Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Structural and optical properties of InAs/GaAs quantum structures

The goal of the thesis was to study fundamental structural and optical properties of InAs islands and In(Ga)As quantum rings. The research was carried out at the Department of Micro and Nanosciences of Helsinki University of Technology. A good surface quality can be essential for the potential applications in optoelectronic devices. For such device applications it is usually necessary to control size, density and arrangement of the islands. In order to study the dependence of the structural properties of the islands and the quantum rings on growth conditions, atomic force microscope was used. Obtained results reveal that the size and the density of the In(Ga)As quantum rings strongly depend on the growth temperature, the annealing time and the thickness of the partial capping layer. From obtained results it is possible to conclude that to get round shape islands and high density one has to use growth temperature of 500 ̊C. In the case of formation of In(Ga)As quantum rings the effect of mobility anisotropy is observed that so the shape of the rings is not symmetric. To exclude this effect it is preferable to use a higher annealing temperature of 570 ̊C. Optical properties were characterized by PL spectroscopy. PL emission was observed from buried InAs quantum dots and In(Ga)As quantum rings grown with different annealing time and temperature and covered with a various thickness of the partial capping layer.

Control and femtosecond time-resolved imaging of torsion in a chiral molecule

We study how the combination of long and short laser pulses can be used to induce torsion in an axially chiral biphenyl derivative (3,5-difluoro-3 ,5 -dibromo-4 -cyanobiphenyl). A long, with respect to the molecular rotational periods, elliptically polarized laser pulse produces 3D alignment of the molecules, and a linearly polarized short pulse initiates torsion about the stereogenic axis. The torsional motion is monitored in real-time by measuring the dihedral angle using femtosecond time-resolved Coulomb explosion imaging. Within the first 4 picoseconds (ps), torsion occurs with a period of 1.25 ps and an amplitude of 3◦ in excellent agreement with theoretical calculations. At larger times, the quantum states of the molecules describing the torsional motion dephase and an almost isotropic distribution of the dihedral angle is measured.We demonstrate an original application of covariance analysis of two-dimensional ion images to reveal strong correlations between specific ejected ionic fragments from Coulomb explosion. This technique strengthens our interpretation of the experimental data

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Categorical quantum computation

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Nonlinear Dynamics of Multiple Quantum Well Lasers: Chaos and Multistability

This thesis presents analytical and numerical results from studies based on the multiple quantum well laser rate equation model. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated.A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor lasers.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Optimal control theory for a unitary operation under dissipative evolution

We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iSWAP gate with superconducting qubits.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Engineering of 3D self-directed quantum dot ordering in multilayer InGaAs/GaAs nanostructures by means of flux gas composition

Lateral ordering of InGaAs quantum dots on the GaAs (001) surface has been achieved in earlier reports, resembling an anisotropic pattern. In this work, we present a method of breaking the anisotropy of ordered quantum dots (QDs) by changing the growth environment. We show experimentally that using As(2) molecules instead of As(4) as a background flux is efficient in controlling the diffusion of distant Ga adatoms to make it possible to produce isotropic ordering of InGaAs QDs over GaAs (001). The control of the lateral ordering of QDs under As(2) flux has enabled us to improve their optical properties. Our results are consistent with reported experimental and theoretical data for structure and diffusion on the GaAs surface.

Directed self-assembly of quantum structures by nanomechanical stamping using probe tips

We demonstrate that nanomechanically stamped substrates can be used as templates to pattern and direct the self-assembly of epitaxial quantum structures such as quantum dots. Diamond probe tips are used to indent or stamp the surface of GaAs( 100) to create nanoscale volumes of dislocation-mediated deformation, which alter the growth surface strain. These strained sites act to bias nucleation, hence allowing for selective growth of InAs quantum dots. Patterns of quantum dots are observed to form above the underlying nanostamped template. The strain state of the patterned structures is characterized by micro-Raman spectroscopy. The potential of using nanoprobe tips as a quantum dot nanofabrication technology are discussed.

Towards coherent optical control of a single hole spin: Rabi rotation of a trion conditional on the spin state of the hole

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Magnetoresistance and transistor-like behavior of a double quantum-dot via crossed Andreev reflections

The electric current and the magnetoresistance effect are studied in a double quantum-dot system, where one of the dots QD(a) is coupled to two ferromagnetic electrodes (F-1; F-2), while the second QD(b) is connected to a superconductor S. For energy scales within the superconductor gap, electric conduction is allowed by Andreev reflection processes. Due to the presence of two ferromagnetic leads, non-local crossed Andreev reflections are possible. We found that the magnetoresistance sign can be changed by tuning the external potential applied to the ferromagnets. In addition, it is possible to control the current of the first ferromagnet (F-1) through the potential applied to the second one (F-2). We have also included intradot interaction and gate voltages at each quantum dot and analyzed their influence through a mean field approximation. The interaction reduces the current amplitudes with respect to the non-interacting case, but the switching effect still remains as a manifestation of quantum coherence, in scales of the order of the superconductor coherence length. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4723000]

Universal zero-bias conductance through a quantum wire side-coupled to a quantum dot

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)