Calculations of various corrections to the $g$ factor of Li-like ions are presented, which result in a significant improvement of the theoretical accuracy in the region $Z=6–92$. The configuration-interaction Dirac-Fock method is employed for the evaluation of the interelectronic-interaction correction of order $1∕Z^2$ and higher. This correction is combined with the $1∕Z$ interelectronic-interaction term derived within a rigorous QED approach. The one-electron QED correction of first order in $\alpha$ is obtained by employing our recent results for the self-energy term and by evaluating the vacuum-polarization contribution. The screening of QED corrections is taken into account to the leading orders in $\alpha Z$ and $1∕Z$.

Anisotropic magnetic nanodots are promising physical realizations of qubits for quantum computing at finite temperature owing to their well-separated low-lying energy levels and scalability. The entanglement of two interacting magnetic nanodots is investigated and shown both analytically and numerically to be resonantly dependent on their interaction strength and on differences in their properties. These results provide criteria for fabricating and coupling magnetic nanodots so that their low-lying eigenstates can be significantly entangled.

We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the $1\to 2$ cloning we find that the $XY$ model saturates the value for the fidelity of the optimal cloner and gives values comparable to it in the general $N\to M$ case. We finally discuss the effect of external noise. Our protocol is much more robust to decoherence than a conventional procedure based on quantum gates.

In this paper we present a theoretical study of the time-dependent probe response in the presence of a strong pump field in a three-level pump-probe configuration. Two situations are investigated: a cw pump with a pulsed probe field and a pulsed pump with a cw probe field. The results are explained as dressed-state nutation and nutation by dynamic Stark switching. Dressed-state quantum beats are also an important feature for both situations. Furthermore, when a 90° phase shift after a $\pi ∕2$ period is introduced in the pulsed probe field, there is a spin locking in the dressed-state transition. Our results give a satisfactory theoretical account of a previous experimental observation [Wei et al., Phys. Rev. Lett. 74, 1083 (1995)].

In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schrödinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of ${}^{87}\mathrm{Rb}$. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.

A mixture of two types of hard-sphere bosons in a disk-shaped harmonic trap is studied through path-integral quantum Monte Carlo simulation at low temperature. We find that the system can undergo a phase transition to break the spatial symmetry of the model Hamiltonian when some of the model parameters are varied. The nature of such a phase transition is analyzed through the particle distributions and angular correlation functions. Comparisons are made between our calculations and the available mean-field results on similar models. Possible future experiments are suggested to verify our findings.

Based on ab initio simulations of the interaction of the hydrogen atom with a multifrequency ultrashort laser pulse in the strong-field regime, coherent population trapping is found. It leads to the inhibition of the ionization process and, hence, electromagnetically induced transparency, provided that certain two-photon resonance conditions are satisfied. This effect opens additional possibilities to detect phase-locked trains of attosecond pulses.

This paper examines the physical mechanisms of reading out spatial-spectral absorption features in an inhomogeneously broadened medium using linear frequency-chirped electric fields. A Maxwell-Bloch model using numerical calculation for angled beams with arbitrary phase modulation is used to simulate the chirped field readout process. The simulation results indicate that any spatial-spectral absorption feature can be read out with a chirped field with the appropriate bandwidth, duration, and intensity. Mapping spectral absorption features into temporal intensity modulations depends on the chirp rate of the field. However, when probing a spatial-spectral grating with a chirped field, a beat signal representing the grating period can be created by interfering the emitted photon echo chirped field with a reference chirped field, regardless of the chirp rate. Comparisons are made between collinear and angled readout configurations. Readout signal strength and spurious signal distortions are investigated as functions of the grating strength and the Rabi frequency of the readout pulse. Using a collinear readout geometry, distortions from optical nutation on the transmitted field and higher-order harmonics are observed, both of which are avoided in an angled beam geometry.

We revisit the topic of atomic center of mass motion of a three level atom Raman coupled strongly to an external laser field and the quantum field of a high-$Q$ optical cavity. We focus on the motion related nonadiabatic effects of the atomic internal dynamics and provide a quantitative answer to the validity regime for the application of the motional insensitive dark state as recently suggested by Duan, Kuzmich, and Kimble [Phys. Rev. A 67, 032305 (2003)].

We investigate the dynamics of the quantum Zeno subspaces which are the eigenspaces of the interaction Hamiltonian, belonging to different eigenvalues. Using the perturbation theory and the adiabatic approximation, we get a general expression of the jump probability between different Zeno subspaces. We applied this result in an interesting practical example. In this example, as the coupling constant of the interaction increases, the measurement keeps the system remaining in its initial subspace and the quantum Zeno effect takes place.

In order to calculate the cross section for electron-positron pair production with capture of the electron into the $K$ shell of the target in relativistic scattering of heavy nuclei, we apply the semiclassical method and solve the time-dependent Dirac equation in time-reversal symmetry, starting with a $1s_{1∕2}$ state at the target. The solution is carried out numerically on a three-dimensional lattice in coordinate space. Cross sections for excitation, ionization, electron transfer, and pair production with capture are obtained for collisions of ${\mathrm{U}}^{92+}(\gamma =1.5)$, ${\mathrm{Au}}^{79+}(\gamma =2)$, and ${\mathrm{U}}^{92+}(\gamma =10000)$ on ${\mathrm{U}}^{91+}\left(1s_{1∕2}\right)$ and ${\mathrm{U}}^{92+}$, where $\gamma$ is the Lorentz factor, and compared with experimental data and other theoretical results.

