The observation of the isotope effect in the high-order-harmonic generation (HHG) of H${}_2$ presents a challenge for time-dependent density-functional-theory (TDDFT) methods, since this effect is related to the dynamics of the ion created in the tunneling ionization step of HHG and it depends on the harmonic order. As an initial step toward describing this effect within current computational capacity, we benchmark a method in which the nuclear and electronic degrees of freedom are separated and both treated quantum mechanically. For the electrons two TDDFT formalisms are adopted. Although the ion-dynamics effect is not described in our method, it reproduces the measured D${}_2$-to-H${}_2$ HHG ratios up to the 25th harmonic when the 35th is the classical cutoff. Beyond the 25th harmonic, however, our results show substantial deviation and are sensitive to the laser intensity. A higher intensity reproduces the experimental results. Analysis reveals an $R$-dependent phase factor as the cause of the isotope effect in our calculation. We isolate this phase factor and propose a strong-field-approximation-phase model, which reproduces experimental data, including those for which the ion-dynamics model has to be further modified. We show that the model that we propose is intrinsically related to the ion-dynamics model. Our model provides a correction to the TDDFT approach when the ion-dynamics effect becomes significant. It also indicates that the isotope effect is not only a probe for the ion created by the external field but is ultimately a more useful probe for the ground-state nuclear wave function. For all molecules whose vertical ionization potential strongly depends on the nuclear geometry, HHG may serve as a sensitive ultrafast probe of nuclear dynamics.

Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized $W$ states do not.

The robustness properties of bipartite entanglement in systems of $N$ bosons distributed in $M$ different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with identical particles. Within this framework, expressions for the robustness and generalized robustness of entanglement can be explicitly given for large classes of boson states: Their entanglement content turns out to be, in general, much more stable than that of distinguishable particles states. Using these results, the geometrical structure of the space of $N$-boson states can be explicitly addressed.

We investigate the relationship between the information gain and the interaction strength between the quantum system and the measuring device. A strategy is proposed to calculate the information gain of the measuring device as a function of the coupling strength. For qubit systems, we prove that the information gain increases monotonically with the coupling strength. It is obtained that the information gain of the projective measurement along the $x$ direction decreases with increasing measurement strength along the $z$ direction, and a complementarity of information gain in the measurements along those two directions is presented.

We demonstrate theoretically that open-loop quantum optimal control techniques can provide efficient tools for the verification of various quantum coherent transport mechanisms in natural and artificial light-harvesting complexes under realistic experimental conditions. To assess the feasibility of possible biocontrol experiments, we introduce the main settings and derive optimally shaped and robust laser pulses that allow for the faithful preparation of specified initial states (such as localized excitation or coherent superposition, i.e., propagating and nonpropagating states) of the photosystem and probe efficiently the subsequent dynamics. With these tools, different transport pathways can be discriminated, which should facilitate the elucidation of genuine quantum dynamical features of photosystems and therefore enhance our understanding of the role that coherent processes may play in actual biological complexes.

A Coulomb density is special because it determines not only its Hamiltonian but the degree of excitation as well. We derive Euler equations for excited-state energies and densities that depend only on the electron density. Unlike existing formulations, additional functions and indices are not required; with these functionals, the equations of excited-state density functional theory strongly resemble those of ground-state theory. A critical analysis of the new functionals is included.

We describe a symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and compare it to conventional density functionals and the conventional weighted density approximation. Even the simplest two-point weighted density approximation gives results comparable to the best generalized gradient approximations. Unlike those functionals, however, the two-point weighted density approximation is fully nonlocal, has no self-interaction error, approximately fulfills the Pauli principle, and preserves the uniform electron gas limit.

