In the theory of operator quantum error correction (OQEC), the notion of correctability is defined under the assumption that states are perfectly initialized inside a particular subspace, a factor of which (a subsystem) contains the protected information. If the initial state of the system does not belong entirely to the subspace in question, the restriction of the state to the otherwise correctable subsystem may not remain invariant after the application of noise and error correction. It is known that in the case of decoherence-free subspaces and subsystems (DFSs) the condition for perfect unitary evolution inside the code imposes more restrictive conditions on the noise process if one allows imperfect initialization. It was believed that these conditions are necessary if DFSs are to be able to protect imperfectly encoded states from subsequent errors. By a similar argument, general operator quantum error-correcting (OQEC) codes would also require more restrictive error-correction conditions for the case of imperfect initialization. In this study, we examine this requirement by looking at the errors on the encoded state. In order to quantitatively analyze the errors in an OQEC code, we introduce a measure of the fidelity between the encoded information in two states for the case of subsystem encoding. A major part of the paper concerns the definition of the measure and the derivation of its properties. In contrast to what was previously believed, we obtain that more restrictive conditions are not necessary for either DFSs or for general OQEC codes. This is because the effective noise that can arise inside the code as a result of imperfect initialization is such that it can only increase the fidelity of an imperfectly encoded state with a perfectly encoded one.

We investigate the generation of quantum operations for one-qubit systems under classical Markovian noise with a $1/f^{\alpha }$ power spectrum, where $2>\alpha >0$. We present an efficient way to approximate the noise with a discrete multistate Markovian fluctuator. With this method, the average temporal evolution of the qubit state operator under $1/f^{\alpha }$ noise can be feasibly determined from recently derived deterministic master equations. We obtain qubit operations such as quantum memory and the NOT gate to high fidelity by a gradient-based optimization algorithm. For the NOT gate, the computed fidelities are qualitatively similar to those obtained earlier for random telegraph noise. In the case of quantum memory, however, we observe a nonmonotonic dependency of the fidelity on the operation time, yielding a natural access rate of the memory.

Noble gas-halogen complexes form the basis of possible excimer lasers. Electron collisions are investigated with the prototypical neon fluoride molecule as a function of internuclear separation. The study concentrates on the four states making up the excimer system: The low-lying $X{{}^2\Sigma }^{+}$ and $A{}^2\Pi$ repulsive states and the high-lying $1{{}^2\Sigma }^{+}$ and $2{}^2\Pi$ charge-transfer states which can support bound states. These states are represented using a configuration-interaction expansion which is shown to yield accurate potential energy curves and target properties. Elastic and inelastic collision cross sections for the four states are calculated ab initio using the $R$-matrix method. Special care is needed to treat the large dipole moments found for the charge-transfer states which are predicted to have electron collision cross sections almost two orders of magnitude bigger than the lower states. Differential and momentum transfer cross sections are also considered for the electron impact on the repulsive ground state. Rate constants for electron deexcitation of the excimer states of NeF have been calculated for electron temperature corresponding up to 10 eV. The superelastic processes are dominated by the $1{{}^2\Sigma }^{+}\to X{{}^2\Sigma }^{+}$ transition with thermal rate constant of $\left(2–5\right)\times {10}^{-9}{\text{cm}}^3{\text{s}}^{-1}$ in the entire range of electron temperature considered.

Rate coefficients for dissociative recombination (DR), dissociative excitation (DE), and vibrational excitation between the helium dimer ion ${}^4\mathrm{He}_2{}^{+}$ and electrons from a few meV up to 40 eV were measured using fast (3.8 and 8.3 MeV) ion beams stored for up to 85 s. Vibrational relaxation to greater than $95\%$ in the $v=0$ level was achieved by collisions with cold electrons over 50 s. Low-energy, strongly $v$-dependent DR rate coefficients are given for $v=0$, 1, and $\ge 2$. The rate coefficients at higher energies for $v=0$, with DR and DE given on an absolute scale, are compared to results from recent wave-packet calculations on the fast dissociation dynamics of the doubly excited helium dimer, where the three processes occur as competing reaction channels. Also given are rate coefficients for vibrationally superelastic electron collisions at near 10 meV average energy and the approximate vibrational excitation cross section for fast collisions with the residual gas.