We suggest using a two-color evanescent light field around a subwavelength-diameter fiber to trap and guide atoms. The optical fiber carries a red-detuned light and a blue-detuned light, with both modes far from resonance. When both input light fields are circularly polarized, a set of trapping minima of the total potential in the transverse plane is formed as a ring around the fiber. This design allows confinement of atoms to a cylindrical shell around the fiber. When one or both of the input light fields are linearly polarized, the total potential has two local minimum points in the transverse plane. This design allows confinement of atoms to two straight lines parallel to the fiber axis. Due to the small thickness of the fiber, we can use far-off-resonance fields with substantially differing evanescent decay lengths to produce a net potential with a large depth, a large coherence time, and a large trap lifetime. For example, a 0.2-μm-radius silica fiber carrying 30 mW of 1.06-μm-wavelength light and 29 mW of 700-nm-wavelength light, both fields circularly polarized at the input, gives for cesium atoms a trap depth of 2.9 mK, a coherence time of 32 ms, and a recoil-heating-limited trap lifetime of 541 s.

The properties of a Bose-Einstein condensate in a two-well potential can be manipulated by periodic modulation of the potential parameters. We study the effects arising from modulating the barrier height and the difference in well depth. At certain modulation frequencies the system exhibits resonances, which may show up in an enhancement of the tunneling rate between the wells. Resonances can be used to control the particle distribution over the wells. Some of the effects occurring in the two-well system also arise for a Bose-Einstein condensate in an optical lattice.

We investigate the resonant motion of neutral spin-$\frac{1}{2}$-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schrödinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the ${}^6\mathrm{Li}$ atom in the $F=\frac{1}{2}$ hyperfine ground state.

It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A. 69, 022310 (2004)] that it is possible to perform exactly faithful remote state preparation using finite classical communication and any entangled state with maximal Schmidt number. Here we give an explicit procedure for performing this remote state preparation. We show that the classical communication required for this scheme is close to optimal for remote state preparation schemes of this type. In addition we prove that it is necessary that the resource state have maximal Schmidt number.

An implementation of the Dirac $R$-matrix theory is presented and applied to the calculation of electron-impact excitation of B-like Fe XXII in the $n=2$ complex. A detailed comparison between the $R$-matrix and relativistic distorted-wave (DW) results is given. Contrary to the previous close-coupling studies of this ion, where significantly different background collision strengths are found for several transitions as compared with the DW results, we obtain excellent agreements between the two methods for most transitions, except for the weak transitions to the higher members of the $2p^3$ configuration, where significant channel-coupling effects are indeed present. We show that the discrepancies found in the previous Dirac $R$-matrix calculation for dipole transtions at high energies are due to the nonconvergence of partial wave summation, despite the explicit inclusion of partial waves up to $l=40$. The reason for large differences in the threshold energy region for some transitions between the present and previous Dirac $R$-matrix results is not clear. We also show that the independent-process, isolated-resonance approximation within the DW framework can describe the near-threshold resonances reasonably well for this ion.

Electron-impact excitation of the $3s3p{}^{1}P^o$ state of Mg-like ions (${\mathrm{S}}^{4+},{\mathrm{Ar}}^{6+}$, and ${\mathrm{Ca}}^{8+}$) from their ground state is studied theoretically using the $R$-matrix method with 31 target states. Results are reported in the range of low incident electron energies for the total and differential cross sections of this excitation process as well as for the polarization fraction and the Stokes parameters $P_1,P_2$, and $P_3$ of the photons emitted on the decay of the excited $3s3p{}^{1}P^o$ state to the ground state. The agreement between experiment and the present results is good. We obtain a polarization fraction of about 35% at low incident electron energies in these ions.

The momentum transfer dependence of double excitations of helium were studied theoretically in order to compare with our previous experimental work [Phys. Rev. Lett. 91, 193203 (2003)]. The calculation was carried out by a series of modified $R$-matrix codes. We elucidate the dynamical correlations in terms of the internal correlation quantum numbers $\mathcal{K}$, $\mathcal{T}$, and $A$. The generalized oscillator strength densities and Fano profile parameters $q$, $f_a$, $f$, and $S$ of doubly excited states ${}_n(1,0)_2^{+}{}^{1}S^e$, ${}_n(1,0)_2^{+}{}^{1}D^e$, and ${}_n(0,1)_2^{+}{}^{1}P^o$ were reported as functions of the momentum transfer squared $K^2$. The present theoretical work accompanied by our previous experiment leads to a deep understanding of the optically allowed and optically forbidden double excitations of helium.

One can use transsonic Bose-Einstein condensates of alkali atoms to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determine the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. The transition to supersonic speed occurs at the potential maximum and the Hawking temperature is entirely determined by the curvature of the potential.

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a $2N\times 2N$ discrete phase space for a system with $N$ orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having $N$ elements. There exists such a field if and only if $N$ is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our $N\times N$ phase space also leads naturally to a method of constructing a complete set of $N+1$ mutually unbiased bases for the state space.