574 research outputs found
Four-dimensional topological lattices through connectivity
Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming
experimentally accessible in various engineered set-ups. In this paper, we
propose a new type of 4D topological system that, unlike other 2D and 4D QH
models, does not require complicated (artificial) gauge fields and/or
time-reversal symmetry breaking. Instead, we show that there are 4D QH systems
that can be engineered for spinless particles by designing the lattice
connectivity with real-valued hopping amplitudes, and we explain how this
physics can be intuitively understood in analogy with the 2D Haldane model. We
illustrate our discussion with a specific 4D lattice proposal, inspired by the
widely-studied 2D honeycomb and brickwall lattice geometries. This also
provides a minimal model for a topological system in Class AI, which supports
nontrivial topological band invariants only in four spatial dimensions or
higher
Momentum-space Harper-Hofstadter model
We show how the weakly trapped Harper-Hofstadter model can be mapped onto a
Harper-Hofstadter model in momentum space. In this momentum-space model, the
band dispersion plays the role of the periodic potential, the Berry curvature
plays the role of an effective magnetic field, the real-space harmonic trap
provides the momentum-space kinetic energy responsible for the hopping, and the
trap position sets the boundary conditions around the magnetic Brillouin zone.
Spatially local interactions translate into nonlocal interactions in momentum
space: within a mean-field approximation, we show that increasing interparticle
interactions leads to a structural change of the ground state, from a single
rotationally symmetric ground state to degenerate ground states that
spontaneously break rotational symmetry.Comment: 10 pages, 7 figure
Quantum Mechanics with a Momentum-Space Artificial Magnetic Field
The Berry curvature is a geometrical property of an energy band which acts as
a momentum space magnetic field in the effective Hamiltonian describing
single-particle quantum dynamics. We show how this perspective may be exploited
to study systems directly relevant to ultracold gases and photonics. Given the
exchanged roles of momentum and position, we demonstrate that the global
topology of momentum space is crucially important. We propose an experiment to
study the Harper-Hofstadter Hamiltonian with a harmonic trap that will
illustrate the advantages of this approach and that will also constitute the
first realization of magnetism on a torus
The 6D quantum Hall effect and 3D topological pumps
Modern technological advances allow for the study of systems with additional
synthetic dimensions. Using such approaches, higher-dimensional physics that
was previously deemed to be of purely theoretical interest has now become an
active field of research. In this work, we derive from first principles using a
semiclassical equation of motions approach, the bulk response of a
six-dimensional Chern insulator. We find that in such a system a quantized bulk
response appears with a quantization originating from a six-dimensional
topological index -- the 3rd Chern number. Alongside this novel six-dimensional
response, we rigorously describe the lower even-dimensional Chern-like
responses that can occur due to nonvanishing 1st and 2nd Chern numbers in
sub-spaces of the six-dimensional space. Last, we propose how to realize such a
bulk response using three-dimensional topological charge pumps in cold atomic
systems.Comment: 12 pages + 13 pages of supporting material, 2 figures, published
versio
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
We theoretically propose how to observe topological effects in a generic
classical system of coupled harmonic oscillators, such as classical pendula or
lumped-element electric circuits, whose oscillation frequency is modulated fast
in time. Making use of Floquet theory in the high frequency limit, we identify
a regime in which the system is accurately described by a Harper-Hofstadter
model where the synthetic magnetic field can be externally tuned via the phase
of the frequency-modulation of the different oscillators. We illustrate how the
topologically-protected chiral edge states, as well as the Hofstadter butterfly
of bulk bands, can be observed in the driven-dissipative steady state under a
monochromatic drive. In analogy with the integer quantum Hall effect, we show
how the topological Chern numbers of the bands can be extracted from the mean
transverse shift of the steady-state oscillation amplitude distribution.
Finally we discuss the regime where the analogy with the Harper-Hofstadter
model breaks down.Comment: 15 pages, 9 figure
Propagating edge states in strained honeycomb lattices
We investigate the helically-propagating edge states associated with
pseudo-Landau levels in strained honeycomb lattices. We exploit chiral symmetry
to derive a general criterion for the existence of these propagating edge
states in the presence of only nearest-neighbour hoppings and we verify our
criterion using numerical simulations of both uni-axially and trigonally
strained honeycomb lattices. We show that the propagation of the helical edge
state can be controlled by engineering the shape of the edges. Sensitivity to
chiral-symmetry-breaking next-nearest-neighbour hoppings is assessed. Our
result opens up an avenue toward the precise control of edge modes through
manipulation of the edge shape
How to directly observe Landau levels in driven-dissipative strained honeycomb lattices
We study the driven-dissipative steady-state of a coherently-driven Bose
field in a honeycomb lattice geometry. In the presence of a suitable spatial
modulation of the hopping amplitudes, a valley-dependent artificial magnetic
field appears and the low-energy eigenmodes have the form of relativistic
Landau levels. We show how the main properties of the Landau levels can be
extracted by observing the peaks in the absorption spectrum of the system and
the corresponding spatial intensity distribution. Finally, quantitative
predictions for realistic lattices based on photonic or microwave technologies
are discussed.Comment: Special Issue Article: Focus on Artificial Graphen
Retrospective Memories of Racialized Experiences
This thesis explores the relationship between individuals? memories of experiences
with children from different racial backgrounds and their present racial identity. After
generating data by collecting responses to an open ended survey about racial identity
and memories of racialized experiences, the results are examined using theoretical
concepts including the white racial frame, critical race theory, and ?colorblind? racism.
The results indicate that racial identity and categorization is formed prior to interaction with children from different racial backgrounds. Additionally, the trope of
"colorblindness" in respondent answers is analyzed, not as evidence of racial progress, but as an extension of white racism
Superfluid vortices in four spatial dimensions
Quantum vortices in superfluids have been an important research area for many
decades. Naturally, research on this topic has focused on two and
three-dimensional superfluids, in which vortex cores form points and lines,
respectively. Very recently, however, there has been growing interest in the
quantum simulation of systems with four spatial dimensions; this raises the
question of how vortices would behave in a higher-dimensional superfluid. In
this paper, we begin to establish the phenomenology of vortices in 4D
superfluids under rotation, where the vortex core can form a plane. In 4D, the
most generic type of rotation is a "double rotation" with two angles (or
frequencies). We show, by solving the Gross-Pitaesvkii equation, that the
simplest case of equal-frequency double rotation can stabilise a pair of vortex
planes intersecting at a point. This opens up a wide number of future research
topics, including unequal-frequency double rotations; the stability and
reconnection dynamics of intersecting vortex surfaces; and the possibility of
closed vortex surfaces
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