The energy dependence of the fluorescence intensity from the $4p^4\left({}^{1}D\right)5p$ states of Kr was studied experimentally across the $3d_{5/2}^{-1}5p$, $3d_{3/2}^{-1}5p$, and $3d_{5/2}^{-1}6p$ resonances. The results of multiconfiguration Dirac-Fock calculations were compared with the measurements and with earlier calculations. The calculated interference effects in the resonant Auger process were found to be very sensitive to the initial state configuration interaction. The addition of the $7p$ orbital in the wave functions did not improve the agreement between experiment and calculation. The effects of cascade processes were also considered with the help of Hartree-Fock calculations.

Guided transmission of highly charged ions through nanocapillaries in insulating PET polymers was investigated. Samples with highly parallel capillaries were used to study the ion guiding with a variety of ionic species, such as ${\text{Ne}}^{7+}$, ${\text{Ne}}^{9+}$, ${\text{Ar}}^{9+}$, ${\text{Ar}}^{13+}$, and ${\text{Xe}}^{25+}$. The incident energy was varied within the range of $3-40$ keV. The fraction of transmitted ions was measured as a function of the capillary tilt angle. The results are used to evaluate the guiding angle, which is a measure of the guiding power specifying the ability of a material to guide ions. Moreover, the angular profile of the transmitted ions was studied as a function of their energy and charge state. The profile width and the guiding angle were found to follow the same scaling law indicating that they are both determined by the main charge patch in the entrance region of the capillary.

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one-, two-, and three-dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-antivortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.

We present a fully analytical solution of the dynamics of two strongly driven atoms resonantly coupled to a dissipative cavity field mode. We show that an initial atom-atom entanglement cannot be increased. In fact, the atomic Hilbert space divides into two subspaces, one of which is decoherence free so that the initial atomic entanglement remains available for applications, even in presence of a low enough atomic decay rate. In the other subspace a measure of entanglement, decoherence, and also purity, are described by a similar functional behavior that can be monitored by joint atomic measurements. Furthermore, we show the possible generation of Schrödinger-cat-like states for the whole system in the transient regime, as well as of entanglement for the cavity field and the atom-atom subsystems conditioned by measurements on the complementary subsystem.

We investigate deflections, spatial entanglement, and localization of an atomic beam due to its interaction with two modes of a standing electromagnetic field in an optical cavity. It is demonstrated that the deflection properties of an atom passing through two crossed standing light waves are crucially modified when photon-number correlated states of light are used instead of independent waves. Depending on the atom-light interaction scheme, various periodic two-dimensional patterns in a subwavelength regime are reported.

Direct characterization of quantum dynamics (DCQD) introduced by Mohseni and Lidar [Phys. Rev. Lett. 97, 170501 (2006)] offers an effective way for estimation of quantum dynamical systems. Employing single-photon two-qubit states, we experimentally implement DCQD of one-qubit dynamics. The requirement of two-body interactions is thus eliminated such that the algorithm can be realized more conveniently. Both DCQD and standard quantum process tomography (SQPT) measurements are performed for several processes. The data from both methods show good agreement. Although the average process fidelities of the data obtained via DCQD are a little lower than that of SQPT, the number of experimental configurations is quadratically reduced evidencing the quadratic advantage of DCQD scheme. Partial information of the quantum dynamics can also be directly extracted via DCQD with fewer measurements.

An interesting monogamy equation with the form of the Pythagorean theorem is found for $2\otimes 2\otimes n$-dimensional pure states, which reveals the relation among bipartite concurrence, concurrence of assistance, and genuine tripartite entanglement. At the same time, a genuine tripartite entanglement monotone as a generalization of 3-tangle is naturally obtained for $(2\otimes 2\otimes n)$-dimensional pure states in terms of a distinct idea. For mixed states, the monogamy equation is reduced to a monogamy inequality. Both results for tripartite quantum states can be employed to multipartite quantum states.

We investigate the quantum decoherence of frequency and polarization variables of photons via polarization mode dispersion in optical fibers. By observing the analogy between the propagation equation of the field and the Schrödinger equation, we develop a master equation under Markovian approximation and analytically solve for the field density matrix. We identify distinct decay behaviors for the polarization and frequency variables for single-photon and two-photon states. For the single-photon case, purity functions indicate that complete decoherence for each variable is possible only for infinite fiber length. For entangled two-photon states passing through separate fibers, entanglement associated with each variable can be completely destroyed after characteristic finite propagation distances. In particular, we show that frequency disentanglement is independent of the initial polarization status. For propagation of two photons in a common fiber, the evolution of a polarization singlet state is addressed. We show that while complete polarization disentanglement occurs at a finite propagation distance, frequency entanglement could survive at any finite distance for Gaussian states.

