Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Entanglement in the steady state of a collective-angular-momentum (Dicke) model

We model the behavior of an ion trap with all ions driven simultaneously and coupled collectively to a heat bath. The equations for this system are similar to the irreversible dynamics of a collective angular momentum system known as the Dicke model. We show how the steady state of the ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement. We calculate the entanglement of this steady state for two ions in the trap and in the case of more than two ions we calculate the entanglement between two ions by tracing over all the other ions. The entanglement in the steady state is a maximum for the parameter values corresponding roughly to a bifurcation of a fixed point in the corresponding semiclassical dynamics. We conjecture that this is a general mechanism for entanglement creation in driven dissipative quantum systems.

Calculation of bound and resonance states of HO2 for nonzero total angular momentum

Bound and resonance states of HO2 have been calculated quantum mechanically by the Lanczos homogeneous filter diagonalization method [Zhang and Smith, Phys. Chem. Chem. Phys. 3, 2282 (2001); J. Chem. Phys. 115, 5751 (2001)] for nonzero total angular momentum J = 1,2,3. For lower bound states, agreement between the results in this paper and previous work is quite satisfactory; while for high lying bound states and resonances these are the first reported results. A helicity quantum number V assignment (within the helicity conserving approximation) is performed and the results indicate that for lower bound states it is possible to assign the V quantum numbers unambiguously, but for resonances it is impossible to assign the V helicity quantum numbers due to strong mixing. In fact, for the high-lying bound states, the mixing has already appeared. These results indicate that the helicity conserving approximation is not good for the resonance state calculations and exact quantum calculations are needed to accurately describe the reaction dynamics for HO2 system. Analysis of the resonance widths shows that most of the resonances are overlapping and the interferences between them lead to large fluctuations from one resonance to another. In accord with the conclusions from earlier J = 0 calculations, this indicates that the dissociation of HO2 is essentially irregular. (C) 2003 American Institute of Physics.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

Chaotic dynamics of cold atoms in far-off-resonant donut beams

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y) plant for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos. [S1063-651X(99)03903-3].

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

Optically driven micromachine elements

We report on a proof of principle demonstration of an optically driven micromachine element. Optical angular momentum is transferred from a circularly polarized laser beam to a birefringent particle confined in an optical tweezers trap. The optical torque causes the particle to spin at up to 350 Hz, and this torque is harnessed to drive an optically trapped microfabricated structure. We describe a photolithographic method for producing the microstructures and show how a light driven motor could be used in a micromachine system. (C) 2001 American Institute of Physics.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

Prediction of absolute rate coefficients and product branching ratios for the C(P-3) plus allene reaction system

Complex chemical reactions in the gas phase can be decomposed into a network of elementary (e.g., unimolecular and bimolecular) steps which may involve multiple reactant channels, multiple intermediates, and multiple products. The modeling of such reactions involves describing the molecular species and their transformation by reaction at a detailed level. Here we focus on a detailed modeling of the C(P-3)+allene (C3H4) reaction, for which molecular beam experiments and theoretical calculations have previously been performed. In our previous calculations, product branching ratios for a nonrotating isomerizing unimolecular system were predicted. We extend the previous calculations to predict absolute unimolecular rate coefficients and branching ratios using microcanonical variational transition state theory (mu-VTST) with full energy and angular momentum resolution. Our calculation of the initial capture rate is facilitated by systematic ab initio potential energy surface calculations that describe the interaction potential between carbon and allene as a function of the angle of attack. Furthermore, the chemical kinetic scheme is enhanced to explicitly treat the entrance channels in terms of a predicted overall input flux and also to allow for the possibility of redissociation via the entrance channels. Thus, the computation of total bimolecular reaction rates and partial capture rates is now possible. (C) 2002 American Institute of Physics.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells-chloroplasts of Spinacia oleracea-in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.