Relativistic Hartree-Fock and random-phase approximation methods for open shells are used to calculate ionization potentials and static scalar polarizabilities of eight superheavy elements with open $6d$ shells, which include Db, Sg, Bh, Hs, Mt, Ds, Rg, and Cn ($Z=105$ to 112). Interelectron correlations are taken into account with the use of the semiempirical polarization potential. Its parameters are chosen to fit the known ionization potentials of lighter atoms. Calculations for lighter atoms are also used to illustrate the accuracy of the approach.

We present photoelectron energy and angular distributions for resonant two-photon ionization via several low-lying Rydberg states of atomic Kr. The experiments were performed by using synchrotron radiation to pump the Rydberg states and a continuous-wave laser to probe them. Photoelectron images, recorded with both linear and circular polarized pump and probe light, were obtained in coincidence with mass-analyzed Kr ions. The photoelectron angular distributions and branching ratios for direct ionization into the $\mathrm{K}{\mathrm{r}}^{+}{}^2{P}_{3/2}$ and ${}^2{P}_{1/2}$ spin-orbit continua show considerable dependence on the intermediate level, as well as on the polarizations of the pump and probe light. Photoelectron images were also recorded with several polarization combinations following two-color excitation of the $\left({}^2{P}_{1/2}\right)5f{\left[5/2\right]}_2$ autoionizing resonance. These results are compared with the results of recent work on the corresponding autoionizing resonance in atomic Xe [E. V. Gryzlova et al., New J. Phys. 17, 043054 (2015)].

We investigate the Bose-Einstein condensation (BEC) patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with density-density interactions, characterized by a global $\mathrm{U}\left(1\right)\oplus \mathrm{U}\left(1\right)$ symmetry [one U(1) transformation for each species]. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site interspecies density-density interaction. We study the phase diagram and the critical behaviors along the transition lines of the BEC of one or both species. We present mean-field calculations and finite-size scaling analyses of quantum Monte Carlo data. We also investigate the nature of the multicritical points where the BEC transition lines of the two species meet. The corresponding universality classes are inferred from a renormalization-group analysis of the corresponding multicritical $\mathrm{U}\left(1\right)\oplus \mathrm{U}\left(1\right)$ Landau-Ginzburg-Wilson ${\mathrm{\Phi }}^4$ theory. We find two distinct critical behaviors, associated with bicritical and tetracritical points, respectively, depending on the relative strength of the interspecies and intraspecies interactions.

We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction, which exhibits two different dynamical behaviors: Josephson oscillation (phonon-Rabi oscillation) and macroscopic self-trapping (phonon blockade). Self-trapping originates from mechanical nonlinearities, meaning that when the nonlinearity exceeds its critical value, the energy exchange between the two resonators is suppressed, and phonon Josephson oscillations between them are completely blocked. An effective classical Hamiltonian for the phonon Josephson junction is derived and its mean-field dynamics is studied in phase space. Finally, we study the phonon-phonon coherence quantified by the mean fringe visibility, and show that the interaction between the two resonators may lead to the loss of coherence in the phononic junction.

We investigate the quantum dynamics of a generic model of light-matter interaction in the context of high-impedance waveguides, focusing on the behavior of the photonic states generated in the waveguide. The model treated consists simply of a two-level system coupled to a bosonic bath (the Ohmic spin-boson model). Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wave function; formally, this approach combines in a single framework ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using numerical renormalization group (NRG) calculations. NRG provides a benchmark for any linear response property throughout the ultrastrong-coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide quantum electrodynamics. Finally, the scattering results using the coherent state wave-function approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.

We present a theoretical study of the experiments on coherent population oscillations and coherent population trapping on the intercombination line of ${}^{174}\mathrm{Yb}$. The transition involves a change of the spin and thus can not be interpreted in terms of an effective lambda system. The reported experiments are done in the regime where both pump and probe fields can saturate the transition. We demonstrate, by both numerical and analytical calculations, the appearance of the interference minimum as both pump and probe start saturating the transition. We present an analytical result for the threshold probe power required for the interference minimum to appear. We also present a detailed study of the appearance of the interference minimum when magnetic fields are applied. The magnetic fields not only create Zeeman splittings, but in addition make the system open because of the couplings to other levels. We show the possibility of interference minimums at the position of subharmonic resonances.