In a previous publication, procedures were proposed for unambiguously extracting amplitudes for single and double ionization from a time-dependent wave packet by effectively propagating for an infinite time following a radiation pulse. Here we demonstrate the accuracy and utility of those methods for describing two-photon single and one-photon double ionization of helium. In particular it is shown how narrow features corresponding to autoionizing states are easily resolved with these methods.

We present experimental and theoretical fully differential cross sections for single ionization by fast, 1-keV $(v=8.6\text{a.u.})$ electron impact. The cross sections were measured using a momentum imaging technique for electrons and ions (reaction microscope), which covers a large fraction of the emission angles for emitted low-energy electrons $(E<15\mathrm{eV})$ and a wide range of scattering angles. Therefore comprehensive data sets are obtained for ionizing collisions at small relative momentum and energy transfer from the projectile to the target system. The experimental data are compared with predictions from several state-of-the-art theoretical calculations. At this high impact energy the calculated cross section for electron emission out of the scattering plane appears to be particularly sensitive to the treatment of higher orders in the projectile-target interaction within perturbative models.

We experimentally measure the kinetic energy and angular distributions of fragment ions of ${\mathrm{N}}_2$ as a function of $820\mathrm{nm}$ femtosecond laser intensity. The angular dependence of fragments directly maps to the orbital symmetry of transient molecular ions. According to the observed energy and angular distribution of different charged fragment ions, reasonable fragmentation channels are proposed. Both the asymmetric channel (3, 1) and the symmetric channel (2, 2) are supposed to be generated directly from (2, 1) by different ionization mechanisms.

We suggest that a box shape trap enables one to observe intrinsic properties of the repulsive Hubbard model in a fixed doping in contrast to the conventional harmonic trap bringing about spatial variations of atom density profiles. In order to predict atomic density profile under the box trap, we apply the directly extended density-matrix renormalization-group method to a four-leg repulsive Hubbard model with the open boundary condition. Consequently, we find that stripe formation is universal in a low-hole-doping range and the stripe sensitively changes its structure with variations of $U∕t$ and the doping rate. A remarkable change is that a stripe formed by a hole pair turns to one by a bihole pair when entering a limited strong $U∕t$ range. Furthermore, a systematic calculation reveals that the Hubbard model shows a change from the stripe to the Friedel like oscillation with increasing the doping rate.

We investigate the interplay dynamics of a cavity QED system, where the two-level atoms are trapped in a double-well potential, and the cavity mode, with a frequency largely detuned from the atomic level splitting, is driven by a probe laser. The interaction between the center-of-mass motion of the atoms and the cavity mode is induced by the position-dependent atom-field coupling. The dynamics of the system is characterized by two distinct time scales, the inverse of the atomic interwell tunneling rate and the inverse of the cavity loss rate. The system shows drastically different (quasi)steady behaviors in the short- and long-time intervals, and the detection of the statistics of atom number distribution from the transmission spectra is available only in the short-time interval.

Numerical simulations are performed for a rotating two-species Bose-Einstein condensate confined by a harmonic potential. The particle numbers of the two species are unequal. When the rotational speed exceeds a critical value, the majority species reside in the center of the potential while the minority species is pushed out to the outskirts, forming a giant vortex hole that contains the majority species. An annular skyrmion forms at the interface of the two species.

Various families of charge-1 vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either focusing or defocusing), infinite vortex families are found. All these families do not bifurcate from Bloch bands; rather, they turn around before reaching the edges of the Bloch bands. It is further revealed that vortices with drastically different topological shapes can belong to the same vortex family, which is quite surprising.

The spatial dependence of the cavity modified spontaneous emission of an atom in a cavity with finite output coupling loss is analyzed. The analysis is based on the quantized nonorthogonal eigenmodes defined by the open cavity boundary condition. The spatial dependence of the Rabi oscillation frequency in the strong coupling regime is also analyzed. For spontaneous decay, the spatial dependence is a sinusoidal modulation on top of a dc value, where the interaction with all cavity modes is considered. For Rabi oscillations, where the atom interacts mainly with only one cavity mode, the oscillation frequency also has a sinusoidal spatial dependence.