We investigate arrays and rotation of spherical microparticles trapped by focusing a circularly polarized Gaussian beam just above the top coverslip-water interface. Particles are trapped in various patterns due to a Fresnel diffraction, such as rings and close-packed structures. We find that rings of particles orbit around the beam axis, whereas close-packed arrays spin in the opposite sense on the beam axis. The sense of the orbiting, as well as that of the spinning, is determined by the input circular polarization handedness. The results are interpreted on the assumption that the spin angular momentum carried by a circularly polarized beam is converted into the orbital angular momentum in the optical process by which the focused Gaussian beam’s shape is transformed due to diffraction.

We investigate the feasibility of using ultracold neutral atoms trapped near a thin superconductor to study vortex noise close to the Kosterlitz-Thouless-Berezinskii transition temperature. Alkali atoms such as rubidium probe the magnetic field produced by the vortices. We show that the relaxation time $T_1$ of the Zeeman sublevel populations can be conveniently adjusted to provide long observation times. We also show that the transverse relaxation times $T_2$ for Zeeman coherences are ideal for studying the vortex noise. We briefly consider the motion of atom clouds held close to the surface as a method for monitoring the vortex motion.

We study a non-Markovian spin-$1∕2$ master equation with exponential memory. We derive the conditions under which the dynamical map describing the reduced system dynamics is completely positive, i.e., the nonunitary evolution of the system is compatible with a description in terms of a closed total spin-reservoir system. Our results show that for a zero-$T$ reservoir, the dynamical map of the model here considered is never completely positive. For moderate- and high-$T$ reservoirs, on the contrary, positivity is a necessary and sufficient condition for complete positivity. We also consider the Shabani-Lidar master equation recently introduced [A. Shabani and D.A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we demonstrate that such a master equation is always completely positive.

In this paper we study the SWAP operation in a two-qubit anisotropic $XXZ$ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter $\lambda$ within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.

In this paper, we study the effect of phase fluctuations of the pump field upon the entanglement generation in a two-photon correlated emission laser (CEL). We consider initial vacuum and coherent state for the two-cavity modes. In both cases, we find reduction in the entanglement due to the phase fluctuations. However, our results indicate that entanglement generation is highly sensitive to phase fluctuations when we have initial coherent state in the two modes.

In this paper, we discuss the problem of determining whether a quantum system is in a pure state, or in a mixed state. We apply two strategies to settle this problem: the unambiguous discrimination and the maximum confidence discrimination. We prove that the optimal versions of both strategies are equivalent. Furthermore, the scheme also provides a method to estimate the purity of quantum states, and the Schmidt number of composed systems.

The energies and autoionization widths of resonances in the collision of low-energy electrons from $\mathrm{H}\mathrm{C}\mathrm{N}{\mathrm{H}}^{+}$ involved in dissociative recombination have been derived from electron-scattering calculations using the complex Kohn variational method. No low-lying resonance state that crosses the ground state of $\mathrm{H}\mathrm{C}\mathrm{N}{\mathrm{H}}^{+}$ in the Franck-Condon region was found. One state, having predominantly valence character, was found to lie close in energy to the $\mathrm{H}\mathrm{C}\mathrm{N}{\mathrm{H}}^{+}$ ion ground state, but remained below the ion ground state for all geometries. The presence of avoided crossings between the resonance states is described and the effects of these crossings on the properties of the resonances are discussed. When C-H and N-H bonds are stretched, there is no significant difference in the shape of the potential-energy surfaces.

We have investigated the stability, electronic, and magnetic properties of transition-metal-doped $M{\mathrm{B}}_n$ clusters ($M=\mathrm{Cr},\mathrm{Mn},\mathrm{Fe},\mathrm{Co},\mathrm{Ni}$, $n⩽7$) using first-principles density functional theory with generalized gradient approximation. The equilibrium structures of $M{\mathrm{B}}_n$ $(n⩽5)$ clusters can be obtained by directly adding $M$ atoms to the ${\mathrm{B}}_n$ clusters, while for $n=6$, hexagon or near-hexagon geometries with a boron atom at the center ring are regarded as the ground-state structures. $n=7$ marks the onset of three-dimensional geometries for $M{\mathrm{B}}_n$ clusters. According to the second-order energy differences, gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital and vertical ionization potentials, we can conclude that $\mathrm{Cr}{\mathrm{B}}_4$, $\mathrm{Cr}{\mathrm{B}}_7$, $\mathrm{Mn}{\mathrm{B}}_3$, $\mathrm{Fe}{\mathrm{B}}_3$, $\mathrm{Fe}{\mathrm{B}}_5$, $\mathrm{Fe}{\mathrm{B}}_7$, and $\mathrm{Co}{\mathrm{B}}_7$ possess relatively higher stabilities. The relative orientation between the magnetic moments of the $M$ atom and those of its neighboring B atoms mainly exhibits an antiferromagnetic alignment for $\mathrm{Cr}{\mathrm{B}}_n$, $\mathrm{Mn}{\mathrm{B}}_n$, and $\mathrm{Fe}{\mathrm{B}}_n$, while it mainly shows a ferromagnetic alignment for $\mathrm{Co}{\mathrm{B}}_n$ and $\mathrm{Ni}{\mathrm{B}}_n$ clusters.

