The variational method in Hylleraas coordinates is applied to calculate the 1$s^2$2$s_0$, 1$s^2$2$p_{-1}$, and 1$s^2$3$d_{-2}$ states of the lithium atom in magnetic fields with field strength up to $2\times {10}^9$ G. The computational method is based on multiple basis sets that are optimized for all nonlinear parameters for a given field strength. The oscillator strengths are also investigated for some transitions in magnetic fields.

We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect of quantum electrodynamics. This allows us to resolve several long-standing controversies regarding the question of universality of the Casimir self-energy; the resolution comes naturally through the connection to the Weyl problem. Specifically we demonstrate that in the case of a scalar field obeying Dirichlet or Neumann boundary conditions on the shell surface the Casimir self-energy is cutoff dependent while in the case of the electromagnetic field perturbed by a conductive shell the Casimir self-energy is universal. We additionally show that an analog nonrelativistic Casimir effect due to zero-point magnons takes place when a nonmagnetic spherical shell is inserted inside a bulk ferromagnet.

We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali-metal atoms, namely, Na${}^{+}$, K${}^{+}$, Rb${}^{+}$, Cs${}^{+}$, and Fr${}^{+}$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virtual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.

In this paper the double ionization of helium by high-energy electron impact is studied. The corresponding four-body Schrödinger equation is transformed into a set of driven equations containing successive orders in the projectile-target interaction. The transition amplitude obtained from the asymptotic limit of the first-order solution is shown to be equivalent to the familiar first Born approximation. The first-order driven equation is solved within a generalized Sturmian approach for an $S$-wave $(e,3e)$ model process with high incident energy and small momentum transfer corresponding to published measurements. Two independent numerical implementations, one using spherical and the other hyperspherical coordinates, yield mutual agreement. From our ab initio solution, the transition amplitude is extracted, and single differential cross sections are calculated and could be taken as benchmark values to test other numerical methods in a previously unexplored energy domain.

We consider positron scattering on the alkali-metal atoms of Li, Na, and K at very low energies, where only the elastic scattering and positronium formation in the ground state are the two open channels. Utilizing the recently developed two-center convergent close-coupling method [Lugovskoy, Kadyrov, Bray, and Stelbovics, Phys. Rev. A 82, 062708 (2010)] we investigate the behavior of the cross sections as the impact energy goes to zero and demonstrate their convergence. The study sets quantitative benchmarks for any rigorous theoretical treatment of the collision problems.

The nonradiative charge-transfer processes for the Be${}^{3+}$(1$s$)+H(1$s$) collisions are investigated by the quantum-mechanical molecular orbital close-coupling method in the energy range of 0.01–10 keV/u. The radiative charge-transfer cross sections are calculated by the optical potential and semiclassical methods in the energy range 10${}^{-6}$–10${}^3$ eV/u. The needed molecular data are obtained by the ab initio multireference single- and double-excitation configuration interaction method. Total and state-selective cross sections are presented and compared with other available theoretical data. Our calculation agrees well with the atomic orbital close-coupling results of Liu et al. [L. Liu, D. Jakimovski, J. G. Wang, and R. K. Janev, J. Phys. B 43, 144005 (2010)], but there exist some discrepancies with the semiclassical molecular orbital close-coupling results of Shimakura [N. Shimakura, J. Phys. B 21, 2485 (1988)]. The present results show that the capture to Si${}^{2+}$(1$s$3$l$) states is dominant in the whole energy range with the exception of a narrow range of 2–4 keV/u. Rotational couplings play an important role not only in the state-selective cross sections, but also in the total charge-transfer results. At energies below 40 eV/u, the radiative charge transfer exceeds the nonradiative process.

We explore the escape geometry of four electrons a few eV above threshold following single-photon absorption from the ground state of Be. We find that the four electrons leave the atom on the vertices of a triangular pyramid instead of a previously predicted regular tetrahedron. To illustrate the physical mechanisms of quadruple ionization we use a momentum transferring attosecond collision scheme which we show to be in accord with the triangular pyramid breakup pattern.

We investigate normal-state properties of spin-orbit-coupled Fermi gases with repulsive $s$-wave interaction, in the absence of molecule formation, i.e., in the so-called “upper branch.” Within the framework of random-phase approximation, we derive analytical expressions for the quasiparticle lifetime ${\tau }_s$, the effective mass $m_s^{*}$, and the Green's function renormalization factor $Z_s$ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit-coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index $s$ and occur in the first order of the spin-orbit-coupling strength. We also calculate experimental observables such as spectral weight, density of state, and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi-liquid parameters would have immediate applications to the spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum.

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong-coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{\left(2\right)}\left(0\right)\approx 2p/\left(n\varepsilon \right)$ in the quantum critical regime, the TLL phase, and the quasiclassical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon =\frac{{\hslash }^2}{2m}{c}^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.

We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multichromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strongly interacting bosons to weakly interacting fermions and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study nonequilibrium expansion dynamics of initially trapped bosons and demonstrate that the extent of partial localization is determined by the single-particle spectrum.