We present the angular distribution of electrons knocked out from an atom in a fast charge particle collision at small momentum transfer. Not only dipole, but also quadrupole transitions determine this distribution. The contribution of these transitions can be considerably enhanced as compared to the case of photoionization. In photoionization angular distribution, the nondipole parameters are suppressed, as compared to the dipole ones, by the factor $\omega R/c\ll 1$, where $\omega$ is the photon energy, $R$ is the ionized shell radius, and $c$ is the speed of light. In fast electron-atom collisions this suppression can be considerably reduced, since the corresponding expansion parameter $\omega R/v\ll 1$ is much bigger than in photoionization, because the speed of the incoming electron $v$is much smaller than $c$. In formation of the angular distribution, it is decisively important that the ionizing field in the collision process is longitudinal, while in photoionization—it is transversal. We demonstrate that contrary to the case of cross sections, the angular anisotropy parameters for secondary electrons in fast charge particle-atom collisions and in photoionization are essentially different. We illustrate the general formulas by concrete results for outer $s$, $p$, and some $nd$ subshells of multielectron noble gas atoms Ar, Kr, and Xe, at several transferred momentum values: $q$ $=$ 0.0, 0.1, 1.1, and 2.1. Even for very small transferred momentum $q$, i.e., in the so-called optical limit, the deviations from the photoionization case are prominent.

Elastic electron scattering from gaseous methylformamide ($N$-methylformamide, C${}_2$H${}_5$NO) has been investigated. Absolute elastic differential cross sections (DCSs) were determined both experimentally and theoretically for the incident energies from 50 to 300 eV. The measurements were performed using a cross-beam technique, for scattering angles from 20° to 110°. Relative elastic DCSs were measured as a function of both the angle and the incident energy and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the SCAR (screen corrected additivity rule) procedure and using an improved quasifree absorption model. Calculated integral cross sections have been presented, as well, both for methylformamide and formamide, in the energy range 10–1000 eV, and discussed. The results are compared with and discussed regarding existing data for other small molecules representing building blocks of large biomolecules.

We analyze the control of field-free molecular orientation at high temperature by use of a two-color laser bipulse strategy proposed in Zhang et al. [Phys. Rev. A 83, 043410 (2011)]. A general study shows that there exist two types of linear molecules for which a different mechanism has to be used. For molecules with a large hyperpolarizability, a monochromatic laser pre-pulse is applied before the two-color laser pulse at a time close to the rotational period $T_r$, while for molecules with a small hyperpolarizability, the optimal delay is found close to $T_r/4$ or $3T_r/4$. We extend this analysis to the case of a ${}^2\Pi$ molecule such as NO where a similar control strategy can be derived. These control processes are robust against temperature effects.

We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternately. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of domain walls, with spatially periodic eyebrowlike spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency, and the period of the optical lattices. Under external disturbances, some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession, are observed.

Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, for example, in early universe inflation or quark-gluon plasma dynamics.

We investigate many-body effects on a mixture of interacting bosons and fermions loaded in an optical lattice using a generalized dynamical mean-field theory combined with the numerical renormalization group. We show that strong correlation effects emerge in the presence of bosonic superfluidity, leading to a renormalized peak structure near the Fermi level in the density of states for fermions. Remarkably, this kind of strong renormalization appears not only in the metallic phase but also in the insulating phases of fermions such as in the empty- and filled-band limit. A systematic analysis of the relation between the quasiparticle weight and the strength of superfluidity reveals that the renormalization effect is indeed caused by the boson degrees of freedom. It is found that such renormalization is also relevant to a supersolid phase consisting of a density-wave ordering of fermions accompanied by bosonic superfluidity. This sheds light on the origin of the peak structure in the supersolid phase.

We consider dynamics of fluctuations in transonically accelerating Bose-Einstein condensates and/or luminous fluids using the hydrodynamic approach. It is known that neglecting the quantum potential (QP) leads to a singular behavior of quantum and classical fluctuations in the vicinity of the Mach (sonic) horizon, which in turn gives rise to Hawking radiation. The neglect of the QP is well founded at not too small distances $\left|x\right|\gg l_h$ from the horizon, where $l_h$ is the healing length. Taking the QP into account, we show that a second characteristic length $l_r>l_h$ exists, such that the linear fluctuation modes become regularized for $\left|x\right|\ll l_r$. At $\left|x\right|\gg l_r$ the modes keep their singular behavior, which, however, is influenced by the QP. As a result we find a deviation of the high frequency tail of the spectrum of Hawking radiation from Planck's black-body radiation distribution, which can be described by an effective Hawking temperature decreasing with increasing frequency.