We investigate the localization properties of single-particle eigenstates in bichromatic one-dimensional optical lattices. Whereas such a lattice with a sufficiently deep primary component and a suitably adjusted incommensurate secondary component provides an approximate realization of the Harper model, the system’s self-duality is broken when the lattice is comparatively shallow. As a consequence, the sharp metal-insulator transition exhibited by Harper’s model is replaced by a sequence of mobility edges in realistic bichromatic optical lattices that do not reach the tight-binding regime.

Stark-chirped rapid adiabatic passage [T. Rickes et al., J. Chem. Phys. 113, 534 (2000); A. A. Rangelov et al. Phys. Rev. A 72, 053403 (2005)] has been proposed as a laser scheme that allows the optical excitation of atoms or molecules with high quantum yields. The laser control proceeds via adiabatic passage assisted by dynamic Stark shifts. We propose several extensions of the scheme with alternative sequences, by frequency tuning or by repeating the pulse sequences, in order to achieve fine state selectivity within multilevel structures and adiabatic passage of quantum superposition states. The efficiency and selectivity of the schemes is compared with that achieved by other optical coherent methods.

We present traps with toroidal $\left(T^2\right)$ and ring-shaped topologies based on adiabatic potentials for radio-frequency-dressed Zeeman states in a ring-shaped magnetic quadrupole field. Simple adjustment of the radio-frequency fields provides versatile possibilities for dynamical parameter tuning, topology change, and controlled potential perturbation. We show how to induce toroidal and poloidal rotations, and demonstrate the feasibility of preparing degenerate quantum gases with reduced dimensionality and periodic boundary conditions. The great level of dynamical and even state-dependent control is useful for atom interferometry.

We report on photoionization of ultracold magnetically trapped Rb atoms on an atom chip. The atoms are trapped at $5\mu \mathrm{K}$ in a strongly anisotropic trap. Through a hole in the chip with a diameter of $150\mu \mathrm{m}$, two laser beams are focused onto a fraction of the atomic cloud. A first laser beam with a wavelength of $778\mathrm{nm}$ excites the atoms via a two-photon transition to the $5D$ level. With a fiber laser at $1080\mathrm{nm}$ the excited atoms are photoionized. Ionization leads to depletion of the atomic density distribution observed by absorption imaging. The resonant ionization spectrum is reported. The setup used in this experiment is suitable not only to investigate mixtures of Bose-Einstein condensates and ions but also for single-atom detection on an atom chip.

The magnetic radiation of the fully condensed states of spinor condensates has been studied. A narrow characteristic spectral line together with a strong background at its violet side have been found. For the condensate of $N={10}^{12}$ atoms of ${}^{23}\mathrm{Na}$ confined in an isotropic and harmonic trap with frequency ${\omega }_o=300{\mathrm{s}}^{-1}$, for instance, the photon energy of the characteristic line is $127.9\hslash {\omega }_o$ with width $<1.\hslash {\omega }_o$ and the probability of transition is $1.44\times {10}^{-34}{\mathrm{s}}^{-1}$. The photon energy and probability have been found to be proportional to $N^{2∕5}$ and $N^{17∕5}$, respectively. It implies that magnetic radiations with higher photon energies and much larger probabilities can be obtained if numerous atoms are trapped. A technique developed by the authors, namely, the analytical forms of the fractional parentage coefficients, was used to calculate analytically the matrix elements between the spin states that conserve the total spin and its $Z$ component.

We introduce standing-light patterns trapped in a Bragg grating written along the radial direction in a self-focusing (SF) or self-defocusing (SDF) optical medium. Unlike previously studied axisymmetric settings that deal with the axial propagation, we consider the propagation of light in the radial directions (outward and inward), which may give rise to annular gap solitons (AGSs), supported by the circular grating. An estimate for the threshold of the modulational instability of the AGS against azimuthal perturbations in the SF medium is obtained analytically, and verified by direct simulations. In the SDF model, stable annular and dipole solitons are found in a numerical form, while multipole patterns and vortex rings are unstable. Similar solitons are possible in the Bose-Einstein condensate.

