The propagation and interaction of two bulk solitary waves, termed nematicons, in a nematic liquid crystal are studied in the local limit. These two nematicons are based on light of two different wavelengths, and so are referred to as two color nematicons. Under suitable boundary conditions the two nematicon beams of different wavelengths can couple, creating a self-localized vector solitary wave. Due to the different diffraction coefficients and indices of refraction for each wavelength, the vector solitary wave shows walk-off. Using a suitable trial function in an averaged Lagrangian formulation of the two color nematicon equations, approximate equations governing the evolution of the two color nematicons are derived. These approximate equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found for the walk-off as given by these approximate equations and by full numerical solutions of the nematicon equations. It is shown that the inclusion of the effect of the shed diffractive radiation is vital in order to obtain this excellent agreement.

The temporal development of extended nonlinear modes of a one-dimensional photonic crystal during the build-up of the nonlinearity is experimentally investigated. For this a prism coupling setup is used, which allows for a direct comparison of linear and nonlinear photonic band structures. The experimental results are compared with numerical calculations which make use of the Floquet-Bloch approach and the finite difference approximation.

We demonstrate high efficiency, broadband coupling between photonic crystal waveguides and photonic crystal fibers (PCFs) using simple two-dimensional design models. We demonstrate an effective large-bandwidth small-footprint beam collimator for light exiting a two-dimensional subwavelength scale photonic crystal waveguide consisting of an air core. This collimator relies on destructive interference between diffracted light from the mouth of the waveguide and the light emitted by surface resonators. We demonstrate efficient coupling between air-core photonic crystal waveguides and various two-dimensional models of photonic crystal fibers. A hollow-core photonic crystal fiber, described by an air defect with a Bragg stack cladding on either side, yields a coupling efficiency of better than 94% over a bandwidth of 25% of the center frequency, with peak transmittance exceeding 98%. A small-mode-area PCF, consisting of a subwavelength solid core attached by spokes to the PCF cladding, is modeled by a slab waveguide. In this latter case, we demonstrate coupling efficiency better than 94% over a bandwidth of 17%, with peak transmittance exceeding 99%. Combining collimation at the photonic crystal exit port and a nonadiabatic taper in a small-mode-area PCF, we obtain over 98% coupling efficiency over a bandwidth of $135\mathrm{nm}$ centered at a wavelength of $1.5\mu \mathrm{m}$. These results provide valuable paradigms for efficient transfer of optical information between photonic band gap (PBG) microcircuits and PCF-enabled telecommunication networks.

We study quantum systems with broken symmetry that can be modeled as cyclic three-level atoms with coexisting one- and two-photon transitions. They can be selectively optically excited to any state. As an example, we show that left- and right-handed chiral molecules starting in the same initial states can evolve into different final states by a purely dynamic transfer process. That means that left- and right-handed molecules can be distinguished purely dynamically.

Two kinds of Bell-state diagonal (BSD) entanglement witnesses (EWs) are constructed by using the algebra of Dirac $\gamma$ matrices in a space-time of arbitrary dimension $d$, where the first kind can detect some BSD relativistic and nonrelativistic $m$-partite multispinor bound entangled states in a Hilbert space of dimension $2^{m\lfloor d/2\rfloor }$, including the bipartite Bell-type and isoconcurrence-type states in four-dimensional space-time $\left(d=4\right)$. By using the connection between the Hilbert-Schmidt measure and the optimal EWs associated with the states, it is shown that, as far as the spin quantum correlations are concerned, the amount of entanglement is not a relativistic scalar and has no invariant meaning. The introduced EWs are manipulated via linear programming (LP) and can be solved exactly by using the simplex method. The decomposability or nondecomposability of these EWs is investigated, the region of nondecomposable EWs of the first kind is partially determined and it is shown that, all of the EWs of the second kind are decomposable. These EWs have the property that in bipartite systems they can determine the region of separable states, i.e., bipartite nondetectable density matrices of the same type as the EWs of the first kind are necessarily separable. Also, multispinor EWs with nonpolygon feasible regions are provided, where the problem is solved by approximate LP, and in contrast to the exactly manipulatable EWs, both the first and second kinds of the optimal approximate EWs can detect some bound entangled states.