The influence of the associated bath beyond a Born approximation (BA) is studied in a basic cavity QED system, i.e., the Rabi model coupled to a bath. It is shown that the application of a BA is valid only at zero temperature for all the baths, including the vacuum field and phonon bath associated with the two-state system, as well as the dissipative bath associated with the monochromatic optical mode. The non-BA process brings a different type of influence which stems from the inherent coupling between the quantum system and the associated bath and is against the building up of the dressed state. The physics behind this type of influence, which we term anticoherence, is analyzed, and a complete picture of influence from the associated bath is developed. To find the observed spectrum beyond a BA, we use the small-polaron theory to examine the state evolution under Fermi's golden rule, and based on it, the contribution from both the BA and non-BA processes can be calculated. The obtained result can help one to understand some peculiar observations in the strong-coupling regime.

Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven longitudinal mode of a large-area optical cavity is dispersively coupled to a deformable mechanical element. Two different models naturally appear in such scenario, for which we predict the formation of periodic patterns, localized structures (cavity solitons), and domain walls, among other complex nonlinear phenomena. Further, we propose a realistic design based on intracavity membranes where our models can be studied experimentally. Apart from its relevance to the field of nonlinear optics, the results put forward here are a necessary step towards understanding the quantum properties of optomechanical systems in the multimode regime of both the optical and the mechanical degrees of freedom.

An atomic chain coupled to a one-dimensional (1D) photonic waveguide can become a very good atom mirror. This atom mirror can have a very high reflectivity for a single-photon pulse due to the collective interaction between the atoms. Two atom arrays coupled to a 1D waveguide can form a good cavity. When a single-photon pulse is incident from one side of the cavity, only a discrete subset of photon frequencies can transmit the cavity and the transmitted frequencies are almost equally spaced, which is similar to a frequency comb. The linewidth of the comb frequency can be reduced if we increase the atom number in the atomic arrays. More interestingly, if the photon pulse is initially inside the cavity, the photon spectrum after a long time of interaction is also discretized with the comb frequencies being significantly amplified while other frequencies being largely suppressed. This single-photon frequency comb may be useful for precision measurement.

We investigate the high-order-harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schrödinger equations (TDSEs) are solved numerically by using $B$-spline basis sets in coordinate space. The energy-band structure and wave vectors can be directly retrieved from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$-space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly with the field strength. We also study HHG driven by intense few-cycle laser pulses and find that the cutoff energy of the harmonic spectrum is sensitive to the changes of the carrier envelope phase.

We propose a scheme to generate macroscopic Schrödinger-cat states in a quantum harmonic oscillator (electromagnetic field or mechanical resonator) coupled to a quantum bit (two-level system) via a conditional displacement mechanism. By driving the qubit monochromatically, the oscillation of the qubit state modifies the effective frequency of the driving force acting on the oscillator, and a resonant or near-resonant driving on the oscillator can be achieved. The displacement of the oscillator is then significantly enhanced due to the small detuning of the driving force and can exceed that of the zero-point fluctuation. This effect can be used to prepare quantum superpositions of macroscopically distinct coherent states in the oscillator. We present detailed studies on this state-generation scheme in both the closed- and open-system cases. This approach can be implemented in various experimental platforms, such as cavity- or circuit-QED systems, electromechanical systems, and spin-cantilever systems.

We propose a theoretical framework that permits us to eliminate the unphysical self-repulsion that occurs if a spatially localized charged particle interacts with its own electric field. As an example of this framework, we study the time-resolved interaction between an electronic and positronic wave packet by solving the coupled set of two-particle Dirac-Maxwell equations. The restriction of the dynamics to only one spatial dimension permits us to neglect the magnetic field and therefore any effects due to retardation are absent. Here the unwanted self-repulsion can be removed by separating the total electric field into two portions, each of which is generated by only one particle and is evolved independently of the other. For example, the Maxwell equation for the electronic field has only the electronic charge density as a source term and only this field is coupled to the positron in the two-particle Dirac equation.

Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in terms of measurable quantities. Witnesses, if properly constructed, succeed in performing this task. We derive a method that is capable to compute witnesses for identifying deterministic evolutions and measurement-induced collapse processes. At the same time, applying the Choi-Jamiołkowski isomorphism, it uncovers the entanglement characteristics of bipartite quantum states. Remarkably, a statistical mixture of unitary evolutions is mapped onto mixtures of maximally entangled states, and classical separable states originate from genuine quantum-state reduction maps. Based on our treatment, we are able to witness these opposing attributes at once and, furthermore, obtain an insight into their different geometric structures. The complementarity is further underpinned by formulating a complementary Schmidt decomposition of a state in terms of maximally entangled states and discrete Fourier-transformed Schmidt coefficients.

