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