# All

The color code is both an interesting example of an exactly solved

topologically ordered phase of matter and also among the most promising

candidate models to realize fault-tolerant quantum computation with minimal

resource overhead. The contributions of this work are threefold. First of all,

we build upon the abstract theory of boundaries and domain walls of topological

phases of matter to comprehensively catalog the objects realizable in color

codes. Together with our classification we also provide lattice representations

We demonstrate a set of tools for microscopic control of neutral strontium

atoms. We report single-atom loading into an array of sub-wavelength scale

optical tweezers, light-shift free control of a narrow-linewidth optical

transition, three-dimensional ground-state cooling, and high-fidelity

nondestructive imaging of single atoms on sub-wavelength spatial scales.

Extending the microscopic control currently achievable in

single-valence-electron atoms to species with more complex internal structure,

Recently, there has been a surge of interest in using R\'enyi entropies as

quantifiers of correlations in many-body quantum systems. However, it is well

known that in general these entropies do not satisfy the strong subadditivity

inequality, which is a central property ensuring the positivity of correlation

measures. In fact, in many cases they do not even satisfy the weaker condition

of subadditivity. In the present paper we shed light on this subject by

The classical and quantum mechanical correspondence for constant mass

settings is used, along with some point canonical transformation, to find the

position-dependent mass (PDM) classical and quantum Hamiltonians. The

comparison between the resulting quantum PDM-Hamiltonian and the von Roos

PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are

strictly determined. Eliminating, in effect, the ordering ambiguity associated

with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in

Dark states are eigenstates or steady-states of a system that are decoupled

from the radiation. Their use, along with associated technique such as

Stimulated Raman Adiabatic Passage, has extended from atomic physics where it

is an essential cooling mechanism, to more recent versions in condensed phase

where it has been demonstrated to be capable of increasing coherence times of

qubits. These states are often discussed in the context of unitary evolution

and found with elegant methods exploiting symmetries, or via the Bruce-Shore

We introduce the generalized equidistant Chebyshev polynomials T(k,h) of kind

k of hyperkind h, where k,h are positive integers. They are obtained by a

generalization of standard and monic Chebyshev polynomials of the first and

second kinds. This generalization is fulfilled in two directions. The

horizontal generalization is made by introducing hyperkind h and expanding it

to infinity. The vertical generalization proposes expanding kind k to infinity

with the help of the method of equidistant coefficients. Some connections of

We describe the design and implementation of a stable high-power 1064 nm

laser system to generate optical lattices for experiments with ultracold

quantum gases. The system is based on a low-noise laser amplified by an array

of four heavily modified, high-power fiber amplifiers. The beam intensity is

stabilized and controlled with a nonlinear feedback loop. Using real-time

monitoring of the resulting optical lattice, we find the stability of the

lattice site positions to be well below the lattice spacing for several hours.

The creation of delocalized coherent superpositions of quantum systems

experiencing different relativistic effects is an important milestone in future

research at the interface of gravity and quantum mechanics. This could be

achieved by generating a superposition of quantum clocks that follow paths with

different gravitational time dilation and investigating the consequences on the

interference signal when they are eventually recombined. Light-pulse atom

Many open quantum systems encountered in both natural and synthetic

situations are embedded in classical-like baths. Often, the bath degrees of

freedom may be represented in terms of canonically conjugate coordinates, but

in some cases they may require a non-canonical or non-Hamiltonian

representation. Herein, we review an approach to the dynamics and statistical

mechanics of quantum subsystems embedded in either non-canonical or

non-Hamiltonian classical-like baths which is based on operator-valued

In a Quantum Walk (QW) the "walker" follows all possible paths at once

through the principle of quantum superposition, differentiating itself from

classical random walks where one random path is taken at a time. This

facilitates the searching of problem solution spaces faster than with classical

random walks, and holds promise for advances in dynamical quantum simulation,

biological process modelling and quantum computation. Current efforts to

implement QWs have been hindered by the complexity of handling single photons