excite a ground-state electron to a resonant Rydberg state with shifted energy level followed by an above-threshold ionization. Due to the tranquility of the nonresonant Rydberg states, Freeman resonance fits the driven two-level atom theoretical model well. With accurate calculation of Bloch-Siegert shift as a function of laser-beam intensity, we determine the peak laser intensities from Freeman resonances of different Rydberg states. Some important features of Freeman resonances are also discussed with this method.