Computational Techniques for Optimal Control of Quantum System

The control of matter and energy at a fundamental level will be a cornerstone of new technologies for years to come. This idea is exemplified in a distilled form by controlling the dynamics of quantum mechanical systems via a time—dependent potential. The contributions detailed within this work focus on the computational aspects of formulating and solving quantum control problems efficiently. The accurate numerical computation of optimal controls of infinite—dimensional quantum control problems is a very difficult task that requires to take into account the features of the original infinite—dimensional problem. An important issue is the choice of the functional space where the minimization process is defined. A systematic comparison of L2— versus H1—based minimization shows that the choice of the appropriate functional space matters and has many consequences in the implementation of some optimization techniques. vi A matrix—free cascadic BFGS algorithm is introduced in the L2 and H1 settings and it is demonstrated that the choice of H1 over L2 results in a substantial performance and robustness increase. A comparison between optimal control resulting from function space minimization and the control obtained by minimization over Chebyshev and POD basis function coefficients is presented. A theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nano electronic devices and quantum computing. This method is based on a reduced Hessian Krylov—Newton scheme applied to a norm—preserving discrete model of a dipole quantum control problem. The use of second—order numerical methods for solving the control problem is justified proving existence of optimal solutions and analyzing first— and second—order optimality conditions. Criteria for the discretization of the non—convex optimization problem and for the formulation of the Hessian are given to ensure accurate gradients and a symmetric Hessian. Robustness of the Newton approach is obtained using a globalization strategy with a robust line- search procedure. Results of numerical experiments demonstrate that the Newton approach presented in this dissertation is able to provide fast and accurate controls for high—energy state transitions. Control of bound—to—bound and bound—to—continuum transitions in open quantum systems and vector field control of two—dimensional systems is presented. An efficient space—time spectral discretization of the time—dependent Schrödinger equation and preconditioning strategy for a fast approximate solution with Krylov methods is outlined

A study of the s-process in the carbon-rich post-AGB stars IRAS06530-0213 and IRAS08143-4406 on the basis of VLT-UVES spectra

In an effort to extend the still limited sample of s-process enriched post-AGB stars, high-resolution, high signal-to-noise VLT+UVES spectra of the optical counterparts of the infrared sources IRAS06530-0213 and IRAS08143-4406 were analysed. The objects are moderately metal deficient by [Fe/H]=-0.5 and -0.4 respectively, carbon-rich and, above all, heavily s-process enhanced with a [ls/Fe] of 1.8 and 1.5 respectively. Especially the spectrum of IRAS06530-0213 is dominated by transitions of s-process species, and therefore resembling the spectrum of IRAS05341+0852, the most s-process enriched object known so far. The two objects are chemically very similar to the 21micron objects discussed in Van Winckel & Reyniers (2000). A homogeneous comparison with the results of these objects reveals that the relation between the third dredge-up efficiency and the neutron nucleosynthesis efficiency found for the 21micron objects, is further strengthened. On the other hand, a detailed comparison with the predictions of the latest AGB models indicates that the observed spread in nucleosynthesis efficiency is certainly intrinsic, and proves that different C-13 pockets are needed for stars with comparable mass and metallicity to explain their abundances.Comment: 14 pages, 10 figures, accepted for publication in A&A; Table 4 is available at ftp://ftp.ster.kuleuven.ac.be/dist/maarten/filescds/ pending upload to CD

Optimal control of number squeezing in trapped Bose-Einstein condensates

We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.Comment: 17 pages, 21 figures, minor correction

Mid-Infrared Imaging and Modelling of the Dust Shell around Post-AGB star HD 187885 (IRAS 19500-1709)

We present 10 and 20 micron images of IRAS 19500-1709 taken with the mid-infrared camera, OSCIR, mounted on the Gemini North Telescope. We use a 2-D dust radiation transport code to fit the spectral energy distribution from UV to sub-mm wavelengths and to simulate the images.Comment: 4 pages, 5 figures. To appear in "Asymmetric Planetary Nebulae III", eds. M.Meixner, J.Kastner, N.Soker & B.Balick. 2004, ASP Conference Serie

