The hyperfine structure (hfs) and the $g$ factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron $g$ factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogenlike bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Accurate numerical values for the remainder functions are provided for $2P$ states and for $\mathit{nS}$ states with $n=1,2,3$.

A new narrow three-atom loss resonance associated with an Efimov trimer crossing the three-atom threshold has recently been discovered in a many-body system of ultracold ${}^6\mathrm{Li}$ atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O’Hara and coworkers have used measurements of the three-body recombination rate in this region to determine the complex three-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the spectrum of Efimov states and for the three-body recombination rate in the universal region above 600 G where all three scattering lengths are large. We predict an atom-dimer loss resonance at $672\pm 2$ G associated with an Efimov trimer disappearing through an atom-dimer threshold. We also predict an interference minimum in the three-body recombination rate at $759\pm 1$ G where the three-spin mixture may be sufficiently stable to allow experimental study of the many-body system.

By a computer simulation approach we study the scattering of $p$- or $s$-polarized light from a two-dimensional, randomly rough, perfectly conducting surface. The pair of coupled inhomogeneous integral equations for two independent tangential components of the magnetic field on the surface are converted into matrix equations by the method of moments, which are then solved by the biconjugate gradient stabilized method. The solutions are used to calculate the mean differential reflection coefficient for given angles of incidence and specified polarizations of the incident and scattered fields. The full angular distribution of the intensity of the scattered light is obtained for strongly randomly rough surfaces by a rigorous computer simulation approach.

We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. This implies that the quantum discord is more useful than the entanglement to describe the quantum correlation involved in quantum systems.

We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic “hydrogen” masses less than 1 u or a “helium” mass of $1.95$ u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ with ${\mathrm{H}}_2$, HD, HT, and DT should be feasible in the near future.

Ultracold atoms whose de Broglie wavelength is of the same order as an extended confining potential can experience waveguiding along the potential. When the transverse kinetic energy of the atoms is sufficiently low, they can be guided in the lowest order mode of the confining potential by analogy with light guided by a single mode optical fiber. We have obtained the first images of the transverse mode structure of guided matter waves in a confining potential with up to $65\%$ of atoms in the lowest order mode. The coherence of the guided atomic de Broglie waves is demonstrated by the diffraction pattern produced when incident upon a two dimensional periodic structure. Such coherent waveguides will be important atom optic components in devices with applications such as atom holography and atom interferometry.

We present a method to measure the geometric phase defined for three internal states of a photon (polarizations) using a three-pinhole interferometer. From the interferogram, we can extract the geometric phase related to the three-vertex Bargmann invariant as the area of a triangle formed by interference fringes. Unlike the conventional methods, our method does not involve the state evolution. Moreover, the phase calibration of the interferometer and the elimination of the dynamical phase are not required. The gauge invariance of the geometric phase corresponds to the fact that the area of the triangle is never changed by the local phase shift in each internal state.

The evolution of two, noninteracting, two-level atoms immersed in a weakly coupled bath can be described by a refined, time-coarse-grained Markovian evolution, still preserving complete positivity. We find that this improved, reduced dynamics is able to entangle the two atoms even when their internal frequencies are unequal, an effect that appears impossible in the standard weak-coupling-limit approach. We study in detail this phenomenon for an environment made of quantum fields.

We address estimation of one-parameter qubit gates in the presence of phase diffusion. We evaluate the ultimate quantum limits to precision, seek optimal probes and measurements, and demonstrate an optimal estimation scheme for polarization encoded optical qubits. An adaptive method to achieve optimal estimation in any working regime is also analyzed in detail and experimentally implemented.

The xenon $L$-subshell Coster-Kronig (CK) transition yields were revisited via high-resolution measurements of the $L{\alpha }_{1,2}$ ($L_3-M_{4,5}$) and $L{\beta }_1$ ($L_2-M_4$) x-ray emission lines. The $L$ x-ray spectra were measured employing a Johansson-type curved crystal spectrometer and energy-tunable synchrotron radiation. The CK yields were derived from the relative $L$ x-ray intensity jumps at the $L$ edges by fitting the fluorescence intensities as a function of the photon energy to the $L$-subshell photoionization cross sections. The latter were obtained from the measured $L$-edge photoabsorption spectrum. Values of $0.118\pm 0.029$, $0.383\pm 0.037$, and $0.096\pm 0.016$ were found for the $f_{23}$, $f_{13}$, and $f_{12}$ CK yields, respectively. Thanks to high resolution, the $L_1$ fluorescence yield of $0.059\pm 0.002$ was also determined from intensity ratios of the well-resolved $L{\beta }_4$ ($L_1-M_2$) and $L{\beta }_1$ ($L_2-M_4$) lines.

