We study theoretically forward and backward second-harmonic generation in a two-dimensional photonic crystal structure made of lithium niobate. The aim of this article is twofold: First, we propose a reliable modal algorithm for describing the light propagation taking into account the vectorial character of the interacting fields as well as the tensorial character of the nonlinearity and verify it by means of the nonlinear finite-difference time-domain method. Second, we propose a photonic crystal where we obtain a giant efficiency increase for backward second-harmonic generation with slow light.

A rigorous combination of multireference perturbation theory and density functional theory (DFT) is proposed. Based on a range separation of the regular two-electron Coulomb interaction, it combines a short-range density functional with second-order strongly contracted $n$-electron valence state perturbation theory (sc-NEVPT2). The huge advantage of the sc-NEVPT2 approach is that the density is unchanged through first order due to a generalized-Brillouin-type theorem so that the computationally cumbersome self-consistency contribution of short-range DFT to the second-order energy correction equals zero. The method yields very promising results for the van der Waals systems ${\mathrm{Be}}_2$, ${\mathrm{Mg}}_2$, and ${\mathrm{Ca}}_2$; including the multireference system ${\mathrm{Be}}_2$.

We examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.

Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss errors and computational errors, with a graceful tradeoff between the threshold for each. We further discuss a number of subtleties that arise when implementing error correction on topological memories. We particularly focus on the role played by degeneracy in the matching algorithms and present a systematic study of its effects on thresholds. We also discuss some of the implications of degeneracy for estimating phase transition temperatures in the random bond Ising model.

A rigorous quantum electrodynamical calculation is presented for energy levels of the $1\hspace{0.5em}{}^{1}S$, $2\hspace{0.5em}{}^{1}S$, $2\hspace{0.5em}{}^{3}S$, $2\hspace{0.5em}{}^1{P}_1$, and $2\hspace{0.5em}{}^3{P}_{0,1,2}$ states of helium-like ions with the nuclear charge $Z=3,\dots ,12$. The calculational approach accounts for all relativistic, quantum electrodynamical, and recoil effects up to orders $m{\alpha }^6$ and $m^2/M{\alpha }^5$, thus advancing the previously reported theory of light helium-like ions by one order in $\alpha$.

In this work, the $\mathrm{KLL}$ dielectronic recombination (DR) resonant strengths of He- through to O-like Xe ions were studied, both through experiment and calculation. The experiments were done using a fast electron beam-energy scanning technique at the Shanghai electron beam ion trap. The calculations were done by using the flexible atomic code (FAC), in which the relativistic configuration interaction (RCI) method was employed. For the total resonant strengths, the present experimental and theoretical results for He-, Be-, B-, C-, N-, and O-like Xe ions agree within experimental uncertainties (about 9%). But the experimental result for Li-like Xe is 14% higher than the calculation. The present FAC calculations of the total DR strengths were compared with the available previous calculations, using RCI or multiconfiguration Dirac-Fock (MCDF) methods, and the agreement was very good. In this work, some intermediate-state resolved $\mathrm{KLL}$ DR strengths were also obtained and compared with theoretical results, and more discrepancies were revealed.

A full four-body implementation of the propagating exterior complex scaling (PECS) method [J. Phys. B 37, L69 (2004)] is developed and applied to the electron-impact of helium in an $S$-wave model. Time-independent solutions to the Schrödinger equation are found numerically in coordinate space over a wide range of energies and used to evaluate total and differential cross sections for a complete set of three- and four-body processes with benchmark precision. With this model we demonstrate the suitability of the PECS method for the complete solution of the full electron-helium system. Here we detail the theoretical and computational development of the four-body PECS method and present results for three-body channels: single excitation and single ionization. Four-body cross sections are presented in the sequel to this article [Phys. Rev. A 81, 022716 (2010)]. The calculations reveal structure in the total and energy-differential single-ionization cross sections for excited-state targets that is due to interference from autoionization channels and is evident over a wide range of incident electron energies.

The propagating exterior complex scaling (PECS) method is extended to all four-body processes in electron impact on helium in an $S$-wave model. Total and energy-differential cross sections are presented with benchmark accuracy for double ionization, single ionization with excitation, and double excitation (to autoionizing states) for incident-electron energies from threshold to 500 eV. While the PECS three-body cross sections for this model given in the preceding article [Phys. Rev. A 81, 022715 (2010)] are in good agreement with other methods, there are considerable discrepancies for these four-body processes. With this model we demonstrate the suitability of the PECS method for the complete solution of the electron-helium system.

Coherent transients occur when a chirped pump pulse excites a two-level transition. They have been observed with an ultrashort probe pulse. Several studies have been dedicated to using various pump shapes. In this study, the roles of the pump and the probe pulses are reversed. With a Fourier-transform-limited pump pulse followed by a chirped-probe pulse, similar effects can be observed. Finally, the case of two pulses with opposite chirps is considered.