The propagation of a wave packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schrödinger equation (Gross-Pitaevskii equation). This problem is directly connected to experiments on expanding Bose gases and to studies of transverse localization in nonlinear optical media. In a nonlinear medium, the energy of the wave packet is stored both in the kinetic and potential parts, and details of its propagation are to a large extent determined by the transfer from one form of energy to the other. A theory describing the evolution of the wave packet has been formulated [Schwiete and Finkel'stein, Phys. Rev. Lett. 104, 103904 (2010)] in terms of a nonlinear kinetic equation. In this paper, we present details of the derivation of the kinetic equation and of its analysis. As an important new ingredient, we study interparticle collisions induced by the nonlinearity and derive the corresponding collision integral. We restrict ourselves to the weakly nonlinear limit, for which disorder scattering is the dominant scattering mechanism. We find that in the special case of a white-noise impurity potential, the mean-squared radius in a two-dimensional system scales linearly with $t$. This result has previously been obtained in the collisionless limit, but it also holds in the presence of collisions. Finally, we indicate different mechanisms through which the nonlinearity may influence localization of the expanding wave packet.

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we model and investigate the effects of a local, two-state, quantum degree of freedom, called a pseudospin, on a one-dimensional tight-binding lattice with position-dependent tunneling amplitudes and a single pair of non-Hermitian, $\mathcal{PT}$-symmetric impurities. We show that if the resulting Hamiltonian is invariant under exchange of two pseudospin labels, the system can be decomposed into two uncoupled systems with tunable threshold for $\mathcal{PT}$ symmetry breaking. We discuss implications of our results to systems with specific tunneling profiles, and open or periodic boundary conditions.

An analytic expression for the tunneling ionization rate of hydrogen atom in a static electric field after taking into account higher-order perturbation of the external field is derived. The formula shows a suppression effect on the ionization rate compared with the conventional tunneling formula and well agrees with the result of numerical solution of time-dependent Schrödinger equation. Our analysis shows that the suppression effect can be attributed to the polarization of the initial wave function induced by the external electric field.

We have demonstrated experimentally a nondegenerate polarization-entangled photon-pair distribution in a commercial telecom dense wave-division multiplexing device (DWDM) with eight channels. A promising point of this experiment is that an entangled photon pair is obtained via spontaneous parametric down conversion in a single type-II periodically poled KTiOPO${}_4$ crystal without postselection. Another promising advantage is that we can actively switch the distribution of the photon pair between different channel pairs in DWDM at will. There is no crosstalk between different channel pairs because of a limited emission bandwidth of the source. Maximum raw visibility of $97.88\%\pm 0.86\%$ obtained in a Bell-type interference experiment and a Clauser-Horne-Shimony-Holt (CHSH) inequality $S$ parameter of $2.63\pm 0.08$ calculated prove high entanglement of our source. Our work is helpful for building quantum communication networks.

An electromagnetic pair-creation cascade seeded by an electron or a photon in an intense plane wave interacts in a complicated way with the external field. Many simulations neglect the vector nature of photons by including their interaction using unpolarized cross sections. After deriving rates for the tree-level processes of nonlinear Compton scattering and pair creation with an arbitrary linearly polarized photon in a constant crossed field, we present results of numerical simulations that include the photon's vector nature. The simulations of seed electrons in a rotating electric field of optical frequency on the one hand support the approximation of using unpolarized cross sections for tree-level processes, which predicts the same number of created particles when using polarized cross section to within around $5\%$. On the other hand, these simulations show that when the polarization of the photon can be influenced by its environment, the asymmetry in the polarization distribution could be used to significantly increase the rates of each process.

Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. The appropriate configuration, such as a $\mathcal{PT}$-symmetric distribution, can lead to a full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagrams of semi-infinite non-Hermitian systems. They consist of finite non-Hermitian clusters and semi-infinite leads. Based on the analysis of the solutions of the concrete systems, it is shown that they can have full real spectra without any requirements on the symmetry, and the wave function within the leads becomes unidirectional plane waves at the exceptional point. This universal dynamical behavior is demonstrated as the persistent emission and reflectionless absorption of wave packets in typical non-Hermitian systems containing complex on-site potentials and non-Hermitian hopping amplitudes.

We study the possibility of taking bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment to nonclassical stationary states by feedback loops based on weak measurements and conditioned linear driving. We derive general analytical upper bounds for the single-mode squeezing and multimode entanglement at steady state, depending only on the Hamiltonian parameters and on the number of thermal excitations of the bath. Our findings show that, rather surprisingly, larger number of thermal excitations in the bath allow for larger steady-state squeezing and entanglement if the efficiency of the optimal continuous measurements conditioning the feedback loop is high enough. We also consider the performance of feedback strategies based on homodyne detection and show that, at variance with the optimal measurements, it degrades with increasing temperature.

Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is so that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate-adaptive information reconciliation protocol, which adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive information reconciliation protocol. The length of the exchanged messages is larger than that of an optimal protocol; however, we prove that the min-entropy reduction is limited. The simulation results, both in the asymptotic and in the finite-length regime, show that this protocol allows to increase the amount of a distillable secret key.

The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking at the averaged partial entropies of various bipartite partitions of the system, namely, the so-called Manhattan distance ($l_1$ norm) of averaged partial entropies (MAPE), and it is proved to be an entanglement measure for pure states. We connected the MAPE with the coefficient matrices, which are important tools in entanglement classification and reexpressed the MAPE for arbitrary-dimensional multipartite pure states by the nonzero singular values of the coefficient matrices. The entanglement properties of the $n$-qubit Dicke states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and $D_3^n$ states are investigated in terms of the MAPE, and the relation between the rank of the coefficient matrix and the degree of entanglement is demonstrated for symmetric states by two examples.