We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace-preserving constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality.

Numerical solutions of the stochastic Schrödinger equation given by quantum state diffusion approach to open quantum systems is used to study dynamics of nearest neighbor qubit pairs in systems of small number of qubits on rings with Heisenberg and transverse Ising interaction and under the influence of the thermal environment. In particular, the dependence of the pair entanglement dynamics on the temperature, number of qubits, the type of coupling, and the type of entanglement in the initial state was analyzed for systems of up to $N=10$ qubits. Periodic recurrence of relatively large values of the pair entanglement with dumping due to decoherence by the thermal noise is observed. It is concluded that the pair entanglement in rings with transverse Ising coupling and prepared in a separable initial state is the most resistant on the decoherence effects of the thermal noise, compared to the Heisenberg coupling or initial states with different types of entanglement.

The two-electron QED contributions to the ground-state binding energy of ${\mathrm{Kr}}^{34+}$ ions have been determined in two independent experiments performed with electron beam ion traps (EBIT) in Heidelberg (HD) and Tokyo (BT, Belfast-Tokyo collaboration). X rays arising from radiative recombination (RR) of free electrons to the ground state of initially bare ${\mathrm{Kr}}^{36+}$ and hydrogenlike ${\mathrm{Kr}}^{35+}$ ions were observed as a function of the interacting electron energy. The $K$ edge absorption by thin Eu and W foils provided fixed photon energy references used to measure the difference in binding energy $\Delta E_{2e}$ between the H- and He-like Kr ions (${\mathrm{Kr}}^{35+}$ and ${\mathrm{Kr}}^{34+}$, respectively). The two values agree well, yielding a final result of $\Delta E_{2e}=641.8\pm 1.7\mathrm{eV}$, confirming recent results of rigorous QED calculations. This accuracy is just of the order required to access screened radiative QED contributions.

Positronium (Ps)-He scattering presents one of the few opportunities for both theory and experiment to tackle the fundamental interactions of Ps with ordinary matter. Below the dissociation energy of $6.8\mathrm{eV}$, experimental and theoretical work has struggled to find agreement on the strength of this interaction as measured by the momentum-transfer cross section $\left({\sigma }_m\right)$. Here, we present work utilizing the Doppler broadening technique with an age-momentum correlation apparatus. This work demonstrates a strong energy dependence for this cross section at energies below $1\mathrm{eV}$ and is consistent with previous experimental results.

We discuss the occupation number correlations in an ultracold system of interacting fermionic atoms. For a system with a special energy-level distribution, viz. two multiply degenerate levels, explicit expressions for the correlation functions are derived in a canonical approach using the exact ground state wave function of the reduced BCS Hamiltonian. We evaluate the correlators numerically for different interaction strengths and find analytical expressions in some limiting cases. Due to the underlying fermionic nature of the pairs the occupations are predominantly anticorrelated and their statistics is a multinomial distribution.

Analysis of the effects of the biased noise fluctuations on the quantum features and statistical properties of the cavity radiation of the two-photon phase-sensitive laser is presented. It turns out that the biased noise fluctuations that enter the cavity via the vibrations of the wall enhance the atomic coherence responsible for the entanglement of the cavity radiation due to the phase sensitivity of the involved cascade transitions. The two-mode squeezing of the superimposed radiation, entanglement of the cavity radiation, and mean number of the photon pairs are found to increase with the rate at which the atoms are injected into the cavity. The two-mode squeezing increases with the intensity of the biased noise fluctuations, but the mean number of the photon pairs decreases. Even then, it is possible to produce quite intense robust continuous variable entanglement in this scheme which is believed to be a motivation for further practical scrutiny. Moreover, the superimposed radiation exhibits super-Poissonian photon statistics with no finite joint probability for getting more photons in mode $b$ than mode $a$.

The cavity-mediated adiabatic transfer (CMAT), which is the physical basis of several implementations of two-qubit gates, is investigated analytically. An upper bound for the success probability of CMAT in the presence of atomic spontaneous emission and cavity photon loss is given by a simple function of only the so-called critical atom number. Moreover, a situation which realizes the upper bound is found, and this is verified by numerical simulation. It also turns out from numerical simulation that standard Gaussian pulses can achieve the success probability close to the upper bound. That is, the standard Gaussian pulses are almost optimal for CMAT.