We demonstrate the intensity enhancement of single harmonics in high-order harmonic generation from laser plasma. We identified several targets (In, Sn, Sb, Cr, and Mn) that demonstrate resonance-induced enhancement of single harmonic, that are spectrally close to ionic transitions with strong oscillator strengths. We optimized and obtained enhancements of the 13th, 17th, 21st, 29th, and 33rd harmonics from the above targets, by varying the chirp of the $800\mathrm{nm}$ wavelength femtosecond laser. We also observe harmonic enhancement by using frequency-doubled pump laser ($400\mathrm{nm}$ wavelength). For Mn plasma pumped by the $400\mathrm{nm}$ wavelength laser, the maximum order of the enhanced harmonic observed was the 17th order $(\lambda =23.5\mathrm{nm})$, which corresponds to the highest photon energy $\left(52.9\mathrm{eV}\right)$ reported for an enhanced single harmonic.

We study the dynamics of time-of-flight expansion of an atomic Fermi system with a finite number of particles $N$ after it is released from a harmonic trapping potential. We consider two different initial states: the Fermi sea state and the paired state. In the former case, we derive exact and simple analytic expressions for the dynamics of the particle density and density-density correlation functions, taking into account the level quantization and possible anisotropy of the trap. To describe the paired state, we use the projection of the grand-canonical BCS wave function onto the subspace with a fixed number of particles, and obtain analytic expressions for the density and its correlators in the leading order with respect to the ratio of the trap frequency and the superconducting gap (the ratio is assumed small). We discuss several dynamic features, such as the time evolution of the peak due to pair correlations, which may be used to distinguish between the Fermi sea and the paired state.

Based on a two-qubit one-dimensional isotropic spin-$1∕2$ Heisenberg spin chain in a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE) and investigate the influence of entanglement between two qubits on basic thermodynamic quantities, i.e., the heat transferred and the work done in a cycle, and the efficiency of the QHE. The validity of the second law of thermodynamics is confirmed in the entangled system. We also find several interesting features of the variation of the efficiency with the entanglement of two different thermal equilibrium states in a work cycle in zero and finite magnetic field. An abrupt transition of efficiency is found in zero field.

A systematic QED treatment of the electron correlation is presented for ions along the lithium isoelectronic sequence. We start with the zeroth-order approximation that accounts for a part of the electron-electron interaction by a local model potential introduced into the Dirac equation. The residual electron correlation is treated by perturbation theory. A rigorous QED evaluation is presented for the first two terms of the perturbative expansion; the third-order contribution is calculated within the many-body perturbation theory. We report accurate numerical results for the electronic-structure part of the ionization potential for the $n=2$ states of all Li-like ions up to uranium.

We present an accurate numerical study of the influence an the external dc electric field on the process of single-photon double ionization of the negative hydrogen ion at photon energies from the threshold to $30\mathrm{eV}$. We demonstrate that the presence of an external dc electric field of the order of $0.005\mathrm{a.u.}$ may considerably alter the cross section of the process.

We investigate the harmonic phase dependence of photoionization of aligned $\mathrm{H}_2{}^{+}$ with three colors: two high-order (uv) harmonics of orders $(q+1)$ and $(q-1)$ in the presence of a “dressing” ir photon such that the absorption of the $(q-1)$ harmonic and one ir photon is resonant with the absorption of the $(q+1)$ harmonic and emission of one ir photon. The transition amplitudes for these two interfering paths are calculated for $\mathrm{H}_2{}^{+}$ for a wide range of uv photon energies, internuclear distances $R$, and orientations. The relative phase of the ionizing harmonic photons controls the interference between the paths in the total photoionization amplitude, thus allowing for its measurement. Calculations are obtained using the $\mathrm{H}_2{}^{+}$ electron continuum wave functions and Green’s functions for two polarizations, parallel $\left(z\right)$ and perpendicular $\left(x\right)$ to the internuclear axis. It is found that the phase differences of the two transition amplitudes, which are made up of harmonic and molecular phases, exhibit a sharp peak when calculated as a function of harmonic order $q$, and internuclear distance $R$. This occurs for near-vanishing total photoexcitation amplitudes where the phase of the amplitude changes abruptly by $\pi$. The orientation dependence of the interfering three-photon photoionization amplitudes provides an additional degree of freedom for harmonic phase measurements using aligned molecules, because of the orientation dependence of the molecular phase inherent in such measurements.