We examine the entanglement dynamics generated by two coupled angular momenta. For initially spin-coherent states, we show that fractional revivals can lead to a well-defined sequence of fractional disentanglements, at which the purity of each subsystem is almost a fractional number $1∕n$ (where $n$ is an integer). This interesting effect is interpreted as the formation of entangled macroscopic superposition states.

We show theoretically that the shape of a beam of matter waves (cold atoms) emerging from one subwavelength aperture pierced in a film can be collimated within a few degrees. By means of an external laser field, a potential well for the atoms in the direction perpendicular to the surface is created. In this way, a running surface matter wave can be excited when atoms diffract from the aperture. If the aperture is surrounded with a finite array of indentations, coherent scattering of the surface matter wave with these indentations molds the angular distribution of the matter wave in the far field.

We study Greenberger-Horne-Zeilinger–type (GHZ-type) and $W$-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin’s version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for $W$-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate $W$-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the $W$-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

We suggest a type of attack on quantum cryptosystems that exploits variations in detector efficiency as a function of a control parameter accessible to an eavesdropper. With gated single-photon detectors, this control parameter can be the timing of the incoming pulse. When the eavesdropper sends short pulses using the appropriate timing so that the two gated detectors in Bob’s setup have different efficiencies, the security of quantum key distribution can be compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84) protocol that if the efficiency mismatch between 0 and 1 detectors for some value of the control parameter gets large enough (roughly 15:1 or larger), Eve can construct a successful faked-states attack causing a quantum bit error rate lower than 11%. We also derive a general security bound as a function of the detector sensitivity mismatch for the BB84 protocol. Experimental data for two different detectors are presented, and protection measures against this attack are discussed.

We investigate the difference in the angular distribution of $\mathrm{Ly}\text{−}{\alpha }_1$ and $K{\alpha }_1$ photons from hydrogenlike and heliumlike ions of uranium after radiative electron capture to the $L$ shell. The strong anisotropy in the former case is changed to a very small one in the latter case. Our calculations support the observation. The effect takes place even in the limiting case of noninteracting electrons, being caused by the Pauli principle.

Spectra of $K$ x rays emitted from a variety of solid targets (atomic number $Z_2=17–32$) under bombardment by fast heavy ions (atomic number $Z_1=6–83$) at $2.5–25\mathrm{MeV}∕\mathrm{amu}$ were measured in high resolution using a curved crystal spectrometer. The spectra were analyzed in order to examine the dependence of $K\alpha$ x-ray satellite structure on the Geometrical Model’s universal variable $X_n$. Scaling rules were established for the apparent average $L$-shell spectator vacancy fraction at the time of $K\alpha$ x-ray emission, the satellite peak centroids, and the satellite peak widths.

We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical ensemble of $N$ noninteracting bosons in terms of a Landau function ${\mathcal{L}}_N^{\mathrm{BEC}}\left(q\right)$ defined by the logarithm of the probability distribution of the order parameter $q$ for BEC. We also discuss the corresponding Landau function for spontaneous symmetry breaking (SSB), which for finite $N$ should be distinguished from ${\mathcal{L}}_N^{\mathrm{BEC}}\left(q\right)$. Only for $N\to \infty$ BEC and SSB can be described by the same Landau function which depends on the dimensionality and on the form of the external potential in a surprisingly complex manner. For bosons confined by a three-dimensional harmonic trap the Landau function exhibits the usual behavior expected for continuous phase transitions.

Ultracold gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.

