We consider the energy shift for an atom close to a nonmagnetic body with a magnetic moment coupled to a quantized magnetic field. The corresponding repulsive Casimir-Polder force is obtained for a perfect conductor, a metal, a dielectric medium, with dielectric properties modeled by a Drude formula, and a superconductor at zero temperature. The dielectric properties of the superconductor are obtained by making use of the Mattis-Bardeen linear-response theory and we present some useful expressions for the low-frequency conductivity. The quantum dynamics with a given initial state is discussed in terms of the well-known Weisskopf-Wigner theory and is compared with corresponding results for a electric-dipole coupling. The results obtained are compatible with a conventional master-equation approach. In order to illustrate the dependence on geometry and material properties, numerical results are presented for the ground state using a two-level approximation.

We present a numerical study of the ultrafast ionization dynamics of $\text{H}_2{}^{+}$ exposed to attosecond extreme ultraviolet (xuv) pulses that goes beyond the Born-Openheimer approximation. The four-dimensional, time-dependent Schrödinger equation was solved using a generalization of the finite-element discrete-variable-representation/real-space–product technique used in our previous calculations to include the dynamical motion of the nuclei. This has enabled us to expose the target to any polarized light at arbitrary angles with respect to the molecular axis. Calculations have been performed at different angles and photon energies ($\hslash \omega =50\text{eV}$ up to 630 eV) to investigate the energy and orientation dependence of the photoionization probability. A strong orientation dependence of the photoionization probability of $\text{H}_2{}^{+}$ was found at a photon energy of $\hslash \omega =50\text{eV}$. At this energy, we found that the ionization probability is three times larger in the perpendicular polarization than in the parallel case. These observations are explained by the different geometric “cross sections” seen by the photoejected electron as it leaves the molecule. This ionization anisotropy vanishes at the higher-photon energy of $\hslash \omega \ge 170\text{eV}$. When these higher-energy xuv pulses are polarized perpendicular to the internuclear axis, a “double-slit-like” interference pattern is observed. However, we find that the diffraction angle only approaches the classical formula ${\varphi }_n={\text{sin}}^{-1}\left(n{\lambda }_{\text{e}}/R_0\right)$, where $n$ is the diffraction order, ${\lambda }_{\text{e}}$ is the released electron wavelength, and $R_0$ is the internuclear distance, when $n{\lambda }_{\text{e}}$ becomes less than 65% of $R_0$. These results illustrate the possibility of employing attosecond pulses to perform photoelectron microscopy of molecules.

This paper examines the problem of molecule production in an atomic fermionic gas close to an $s$-wave Feshbach resonance by means of a magnetic field sweep through the resonance. In the solvable case of a narrow resonance, the density of molecules at the end of the process is derived for a slow sweep. It is shown that the density of the produced molecules is lower than what an application of a naive Landau-Zener formula for level crossing would imply. However, in the limit of a very slow sweep it is still possible to achieve full conversion of fermions into the molecules. It appears that the origin of the failure of the Landau-Zener picture of the molecule production is due to the fact that the sweep goes through a quantum phase transition in the limit of an infinitely narrow resonance, in agreement with general results recently discussed in the literature. However, the precise connection of this problem to other problems with this feature is not established.

We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasiparticle states of a gas of strongly interacting ultracold atoms. This technique is inspired by angle-resolved photoemission spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to rf spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.

We give a rigorous semianalytical definition of impedance for square and triangular (hexagonal) lattice two-dimensional photonic crystals (PCs). Our impedance is a small matrix, derived from transfer matrices, which stores the information required to calculate the reflection and the transmission between PCs. We apply our definition to design PC antireflection coatings efficiently. This task is $O\left(n\right)$ with the number of candidate PCs as only one simulation per PC is required to find the impedances; the reflection and the transmission properties of a large number of coatings may then be evaluated quickly using the impedances in a simple matrix equation, in a way similar to the design of thin-film coatings. This is much faster than directly finding the reflections and the transmissions between pairs of candidate PCs, which requires one simulation per pair, a task that is $O\left(n^2\right)$.

We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.

We investigate how two spatially separated qubits coupled to a common heat bath can be entangled by purely dissipative dynamics. We identify a dynamical time scale associated with the lifetime of the dissipatively generated entanglement and show that it can be much longer than either the typical single-qubit decoherence time or the time scale on which a direct exchange interaction can entangle the qubits. We give an approximate analytical expression for the long-time evolution of the qubit concurrence and propose an ion trap scheme in which such dynamics should be observable.

We outline an interferometric scheme for the detection of bimode and multimode spatial entanglement of finite-temperature interacting Bose gases. Whether entanglement is present in the gas depends on the existence of the single-particle reduced density matrix between different regions of space. We apply the scheme to the problem of a harmonically trapped repulsive boson pair and show that while entanglement is rapidly decreasing with temperature, a significant amount remains for all interaction strengths at zero temperature. Thus, by tuning the interaction parameter, the distribution of entanglement between many spatial modes can be modified.