We derive complementarity relations for arbitrary quantum states of multiparty systems of any number of parties and dimensions between the purity of a part of the system and several correlation quantities, including entanglement and other quantum correlations as well as classical and total correlations, of that part with the remainder of the system. We subsequently use such a complementarity relation between purity and quantum mutual information in the tripartite scenario to provide a bound on the secret key rate for individual attacks on a quantum key distribution protocol.

The wavelengths and rates of electric dipole transitions between states with $n=2$ and $n=1$ of doubly excited Li-like ions have been studied for some selected ions in the range $13\le Z\le 54$ using fully relativistic multiconfiguration Dirac-Fock wave functions in the active space approximation with the inclusion of finite nuclear size, Breit interaction, self-energy, and vacuum polarization. A detailed discussion on the effects of intercomplex correlation around $Z=26$ and intracomplex correlation around $Z=37$ leading to irregularities and sharp discontinuities in the x-ray rates noticed for a few transitions has been provided. An unusually large contribution of Breit interaction has been found for intercomplex correlation in certain cases. The present results are compared with other available experimental and theoretical data. The errors associated with the transitions are highlighted for some experimentally available lines taking into account the uncertainties on the fine-structure energy levels and also on the line strengths.

Singly, doubly, and triply differential information, obtained from coincidence measurements, are presented for 250-eV positron- and electron-impact ionization of molecular nitrogen. Comparisons of these data as functions of energy loss, scattering, and emission angles illustrate differences associated with the sign of the projectile charge. Via a deconvolution and normalization procedure, the triply differential data are converted to absolute cross sections. By fitting the triply differential cross sections for single ionization with simple functions, the intensities, directions, and peak to background intensities of the binary peaks plus the ratio of recoil to binary interactions are compared for positron and electron impact. Formulas for the binary and recoil intensities plus for the orientation of the binary peak as a function of momentum transfer are extracted from the data. Differences in the relative amount of fragmentation as a function of energy loss are also observed.

We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 $XXZ$ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.

Generalizations of the classic Bell inequality to higher-dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise but such claims are based on one particular noise model. We analyze the violation of the Collins-Gisin-Linden-Massar-Popescu inequality subject to more realistic noise sources and their scaling with dimension. This analysis is inspired by potential Bell inequality experiments with superconducting resonator-based qudits. We find that the robustness of the inequality to noise generally decreases with increasing qudit dimension.

We develop an approach for controllable single-photon transport between two remote one-dimensional coupled-cavity arrays, used as quantum registers, mediated by an additional one-dimensional coupled-cavity array, acting as a quantum channel. A single two-level atom located inside one cavity of the intermediate channel is used to control the long-range coherent quantum coupling between two remote registers, thereby functioning as a quantum switch. With a time-independent perturbative treatment, we find that the leakage of quantum information can in principle be made arbitrarily small. Furthermore, our method can be extended to realize a quantum router in multiregister quantum networks, where single-photons can be either stored in one of the registers or transported to another on demand. These results are confirmed by numerical simulations.

We examine the interaction of thermal light with matter with emphasis on two aspects that have not been considered before. By employing a fully quantized Jaynes-Cummings–type interaction model on a $V$-type three-level system, we show that multimode thermal light induces coherence in the excited material states. This is in contrast to previous studies that suggest thermal light cannot induce coherence in material systems. We also show that the ratio between the field detuning and the interaction constant has a significant influence on the characteristic time-dependent dynamics. In particular, for some ratio regimes, the thermal light induces dynamics with a “coherentlike” collapse and revivals pattern rather than the familiar pattern. We then extend the Jaynes-Cummings model to a two-state Born-Oppenheimer potential energy surface molecular system where the internal vibrational degrees of freedom are fully taken into account. The matter-field bipartite system is represented, and propagated, in the full electronic bond-coordinate Fock product space. We show that single-mode thermal light induces extensive excited-state vibrational coherence in the molecule that, when observed in coordinate space, exhibits wave-packet-like dynamics. The molecular Jaynes-Cummings model we propose is useful for cavity molecular dynamics simulations.