We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor $\mathit{XY}$ spin chain through control of a single site and its interaction with its neighbor. Control of an array of sites yields sufficient parallelism for the implementation of fault-tolerant circuits. The framework exposes contradictions between the control theoretic concept of controllability with the ability of a system to perform quantum computation.

Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.

We observe the interaction of a single trapped calcium ion with single photons produced by a narrow-band, resonant down-conversion source [A. Haase et al., Opt. Lett. 34, 55 (2009)], employing a quantum jump scheme. Using the temperature dependence of the down-conversion spectrum and the tunability of the narrow source, absorption of the down-conversion photons is quantitatively characterized.

For sufficiently low reservoir temperatures, it is known that open quantum systems subject to decoherent interactions with the reservoir relax toward their ground state in the weak coupling limit. Within the framework of quantum master equations, this is formalized by the Born-Markov-secular (BMS) approximation, where one obtains the system Gibbs state with the reservoir temperature as a stationary state. When the solution to some problem is encoded in the (isolated) ground state of a system Hamiltonian, decoherence can therefore be exploited for computation. The computational complexity is then given by the scaling of the relaxation time with the system size $n$. We study the relaxation behavior for local and nonlocal Hamiltonians that are coupled dissipatively with local and nonlocal operators to a bosonic bath in thermal equilibrium. We find that relaxation is generally more efficient when coherences of the density matrix in the system energy eigenbasis are taken into account. In addition, the relaxation speed strongly depends on the matrix elements of the coupling operators between initial state and ground state. We show that Dicke superradiance is a special case of our relaxation models and can thus be understood as a coherence-assisted relaxation speedup.

The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back action, the quantum state reconstruction is also valid for the postselected subensembles usually considered in weak measurement paradoxes. It is shown that postselection can then be identified with a statistical decomposition of the initial density matrix into transient density matrices conditioned by the anticipated measurement outcomes. This result indicates that it is possible to ascribe the properties determined by the final measurement outcome to each individual quantum system before the measurement has taken place. The “collapse” of the pure state wave function in a measurement can then be understood in terms of the classical “collapse” of a probability distribution as new information becomes available.

We study the transmission of both classical and quantum information through all the phases of a finite XXZ spin chain. This characterizes the merit of the different phases in terms of their ability to act as a quantum wire. As far as quantum information is concerned, we need only consider the transmission of entanglement as the direct transmission of a quantum state is equivalent. The isotropic AFM spin chain is found to be the optimal point of the phase diagram for the transmission of quantum entanglement when one considers both the amount of transmitted entanglement and the velocity with which it is transmitted. However, this optimal point in the phase diagram moves to the Néel phase when decoherence or thermal fluctuations are taken to account. This chain may also be able to transfer classical information even when, due to a large magnitude of the noise, quantum information is not transmitted at all. For a certain range of anisotropies of the model, a curious feature is found in the flow of quantum information inside the chain, namely, a hopping mode of entanglement transfer which skips the odd-numbered sites. Our predictions will potentially be testable in several physical systems.

We present results of the study of a simultaneously confined metastable helium (He${}^{*}$) and rubidium magneto-optical trap (MOT). By monitoring the trap decay of the ${}^{87}\mathrm{Rb}$ MOT with and without a He${}^{*}$ MOT present, we find the light-assisted, two-body loss rate to be ${\beta }_{\mathrm{Rb}–{\mathrm{He}}^{*}}=(6\pm 2)\times {10}^{-10}\hspace{0.5em}{\mathrm{cm}}^3/\mathrm{s}$. Moreover, we find that it is possible to create a large, robust ${}^{87}\mathrm{Rb}$-He${}^{*}$ MOT, opening the possibility of creating a ${}^{87}\mathrm{Rb}$-He${}^{*}$ Bose-Einstein condensate. This would be the first dual-species condensate incorporating an alkali metal ground-state atom and an excited-state noble gas atom.

Fermionic polar molecules in deep one-dimensional (1D) optical lattices may form self-assembled filaments when the electric dipoles are oriented along the lattice axis. These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, which we discuss in detail for the simplest case of a three-well potential. We show that the interplay among filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers. We study the intriguing zero-temperature and finite-temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and we discuss possible methods to probe these chain mixtures.

The localization of electromagnetic waves in defect-free circular photonic crystals (CPCs) is investigated using a multiple-scattering method. It is shown that electromagnetic waves of certain freqencies are localized in some special regions inside a perfect CPC with a high order of rotational symmetry. Localized modes with a high $Q$ factor, greater than ${10}^6$, are obtained. In particular, some unique localized modes such as circular modes and localized modes for both polarized waves are found in the present system, which are completely different from those in defect-free photonic quasicrystals and periodic structures. Their physical properties are also analyzed.

We expand recent results on the nonlinear Schrödinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.