We study low-energy scattering of a neutral atom by a perfectly conducting cylindrical nanowire. Based on the exact atom-wire potential given recently by Eberlein and Zietal [Phys. Rev. A 80, 012504 (2009)] we derive tractable expressions for both the nonretarded van der Waals limit and the highly retarded limit as well as a realistic description of the transition between these two limits. For real atoms and wire radii greater than a few atomic units, the nonretarded van der Waals limit is insufficient, whereas the highly retarded limit of the atom-wire potential gives an accurate description of low-energy elastic scattering and absorption cross sections.

We present Bell tests for optical continuous-variable systems, combining both hybrid measurements (i.e., measuring both particle and wave aspects of light) and heralded amplifiers. We discuss two types of schemes, in which the amplifier is located either at the source or at the parties' laboratories. The inclusion of amplifiers helps to reduce the detrimental effect of losses in the setup. In particular, we show that the requirements for a loophole-free Bell test in terms of detection efficiency and transmission losses are significantly reduced, approaching the experimentally accessible regime.

It is generally believed that network structure has a profound impact on diverse dynamical processes taking place on networks. Tiny changes in the structure may cause completely different dynamics. In this paper, we study the impact of single extra link on the coherent dynamics modeled by continuous-time quantum walks. For this purpose, we consider the continuous-time quantum walk on the cycle with an additional link. We find that the additional link in cycle indeed causes a very different dynamical behavior compared to the dynamical behavior on the cycle. We analytically treat this problem, calculate the Laplacian spectrum, and approximate the eigenvalues and eigenstates using the Chebyshev polynomial technique and perturbation theory. It is found that the probability evolution exhibits a similar behavior like the cycle if the exciton starts far away from the two ends of the added link. We explain this phenomenon by the eigenstate of the largest eigenvalue. We prove symmetry of the long-time averaged probabilities using the exact determinant equation for the eigenvalues expressed by Chebyshev polynomials. In addition, there is a significant localization when the exciton starts at one of the two ends of the extra link; we show that the localized probability is determined by the largest eigenvalue and there is a significant lower bound for it even in the limit of infinite system. Finally, we study the problem of trapping and show the survival probability also displays significant localization for some special values of network parameters, and we determine the conditions for the emergence of such localization. All our findings suggest that the different dynamics caused by the extra link in cycle is mainly determined by the largest eigenvalue and its corresponding eigenstate. We hope the Laplacian spectral analysis in this work provides a deeper understanding for the dynamics of quantum walks on networks.

We consider an exact state swap, defined as the swap between two quantum states $|A\rangle$ and $|B\rangle$ in the Hilbert space of a quantum system. We show that given an arbitrary Hamiltonian dynamics, there is a straightforward approach to calculating the probability of the occurrence of an exact state swap by employing an exchange operator $P_{AB}$. For a given dynamics, the feasibilities of proposed quantum setups, such as quantum-state amplifications and transfers, can be evaluated. These setups are only distinguished by different forms of $P_{AB}$, which easily lead to innovative designs of quantum setups or devices. We illustrate the method with the isotropic XY model, whose unnoticed features are revealed.

The combined fine and hyperfine structure of the $2{}^{3}P$ states in ${}^3$He is calculated within the framework of nonrelativistic quantum electrodynamics. The calculation accounts for the effects of order $m{\alpha }^6$ and increases the accuracy of theoretical predictions by an order of magnitude. The results obtained are in good agreement with recent spectroscopic measurements in ${}^3$He.