Electron-impact ionization cross sections for all atomic ions in the W isonuclear sequence are calculated using a variety of theoretical methods. For the direct ionization process, a semirelativistic configuration-average distorted-wave method is used for low to moderately charged ions, while a fully relativistic subconfiguration-average distorted-wave method is used for highly charged ions. For the indirect ionization process of excitation autoionization, a semirelativistic configuration-average distorted-wave method is used for the bulk of the transitions, but a semirelativistic level-resolved distorted-wave method is used for selective strong transitions that may straddle the ionization threshold. For moderately charged ions it is important to include radiation damping of the excitation-autoionization process through explicit calculation of autoionization branching ratios. Checks are made on the theoretical predictions by comparison with available crossed-beams experimental measurements, which only exist for low stages of ionization. The ionization cross sections for the entire W isonuclear sequence are converted to temperature-dependent rate coefficients and put in a collisional-radiative format that should prove useful in modeling laboratory plasmas that contain W impurities.

Photodissociation of $\mathrm{D}_2{}^{+}$ molecular ions in a beam from an ion source has been studied with $785\mathrm{nm}$ intense femtosecond laser pulses. Using a high-resolution velocity imaging technique, the neutral fragments from single vibrational levels of the $\mathrm{D}_2{}^{+}$ molecules have been resolved. The effects of one- and net two-photon bond softening: level shifting, vibrational trapping, and molecular alignment are observed in the kinetic energy and angular distributions and are discussed in detail. In comparison with our previous study on $\mathrm{H}_2{}^{+}$, we observe smaller widths of the peaks in the kinetic energy distributions of the $\mathrm{D}_2{}^{+}$ fragments from single vibrational levels. We attribute this to the longer lifetimes of $\mathrm{D}_2{}^{+}$ vibrational states in the light-induced potentials. The width of the angular distributions increases for lowest fragment energies, which suggests vibrational trapping of the levels close to the three-photon crossing.

We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang et al. [Chin. Phys. Lett. 20, 799 (2003)], is shown to be a good indication for Bose-Einstein condensation. Our study also supports the use of the average width of a trapped Bose gas for a nondestructive calibration of its temperature.

We propose a method of using spin exchange dynamics to determine the coefficient of the spin-singlet pair term of a spin-2 Bose-Einstein condensate (BEC) by preparing the initial populations in the magnetic sublevels 0 and $\pm 2$ with appropriate relative phases. This method is suitable for a BEC with a short lifetime, since only the initial change in the population of each magnetic sublevel is needed. Our method therefore enables the determination of the ground-state phase of a spin-2 ${}^{87}\mathrm{Rb}$ BEC at zero magnetic field, which is considered to lie in the immediate vicinity of the boundary between the antiferromagnetic and cyclic phases. We propose a scheme to prepare the initial state in which the relative phases between the magnetic sublevels are controlled. We also propose a simple scheme to distinguish between the antiferromagnetic and cyclic phases under a situation of very low bias magnetic field.

We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the inversely linear dependence on the bare on-site interaction $U_0$ is explained both in smaller and larger $U_0$. For a smaller $U_0$, it comes from a second order correction. For a larger $U_0$, except the breakdown of adiabaticity as analyzed by Gerbier et al., there might be another source to cause this deviation, which is the diversity between $U_0$ determined by the single atom Wannier function and the effective on site interaction $U_{\mathrm{eff}}$ for a multioccupation per site.

The quantum theory of the cold-atom micromaser including the effects of gravity is considered. We show that gravity does not break the special properties of the induced emission probability for the micromaser in the cold atom regime and rather new effects are predicted. In particular, we show that the cavity acts in the gravity field as an additional repulsive and attractive potential, resulting in quasibound states of the atomic motion. This feature gives rise to fine resonances in the induced emission probability that are not restricted to any particular cavity mode function, in contrast to the usual cold-atom micromaser. It is also shown that the atom is able to emit a photon inside the cavity, though classically it does not reach the interaction region. Predictions about the photon number statistics when the cavity is pumped by a flux of excited atoms are finally given. Unusual highly nonclassical “dragon” distributions are still predicted in the vertical geometry.