We present the transformation in the Hanle configuration of the transmission that results from coherent population trapping (CPT) into the level-crossing absorption (LCA) that results from the single-photon optical pumping in the ${}^{87}\mathrm{Rb}$ $D_1$ line of a Rb vapor cell with a Ne buffer gas when the polarization of the laser field is changed from linear to circular. The LCA spectrum, with a narrow spectral width of $2.4$ mG ($1.7$ kHz), was observed in the $F_g\to F_e⩽F_g$ transition with the circularly polarized laser. This may be because the LCA is both related to the transverse magnetic field and the atom-laser interaction time resulting from diffusive atomic motion in the cell with the buffer gas. The CPT and LCA spectra were calculated numerically using the full density matrix equations for the relevant magnetic sublevels of the hyperfine levels, considering the residual magnetic fields perpendicular to laser propagation and the collision effects resulting from the buffer gas. There was good qualitative agreement between theoretical and experimental results.

We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system being made of noninteracting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions interacting with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to that observed in the absence of BEC but with the Rabi frequencies of fermionic excited states explicitly depending on the number of bosons and on the boson-fermion interaction strength. From this, the possibility of controlling quantum fermionic dynamics by means of Feshbach resonances is suggested.

We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.

We consider a solitonic solution of the self-attractive Bose-Einstein condensate in a one-dimensional external potential of a shallow optical lattice with large periodicity when the lattice is horizontally shaken. We investigate the dynamics of the bright soliton through the properties of the fixed points. The special type of bifurcation results in a simple criterion for the stability of the fixed points depending only on the amplitude of the shaking lattice. Because of the similarity of the equations with those of an ac-driven Josephson junction, some results may find applications in other branches of physics.

Recent experiments on strongly coupled cavity quantum electrodynamics present new directions in “matter-light” systems. Following on from our previous work [Phys. Rev. Lett. 102, 135301 (2009)] we investigate Bose-Hubbard models coupled to a cavity light field. We discuss the emergence of photoexcitations or “polaritons” within the Mott phase, and obtain the complete variational phase diagram. Exploiting connections to the super-radiance transition in the Dicke model we discuss the nature of polariton condensation within this novel state. Incorporating the effects of carrier superfluidity, we identify a first-order transition between the super-radiant Mott phase and the single component atomic superfluid. The overall predictions of mean field theory are in excellent agreement with exact diagonalization and we provide details of superfluid fractions, density fluctuations, and finite size effects. We highlight connections to recent work on coupled cavity arrays.

In a recent publication [K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, Phys. Rev. Lett. 103, 063005 (2009)] we have shown the possibility to achieve strong coupling of the quantized motion of a micron-sized mechanical system to the motion of a single trapped atom. In the proposed setup the coherent coupling between a SiN membrane and a single atom is mediated by the field of a high finesse cavity and can be much larger than the relevant decoherence rates. This makes the well-developed tools of cavity quantum electrodynamics with single atoms available in the realm of cavity optomechanics. In this article we elaborate on this scheme and provide detailed derivations and technical comments. Moreover, we give numerical as well as analytical results for a number of possible applications for transfer of squeezed or Fock states from atom to membrane as well as entanglement generation, taking full account of dissipation. In the limit of strong-coupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.

We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the “colored” electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.

The dynamics of a (quasi-) one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schrödinger equation. If the static field is varied, the system shows a plethora of dynamical phenomena. In the strong field limit, we demonstrate the existence of (almost) nonspreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so-called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields, we find subdiffusive dynamics with a wave-packet width growing as $t^{1/4}$.

We investigate three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. Depending on the anisotropy of the repulsive interactions, either a color density-wave state or a color-selective staggered state appears at half filling. In the former state, pairs of atoms with two of the three colors and atoms with the third color occupy different sites alternately. In the latter state, atoms with two of the three colors occupy different sites alternately and atoms with the third color are itinerant throughout the system. When the interactions are isotropic, both states are degenerate. We discuss the results using an effective model.

This paper reports a systematic study of the dependence on atomic number of the dielectronic recombination resonance strengths for He-like, Li-like and Be-like ions. Recent measurements of dielectronic recombination resonance strengths for the KLL and KLM manifolds for iron, yttrium, iodine, holmium, and bismuth are also described. The resonance strengths were normalized to calculated electron impact ionization cross sections. The measured resonance strengths generally agree well with theoretical calculations using the distorted wave approximation. However, KLM resonance strength measurements on high atomic number open-shell ions gave higher values than those suggested by calculations. Using recently measured data, along with existing results, scaling laws have been generated as a function of atomic number for He-like, Li-like, and Be-like ions in the KLL and KLM manifolds.

A theoretical treatment of charge-transfer processes induced by collision of phosphorus ${\mathrm{P}}^{3+}(3s^2){}^{1}S$ ions on atomic hydrogen and helium has been carried out using ab initio potential-energy curves and couplings at the multireference configuration interaction level of theory. The cross sections calculated by means of semiclassical collision methods show the existence of a significant charge transfer in the $0.1-700$-keV laboratory energy range. Radial and rotational coupling interactions were analyzed for both collision systems.