Post-main sequence evolution of A star debris discs

While the population of main sequence debris discs is well constrained, little is known about debris discs around evolved stars. This paper provides a theoretical framework considering the effects of stellar evolution on debris discs, particularly the production and loss of dust within them. Here we repeat a steady state model fit to disc evolution statistics for main sequence A stars, this time using realistic grain optical properties, then evolve that population to consider its detectability at later epochs. Our model predicts that debris discs around giant stars are harder to detect than on the main sequence because radiation pressure is more effective at removing small dust around higher luminosity stars. Just 12% of first ascent giants within 100pc are predicted to have discs detectable with Herschel at 160um. However this is subject to the uncertain effect of sublimation on the disc, which we propose can thus be constrained with such observations. Our model also finds that the rapid decline in stellar luminosity results in only very young white dwarfs having luminous discs. As such systems are on average at larger distances they are hard to detect, but we predict that the stellar parameters most likely to yield a disc detection are a white dwarf at 200pc with cooling age of 0.1Myr, in line with observations of the Helix Nebula. Our model does not predict close-in (<0.01AU) dust, as observed for some white dwarfs, however we find that stellar wind drag leaves significant mass (~10^{-2}Msolar), in bodies up to ~10m in diameter, inside the disc at the end of the AGB phase which may replenish these discs

Quantum control theory for coupled 2-electron dynamics in quantum dots

We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrodinger equation is solved nonperturbatively in conjunction with several quantum control strategies. This results in optimized electric pulses in the THz regime which can populate combinations of states with very short transition times. The speedup compared to intuitively constructed pulses is an order of magnitude. We furthermore make use of optimized pulse control in the simulation of an experimental preparation of the molecular quantum dot system. It is shown that exclusive population of certain excited states leads to a complete suppression of spin dephasing, as was indicated in Nepstad et al. [Phys. Rev. B 77, 125315 (2008)].Comment: 24 pages, 9 figure

Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains

We describe a multidomain spectral-tau method for solving the three-dimensional helically reduced wave equation on the type of two-center domain that arises when modeling compact binary objects in astrophysical applications. A global two-center domain may arise as the union of Cartesian blocks, cylindrical shells, and inner and outer spherical shells. For each such subdomain, our key objective is to realize certain (differential and multiplication) physical-space operators as matrices acting on the corresponding set of modal coefficients. We achieve sparse banded realizations through the integration "preconditioning" of Coutsias, Hagstrom, Hesthaven, and Torres. Since ours is the first three-dimensional multidomain implementation of the technique, we focus on the issue of convergence for the global solver, here the alternating Schwarz method accelerated by GMRES. Our methods may prove relevant for numerical solution of other mixed-type or elliptic problems, and in particular for the generation of initial data in general relativity.Comment: 37 pages, 3 figures, 12 table

Multidomain Spectral Method for the Helically Reduced Wave Equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the "eigenspectral method." Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.Comment: 57 pages, 11 figures, uses elsart.cls. Final version includes revisions based on referee reports and has two extra figure

The Halo and Rings of the Planetary Nebula NGC 40 in the Mid-Infrared

We present imaging and spectroscopy of NGC 40 acquired using the Spitzer Space Telescope (Spitzer), and the Infrared Space observatory (ISO). These are used to investigate the nature of emission from the central nebular shell, from the nebular halo, and from the associated circumnebular rings. It is pointed out that a variety of mechanisms may contribute to the mid-infrared (MIR) fluxes, and there is evidence for a cool dust continuum, strong ionic transitions, and appreciable emission by polycyclic aromatic hydrocarbons (PAHs). Prior observations at shorter wavelengths also indicate the presence of warmer grains, and the possible contribution of H2 transitions. It is suggested that an apparent jet-like structure to the NE of the halo represents one of the many emission spokes that permeate the shell. The spokes are likely to be caused by the percolation of UV photons through a clumpy interior shell, whilst the jet-like feature is enhanced due to locally elevated electron densities; a result of interaction between NGC 40 and the interstellar medium. It is finally noted that the presence of the PAH, 21 microns and 30 microns spectral features testifies to appreciable C/O ratios within the main nebular shell. Such a result is consistent with abundance determinations using collisionally excited lines, but not with those determined using optical recombination linesComment: 13 pages, 8 figures, Accepted for publication in MNRAS. 37 pages in arXi