Semiclassical quantization is exact only for the so-called solvable potentials, such as the harmonic oscillator. In the nonsolvable case, the semiclassical phase, given by a series in $\hslash$, yields more or less approximate results and eventually diverges due to the asymptotic nature of the expansion. A quantum phase is derived to bypass these shortcomings. It achieves exact quantization of nonsolvable potentials and allows us to obtain the quantum wave function while locally approaching the best predivergent semiclassical expansion. An iterative procedure allowing us to implement practical calculations with a modest computational cost is also given. The theory is illustrated on two examples for which the limitations of the semiclassical approach were recently highlighted: cold atomic collisions and anharmonic oscillators in the nonperturbative regime.

A critical dependence of the quantum interference on the optical Stark spectral shift produced when two-color laser pulses interact with a two-level medium is observed. The four-wave mixing of two ultrashort phase-locked $\omega \text{−}3\omega$ laser pulses propagating coherently in a two-level system depends on the pulses’ relative phase. The phase dominating the efficiency of the coupling to the anti-Stokes Raman component is found to be determined by the sign of the total ac Stark shift induced in the system, in such a way that the phase sensitivity disappears precisely where the ac Stark effect due to both pulses is compensated. A coherent control scheme based on this phenomenon can be contemplated as the basis for nonlinear optical spectroscopy techniques.

The possibility of cloning a $d$-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine for qubits found in Phys. Rev. A 60, 2764 (1999). We prove the impossibility of constructing an economical version of the optimal universal $1\to 2$ cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the $d$-dimensional $1\to 2$ phase-covariant cloner, which optimally clones all balanced superpositions with arbitrary phases, can be realized economically only in dimension $d=2$. The used ansatz is supported by numerical evidence up to $d=7$. An economical phase-covariant cloner can nevertheless be constructed for $d>2$, albeit with a slightly lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the $1\to 2$ Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension $d=2$.

We give the optimal decomposition of a universal two-qubit circuit using Heisenberg exchange interactions and single qubit rotations. Tuning the strength and duration of the Heisenberg exchange allows one to implement ${\left(\mathrm{SWAP}\right)}^{\alpha }$ gates. Our optimal circuit is constructed from only three ${\left(\mathrm{SWAP}\right)}^{\alpha }$ gates and six single qubit gates. We show that three ${\left(\mathrm{SWAP}\right)}^{\alpha }$ gates are not only sufficient, but necessary. Since six single-qubit gates are already known to be necessary, our implementation is optimal in gate count.

The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states and, hence, describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of ${\mathbb{R}}^6$, which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.

Theoretical investigations on single charge-transfer processes in collisions of ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ and its reverse process have been carried out at collision energies from $20\mathrm{eV}∕\mathrm{u}\text{to}10\mathrm{keV}∕\mathrm{u}$. The molecular orbital expansion method within the semiclassical impact parameter formalism has been employed for the scattering dynamics, while the ab initio multireference single- and double-excitation configuration interaction (MRD-CI) method was adopted for determination of molecular electronic states. The initial channels correspond to the quintet and triplet states for the corresponding collision processes, respectively. Four molecular states in the quintet manifold and eight molecular states in the triplet manifold were coupled. In the quintet manifold, the charge-transfer cross sections for ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ range from $1.3\times {10}^{-22}{\mathrm{cm}}^2$ at $20\mathrm{eV}∕\mathrm{u}\text{to}2.5\times {10}^{-15}{\mathrm{cm}}^2$ at $10\mathrm{keV}∕\mathrm{u}$. The cross sections of the reverse process, ${\mathrm{F}}^{+}+{\mathrm{H}}^{+}\to {\mathrm{F}}^{2+}+\mathrm{H}$, range from $3.0\times {10}^{-22}{\mathrm{cm}}^2\text{to}2.3\times {10}^{-15}{\mathrm{cm}}^2$ in the same energy range. In the triplet states, the charge-transfer cross sections for ${\mathrm{F}}^{2+}+\mathrm{H}\to {\mathrm{F}}^{+}+{\mathrm{H}}^{+}$ range from $1.1\times {10}^{-18}{\mathrm{cm}}^2\text{to}2.5\times {10}^{-16}{\mathrm{cm}}^2$, and its reverse process gives charge-transfer cross sections ranging from $1.7\times {10}^{-24}{\mathrm{cm}}^2\text{to}1.5\times {10}^{-17}{\mathrm{cm}}^2$.

