We study time-minimum optimal control for a class of quantum two-dimensional dissipative systems whose dynamics are governed by the Lindblad equation and where control inputs acts only in the Hamiltonian. The dynamics of the control system are analyzed as a bi-linear control system on the Bloch ball after a decoupling of such dynamics into intra- and inter-unitary orbits. The (singular) control problem consists of finding a trajectory of the state variables solving a radial equation in the minimum amount of time, starting at the completely mixed state and ending at the state with the maximum achievable purity. The boundary value problem determined by the time-minimum singular optimal control problem is studied numerically. If controls are unbounded, simulations show that multiple local minimal solutions might exist. To find the unique globally minimal solution, we must repeat the algorithm for various initial conditions and find the best solution out of all of the candidates. If controls are bounded, optimal controls are given by bang-bang controls using the Pontryagin minimum principle. Using a switching map we construct optimal solutions consisting of singular arcs. If controls are bounded, the analysis of our model also implies classical analysis done previously for this problem.

In this paper, we demonstrate that the dynamics of an n-dimensional Lindblad control system can be separated into its inter- and intraorbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density operator spectra, where projectors representing the eigenspaces are viewed as control variables. The local controllability properties of this control system can be analyzed when the control set of projectors is limited to a finite subset. In particular, there is a natural finite subset of n! projector tuples that are effective for low-purity orbits.

In this paper, we study the stationary orbits of quantum Lindblad systems. We show that they can be characterized in terms of trees and forests on a directed graph with edge weights that depend on the Lindblad operators and the eigenbasis of the density operator. For a certain class of typical Lindblad systems, this characterization can be used to find the asymptotic end-states. There is a unique end-state for each basin of the graph (the strongly connected components with no outgoing edges). In most cases, every asymptotic end-state must be a linear combination thereof, but we prove necessary and sufficient conditions under which symmetry in the Lindblad and Hamiltonian operators hide other end-states or stable oscillations between end-states.

The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equation. The controls appear only in the Hamiltonian. Using recent results regarding the decoupling of such dissipative dynamics into intra- and inter-unitary orbits, we transform the control system into a bi-linear control system on the Bloch ball (the unitary sphere together with its interior). We then design a numerical algorithm to construct an optimal path to achieve a desired point given initial states close to the origin (the singular point) of the Bloch ball. This is done both for the minimum-time and minimum-energy control problems.

In this paper, we demonstrate that the dynamics of an $n$-dimensional Lindblad control system can be separated into its inter- and intra-orbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density operator spectra, where the flag representing the eigenspaces is viewed as a control variable. The local controllability properties of this control system can be analyzed when the control-set of flags is limited to a finite subset. In particular, there is a natural finite subset of $n!$ flags that are effective for low-purity orbits.

In this paper, we demonstrate that the dynamics of an n-dimensional Lindblad control system can be separated into its interand intra-orbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density operator spectra, where projectors representing the eigenspaces are viewed as control variables. The local controllability properties of this control system can be analyzed when the control-set of projectors is limited to a finite subset. In particular, there is a natural finite subset of n! projector-tuples that are effective for low-purity orbits.

This paper investigates the fast Hamiltonian control of n = 2 density operators by continuously varying the flag (i.e., the eigenspaces) as one moves away from the completely mixed state. In general, the critical points and zeros of the purity derivative can only be solved analytically in the limit of minimal purity. We derive differential equations that maintain these features as the purity increases. In particular, there is a thread of points in the Bloch ball that locally maximizes the purity derivative and a corresponding thread that minimizes it. Additionally, we show there is a closed surface of points inside of which the purity derivative is positive and outside of which is negative. We argue that this approach may be useful in studying higher-dimensional systems.

Control of quantum dissipative systems can be challenging because control variables are typically part of the system Hamiltonian, which can only generate motion along unitary orbits of the system. To transit between orbits, one must harness the dissipation super-operator. To separate the inter-orbit dynamics from the Hamiltonian dynamics for a generic two-dimensional system, we project the Lindblad master equation onto the set of spectra of the density matrix, and we interpret the location along the orbit to be a new control variable. The resulting differential equation allows us to analyze the controllability of a general two-dimensional Lindblad system, particularly systems where the dissipative term has an anti-symmetric part. We extend this to categorize the possible purifiable systems in two dimensions.

We present experimental and theoretical results for the changes in the optical-plasmon resonance of gold-nanoparticle dimers immobilized on a surface when coated with an organic dielectric material. The plasmon band of a nanoparticle dimer shifts to a higher wavelength when the distance between neighboring particles is decreased, and a well-separated second peak appears. This phenomenon is called cross-talk. We find that an organic coating lets cross-talk start at larger separation distances than for uncoated dimers by bridging the gap between immobilized nanoparticles (creating optical clusters). We study this optical clustering effect as a function of the polarization of the applied light, of the inter-particle distance, of the surrounding environment, and of the optical properties of the coating layer. Theoretical discrete-dipole approximation calculations support the experimental absorption spectroscopy results of gold nanoparticles on glass substrates and on optical waveguides.

Various calix[4]arene derivatives, fixed in the cone conformation by decylether groups and functionalized at their wide rim by urea residues, were synthesized. In two compounds (,) sulfur functions were attached to the urea groups via different spacers in order to allow binding to metal surfaces. While they exist as single molecules in polar solvents, tetraurea calix[4]arenes of this type () combine to form dimeric capsules in aprotic, apolar solvents. A solvent molecule is usually included in such a capsule, if no guest with a higher affinity is present. In the presence of an equimolar amount of the tetratosylurea, the exclusive formation of heterodimers, consisting of one molecule of and, is observed. The homo- and heterodimerization of the newly prepared derivatives, were studied by 1H NMR to establish the conditions under which they exhibit the desired dimerization behaviour. Self-assembled monolayers (SAMs) were formed using the single calix[4]arenes, and the heterodimeric capsules. Chloroform, dichloromethane and ferrocenium cations were used as guests in these immobilized heterodimeric capsules. The particular supramolecular architecture of the heterodimers should ensure that, after the immobilization on the metal surface, decomposition of the capsules and release or exchange of the guest is impossible or at least hindered. The self-assembly process and the stability of SAMs formed by capsules filled with ferrocenium cations in electrolyte solutions were tested with surface plasmon spectroscopy. The inclusion of guests, such as dichloromethane or ferrocenium, in the immobilized capsules were confirmed by classical surface plasmon spectroscopy, by gold nanoparticle absorption spectroscopy and by time-of flight secondary ion mass spectrometry (ToF-SIMS). The film stability and quality was tested by cyclic voltammetry.