That the external potential $v_{\mathit{ext}}\left(\vec{r}\right)$ of a system of electrons is determined uniquely by the ground-state density is one of the central statements of the first Hohenberg-Kohn theorem. It is known that the validity of this statement extends to densities $n\left(\vec{r}\right)$ with noninteger particle number [i.e., $n\left(\vec{r}\right)$ integrates to a number that is not an integer] if the functional derivative of $T_s\left[n\left(\vec{r}\right)\right]+U\left[n\left(\vec{r}\right)\right]+E_{xc}\left[n\left(\vec{r}\right)\right]$ exists or (without relying on the existence of functional derivatives) if the ground-state energy is a strictly convex function of the particle number. In the present article, a proof that relies neither on the existence of the above functional derivative nor on the strict convexity of the ground-state energy is presented. The fact that the density determines the external potential leads to a noncrossing theorem for ground-state densities. The noncrossing theorem produces knowledge as to what the integer-particle-number ground-state densities of a system cannot be. The noncrossing theorem produces inequalities that the functional derivatives of the exchange-correlation energy functional $E_{xc}\left[n\left(\vec{r}\right)\right]$ and the noninteracting kinetic energy functional $T_s\left[n\left(\vec{r}\right)\right]$ must fulfill.

The dipole polarizabilities of two families of low-lying structures, cage, and space filling, of the medium-sized ${\mathrm{Au}}_N$ $(N=32,38,44,50,56)$ clusters are studied using gradient-corrected density functional theory and finite field method. Both dipole moments and polarizabilities exhibit clear shape-dependent features and the cage structures have systematically smaller dipole moments and larger polarizabilities than the space-filling isomers. The mean polarizability per atom increases with cluster size for the cage structures, but it decreases slowly and tends to approach a constant for the space-filling structures. A linearly correlation between polarizability and cluster volume is noted, complying with the jellium model prediction for spherical metal clusters. The electronic effects including HOMO-LUMO gap and ionization energy on polarizabilities are also explored. The geometric effects play a dominant role on the determination of the polarizability of the cluster over the electronic effects.

By means of analytical and numerical methods, we study how the residual three dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective one-dimensional (1D) Gross-Pitaevskii equation that includes an additional quintic self-focusing term, generated by the tight transverse confinement, we find a family of exact one-soliton solutions and demonstrate stability of the entire family, despite the possibility of collapse in the 1D equation with the quintic self-focusing nonlinearity. Simulating collisions between two solitons in the same setting, we find a critical velocity, $V_c$, below which merger of identical in-phase solitons is observed. Dependence of $V_c$ on the strength of the transverse confinement and number of atoms in the solitons is predicted by means of the perturbation theory and investigated in direct simulations. The simulations also demonstrate symmetry breaking in collisions of identical solitons with a nonzero phase difference. This effect is qualitatively explained by means of an analytical approximation.

Identity synchronization is observed experimentally and numerically in the chaotic dynamics of a system of two unidirectionally coupled semiconductor lasers. The transmitter and receiver lasers are subjected to polarization-rotated optical feedback and injection, respectively. Numerical and analytical results show that identity synchronization requires parameter matching through a relationship between the injection and feedback strengths, and linewidth enhancement factors of the lasers. Inverse synchronization is also observed experimentally.

We report on experimental observation of radiation-pressure induced effects in a high-power optical cavity. These effects play an important role in next-generation gravitational wave detectors, as well as in quantum nondemolition interferometers. We measure the properties of an optical spring, created by coupling of an intense laser field to the pendulum mode of a suspended mirror, and also the parametric instability (PI) that arises from the coupling between acoustic modes of the cavity mirrors and the cavity optical mode. We measure an unprecedented optical rigidity of $K=(3.08\pm 0.09)\times {10}^4\mathrm{N}∕\mathrm{m}$, corresponding to an optical rigidity that is 6000 times stiffer than the mechanical stiffness, and PI strength $R\approx 3$. We measure the unstable nature of the optical spring resonance, and demonstrate that the PI can be stabilized by feedback to the frequency of the laser source.