It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

We consider the binding energy and the wave function of Feshbach molecules confined in a one-dimensional matter waveguide. We compare the binding energy with the experiment of Moritz et al. [Phys. Rev. Lett. 94, 210401 (2005)] and find excellent agreement for the full magnetic field range explored experimentally.

For a weakly interacting Bose-Einstein condensate in a double well, an appropriate time-dependent modulation of the trapping potential counteracts the “self-trapping” effects of the interactions, thereby allowing tunneling between the wells. It is demonstrated numerically that this modulation can be employed for transferring the condensate from one well to the other in a controlled way. Moreover it allows the production of mesoscopic entangled states on short time scales.

We analyze in a multimode model a recent scheme [Tsujino et al., Phys. Rev. Lett. 92, 153602 (2004)] to distinguish entangled four-photon polarization state from two independent polarization entangled pairs of photons in a single type-II parametric down-conversion process. The fraction of the four-photon entangled state among the two detected photon pairs is found to be related to a quantity that is responsible for the temporal mode match between the photon pairs. A comparison with the single mode models is discussed.

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum nondemolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum nondemolition and projective measurements are implemented using a cavity quantum electrodynamics system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

We study the dynamics of entanglement in the infinite asymmetric $XY$ spin chain, in an applied transverse field. The system is prepared in a thermal equilibrium state (ground state at zero temperature) at the initial instant, and it starts evolving after the transverse field is completely turned off. We investigate the evolved state of the chain at a given fixed time, and show that the nearest-neighbor entanglement in the chain exhibits a critical behavior (which we call a dynamical phase transition), controlled by the initial value of the transverse field. The character of the dynamical phase transition is qualitatively different for short and long evolution times. We also find a nonmonotonic behavior of entanglement with respect to the temperature of the initial equilibrium state. Interestingly, the region of the initial field for which we obtain a nonmonotonicity of entanglement (with respect to temperature) is directly related to the position and character of the dynamical phase transition in the model.

We present a method for checking the Peres separability criterion in an arbitrary bipartite quantum state ${\rho }_{\mathrm{AB}}$ within local operations and classical communication scenario. The method does not require noise operation which is needed in making the partial transposition map physically implementable. The main task for the two observers, Alice and Bob, is to measure some specific functions of the partial transposed matrix. With these functions, they can determine the eigenvalues of ${\rho }_{\mathrm{AB}}^{T_{\mathrm{B}}}$, among which the minimum serves as an entanglement witness.

Suppose we are given two identical copies of an unknown quantum state and we wish to delete one copy from among the given two copies. The quantum no-deletion principle restricts us from perfectly deleting a copy but it does not prohibit us from deleting a copy approximately. Here we construct two types of a “universal quantum deletion machine” which approximately deletes a copy such that the fidelity of deletion does not depend on the input state. The two types of universal quantum deletion machines are (1) a conventional deletion machine described by one unitary operator and (2) a modified deletion machine described by two unitary operators. Here it is shown that the modified deletion machine deletes a qubit with fidelity $3∕4$, which is the maximum limit for deleting an unknown quantum state. In addition to this we also show that the modified deletion machine retains the qubit in the first mode with average fidelity 0.77 (approx.) which is slightly greater than the fidelity of measurement for two given identical states, showing how precisely one can determine its state [S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995)]. We also show that the deletion machine itself is input state independent, i.e., the information is not hidden in the deleting machine, and hence we can delete the information completely from the deletion machine.