We have shown by using the exact solutions for the two-electron system in a parabolic confinement and a homogeneous magnetic field [M. Taut, J. Phys. A 27, 1045 (1994); J. Phys. A 27, 4723 (1994)] that both exact densities (charge and the paramagnetic current density) can be noninteracting $\mathcal{V}$-representable (NIVR) only in a few special cases, or equivalently, that an exact Kohn-Sham (KS) system does not always exist. All those states at nonzero $B$ can be NIVR, which are continuously connected to the singlet or triplet ground states at $B=0$. In more detail, for singlets (total orbital angular momentum $M_L$ is even) both densities can be NIVR if the vorticity $\mathbf{\gamma }\left(\mathbf{r}\right)=\mathbf{\nabla }\times \left[{\mathbf{j}}^p\left(\mathbf{r}\right)/n\left(\mathbf{r}\right)\right]$ of the exact solution vanishes. For $M_L=0$ this is trivially guaranteed because the paramagnetic current density vanishes. The vorticity based on the exact solutions for the higher $\left|M_L\right|$ does not vanish, in particular for small $r$. In the limit $r\to 0$ this can even be shown analytically. For triplets ($M_L$ is odd) and if we assume circular symmetry for the KS system (the same symmetry as the real system) then only the exact states with $\left|M_L\right|=1$ can be NIVR with KS states having angular momenta $m_1=0$ and $\left|m_2\right|=1$. Without specification of the symmetry of the KS system the condition for NIVR is that the small $r$ exponents of the KS states are 0 and 1.

We report the combination of the Amsterdam density-functional relativistic quantum-chemistry program and electron-momentum spectroscopy to interpret electronic structures of molecules. We calculate momentum profiles of molecular orbital using the two-component relativistic theory. The momentum profiles of the complete valence shell orbitals of ${\text{I}}_2$ and ${\text{Au}}_2$ molecules are obtained in comparison between the nonrelativistic and relativistic calculations. The theoretical results show that relativistic effects have significant influences on the momentum distributions for valence orbitals of ${\text{I}}_2$ and ${\text{Au}}_2$. In order to verify the validity of the calculations, the high-resolution experimental momentum distributions of the $5P_{3/2}$ and $5P_{1/2}$ states of xenon are presented in comparison with relativistic quantum-chemistry theories.

We present a detailed formulation of the relativistic convergent close-coupling (RCCC) method which is based on the solution of the Dirac equation describing electron scattering from quasi-one-electron atoms. A square-integrable Dirac $L$ spinor basis has been used to obtain a set of target states representing both the bound and continuum spectra of the target. A set of momentum-space coupled Lippmann-Schwinger equations for the $T$ matrix is then formulated and solved. We use spin asymmetries, particularly those that are identically zero in a nonrelativistic formulation, to check the accuracy of the RCCC method and find good agreement with experiment on a broad energy range.

We present an efficient algorithm for generating unitary maps on a $d$-dimensional Hilbert space from a time-dependent Hamiltonian through a combination of stochastic searches and geometric construction. The protocol is based on the eigendecomposition of the map. A unitary matrix can be implemented by sequentially mapping each eigenvector to a fiducial state, imprinting the eigenphase on that state, and mapping it back to the eigenvector. This requires the design of only $d$ state-to-state maps generated by control wave forms that are efficiently found by a gradient search with computational resources that scale polynomially in $d$. In contrast, the complexity of a stochastic search for a single wave form that simultaneously acts as desired on all eigenvectors scales exponentially in $d$. We extend this construction to design maps on an $n$-dimensional subspace of the Hilbert space using only $n$ stochastic searches. Additionally, we show how these techniques can be used to control atomic spins in the ground-electronic hyperfine manifold of alkali metal atoms in order to implement general qudit logic gates as well to perform a simple form of error correction on an embedded qubit.

We investigate the time dynamics of a four-level rubidium atomic system excited by a train of $0\pi$ pulses. Resonant $0\pi$ pulse shaping is achieved by propagation of weak femtosecond pulses through rubidium vapor and characterized using frequency-resolved optical gating and within the linear dispersion theory. The excitation of the Rb atoms by $0\pi$ pulse train is studied experimentally by modified direct frequency comb spectroscopy and theoretically within the density-matrix approach. We show that accumulation of populations and coherences, as typical pulse train excitation effects, strongly depend on the strength of the resonant $0\pi$ pulse shaping. Stronger pulse shaping reduces the coherent accumulation effects, eventually leading to the disappearance of the velocity selective optical pumping observed in the frequency domain.

We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of $n_f=3∕4$ with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of ${}^{87}\mathrm{Rb}{}^{40}\mathrm{K}$ and ${}^{23}\mathrm{Na}{}^6\mathrm{Li}$, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.

The temporal evolution of parametrically created collective excitations is studied in an ultracold two-component atomic Fermi gas. We consider quasi-one-dimensional geometry with a permanent modulation of the transverse trap frequency leading to the generation of longitudinal modes for both density and spin branches. After involvement of the interaction between excitations, the evolution comes to the formation of the stationary state with macroscopic filling of a single density or spin mode and zero occupancy for other modes located within the parametric energy interval. In the presence of this state correlation properties of fermions change essentially. Analysis of one-particle density matrix and density-density correlators reveals possibilities for experimental study of density and spin branches.

Open dielectric resonators of different shapes are widely used for the manufacture of microlasers. A precise determination of their resonance frequencies and widths is crucial for their design. Most microlasers have a flat cylindrical geometry, and a two-dimensional approximation, the so-called method of the effective index of refraction, is commonly employed for numerical calculations. Our aim has been an experimental test of the precision and applicability of a model based on this approximation. We performed very thorough and accurate measurements of the resonance frequencies and widths of two passive circular dielectric microwave resonators and found significant deviations from the model predictions. From this we conclude that the model generally fails in the quantitative description of three-dimensional dielectric resonators.

Well-resolved and long-lived atomic Bloch oscillations provide straightforward access to intriguing yet fascinating self-similar patterns. These could be observed in the quasienergy spectra of ultracold atomic wave packets subject to gravity in a driven optical lattice potential. As for the Hofstadter butterflylike energy spectra of crystal electrons in a uniform magnetic field, these atomic quasienergy spectra are shown to originate from commensurability between the Bloch oscillations period and the lattice driving period.