We introduce a method for analyzing ground-state properties of quantum many-body systems, based on the characterization of separability and entanglement by single subsystem unitary operations. We apply the method to the study of the ground-state structure of several interacting spin-1/2 models, described by Hamiltonians with different degrees of symmetry. We show that the approach based on single-qubit unitary operations allows us to introduce “entanglement excitation energies,” a set of observables that can characterize ground-state properties, including the quantification of single-site entanglement and the determination of quantum critical points. The formalism allows us to identify the existence and location of factorization points, and a purely quantum “transition of entanglement” that occurs at the approach of factorization. This kind of quantum transition is characterized by a diverging ratio of excitation energies associated with single-qubit unitary operations.

A numerically solvable two-dimensional model introduced by the authors [Phys. Rev. A 73, 032721 (2006)] is used to investigate the validity of the nonlocal approximation to the dynamics of resonant collisions of electrons with diatomic molecules. The nonlocal approximation to this model is derived in detail, all underlying assumptions are specified, and explicit expressions for the resonant and nonresonant (background) $T$ matrix for the studied processes are given. Different choices of the so-called discrete state, which fully determines the nonlocal approximation, are discussed, and it is shown that a physical choice of this state can in general give poorer results than other choices that minimize the nonadiabatic effects and/or the background terms of the $T$ matrix. Background contributions to the $T$ matrix, which are usually not considered in the resonant theory of electron-molecule collisions, can contribute significantly not only to elastic but also to vibrational excitation cross sections. Dissociative attachment cross sections, however, are found to be properly described in the nonlocal model with any choice of discrete state that minimizes the importance of nonadiabatic effects and goes to the proper limit at large internuclear separation.

We consider a strongly driven two-level (spin) system, with a periodic external field that induces a sequence of avoided level crossings. The spin system interacts with a bosonic reservoir which leads to decoherence. A Markovian dynamical equation is introduced without relying on the rotating wave approximation in the system-external field interaction. We show that the time evolution of the two-level system is directed toward an incoherent sum of periodic Floquet states regardless of the initial state and even the type of the coupling to the environment. Analyzing the time scale of approaching these time-dependent pointer states, information can be deduced concerning the nature and strength of the system-environment coupling. The inversion as a function of the external field is usually multivalued, and the form of these hysteresis curves is qualitatively different for low and high temperatures. For moderate temperatures we found that the series of Landau-Zener-Stückelberg-type transitions still can be used for state preparation, regardless of the decoherence rate. Possible applications include quantum information processing and molecular nanomagnets.

We show that optical spring damping in an optomechanical resonator can be enhanced by injecting a phase delay in the laser frequency-locking servo to rotate the real and imaginary components of the optical spring constant. This enhances damping at the expense of optical rigidity. We demonstrate enhanced parametric damping which reduces the $Q$ factor of a 0.1-kg-scale resonator from $1.3\times {10}^5$ to $6.5\times {10}^3$. By using this technique adequate optical spring damping can be obtained to damp parametric instability predicted for advanced laser interferometer gravitational-wave detectors.

Using the closed $F_g\to F_e=F_g+1$ $D2$ line transition of Rb atoms, we report experimental and numerical evidence of influence of additional transverse magnetic field when examining electromagnetically induced absorption (EIA) in the Hanle configuration. The effect was analyzed with two directions of additional magnetic field and in the cases of excitation with linear, elliptical, and circular laser light polarization. The transverse magnetic field brings substantial differences in the resonance line shape, amplitude, and width. Our theoretical model includes Doppler broadening. Numerical solutions of our theoretical model are in good agreement with experimental results. This analysis points out the importance of the presence of stray magnetic fields when studying EIA.

We study various distancelike entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement, and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal local operations and classical communication discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.

Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is analogous to quantum computation but does not involve quantum mechanics. We discuss in detail similarities and differences between the two approaches and illustrate the formulas by explicit geometric objects where multivector versions of the Bell-basis, Greenberger-Horne-Zeilinger, and Hadamard states are visualized by means of colored oriented polylines.