We propose a two-qubit collisional phase gate that can be implemented with available atom chip technology and present a detailed theoretical analysis of its performance. The gate is based on earlier phase gate schemes, but uses a qubit state pair with an experimentally demonstrated, very long coherence lifetime. Microwave near fields play a key role in our implementation as a means to realize the state-dependent potentials required for conditional dynamics. Quantum control algorithms are used to optimize gate performance. We employ circuit configurations that can be built with current fabrication processes and extensively discuss the impact of technical noise and imperfections that characterize an actual atom chip. We find an overall infidelity compatible with requirements for fault-tolerant quantum computation.

We present measurements of photoionization cross sections of the $3p{}^{1}P$ and $3p{}^{3}P$ excited states of helium, at threshold and near-threshold region $(0–0.2\mathrm{Ry})$. The experiments have been performed using a dc glow discharge and employed the saturation technique to determine the photoionization cross sections. A smooth frequency dependence of the cross section has been observed for both the excited states in accordance to the theoretical calculations. The measured values of the photoionization cross section, using a simple experimental setup, are in good agreement with the earlier reported theoretical and experimental values.

A blue line shape asymmetry near the center of the Cd $326.1\text{−}\mathrm{nm}$ line induced by low-polarizability perturbers (He, Ne) is explained by including the quasistatic contributions to the broadening rate associated with free-free transitions between repulsive branches of potential curves. The resulting shape in the near blue wing is represented by the addition to the Lorentzian and dispersion profiles of a quasistatic component. It is shown that for heavy perturbers (Ar, Kr, Xe) the quasistatic contributions play a marginal role near the line center and the line shape asymmetry arises mainly due to the finite duration of collision. It is also shown that for light perturbers (He, Ne) the quasistatic contributions are much more significant than those due to the collision duration and can adequately describe the blue asymmetry in the core region.

We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates (BEC’s) with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice potential. We discuss the complex structure of matter-wave phase singularities associated with different types of stationary gap vortices and suggest two different excitation methods. In one method, the condensate is adiabatically driven to the edge of the Brillouin zone where a vortex phase is subsequently imprinted onto the condensate wave packet. Alternatively, a vortex is created in a condensate confined in a harmonic trap and then is nonadiabatically released into the lattice potential. We find that only the latter method leads to robust and reliable generation of vortices within the gap of the matter-wave band-gap spectrum. Moreover, the nonadiabatic excitation can lead to the formation of broad gap vortices from the initial BEC wave packets with a large number of atoms. These broad vortices are intimately connected to self-trapped nonlinear states of the BEC recently demonstrated in experiments with a one-dimensional optical lattice. Our numerical simulations also confirm the feasibility of a homodyne interferometric detection of broad gap vortices.

Superfluidity in an ultracold Fermi gas is usually associated with either a negative scattering length or the presence of a two-body bound state. We show that none of these ingredients is necessary to achieve superfluidity. Using a narrow Feshbach resonance with strong repulsive background interactions, the effective interactions can be repulsive for small energies and attractive for energies around the Fermi energy, similar to the effective interactions between electrons in a metallic superconductor. This can result in BCS-type superfluidity while the scattering length is positive.

We consider a gedanken experiment with a beam of atoms in their ground state that are accelerated through a single-mode cavity. We show that taking into account of the “counterrotating” terms in the interaction Hamiltonian leads to the excitation of an atom with simultaneous emission of a photon into a field mode. In free space, when the atom-field interaction is turning on/off adiabatically, the only nonadiabatic effect that causes the excitation is the time-dependent Doppler shift. The resulting ratio of emission and absorption probabilities is exponentially small and is described by the Unruh factor. In the opposite case of rapid turn on of the interaction on the cavity boundaries the above ratio is much greater and radiation is produced with an intensity which can exceed the intensity of radiation in free space by many orders of magnitude. In both cases real photons are produced. The cavity field at steady state has a thermal density matrix. However, under some conditions laser gain is possible. We present a detailed discussion of how the acceleration of atoms affects the generated cavity field in different situations. We identify a common physical mechanism behind the Unruh effect and similar QED radiation processes.