260 research outputs found
Synthetic Gauge Fields for Vibrational Excitations of Trapped ions
The vibrations of a collection of ions in a microtrap array can be described
in terms of hopping phonons. We show theoretically that the vibrational
couplings may be tailored by using a gradient of the microtrap frequencies,
together with a periodic driving of the trapping potential. These ingredients
allow us to induce effective gauge fields on the vibrational excitations, such
that phonons mimic the behavior of charged particles in a magnetic field. In
particular, microtrap arrays are ideally suited to realize the famous
Aharonov-Bohm effect, and observe the paradigmatic edge states typical from
quantum-Hall samples and topological insulators.Comment: replaced with published versio
The role of a form of vector potential - normalization of the antisymmetric gauge
Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak
are compared with those based on pure group-theoretical considerations and
corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary
conditions one has to be very careful since the first gauge leads to a factor
system which is not normalized. A period N introduced in Brown's and Zak's
papers should be considered as a magnetic one, whereas the crystal period is in
fact 2N. The `normalization' procedure proposed here shows the equivalence of
Brown's, Zak's, and other approaches. It also indicates the importance of the
concept of magnetic cells. Moreover, it is shown that factor systems (of
projective representations and central extensions) are gauge-dependent, whereas
a commutator of two magnetic translations is gauge-independent. This result
indicates that a form of the vector potential (a gauge) is also important in
physical investigations.Comment: RevTEX, 9 pages, to be published in J. Math. Phy
Hofstadter butterfly for a finite correlated system
We investigate a finite two-dimensional system in the presence of external
magnetic field. We discuss how the energy spectrum depends on the system size,
boundary conditions and Coulomb repulsion. On one hand, using these results we
present the field dependence of the transport properties of a nanosystem. In
particular, we demonstrate that these properties depend on whether the system
consists of even or odd number of sites. On the other hand, on the basis of
exact results obtained for a finite system we investigate whether the
Hofstadter butterfly is robust against strong electronic correlations. We show
that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when
the magnetic field increases.Comment: 7 pages, 5 figures, revte
Predicted signatures of p-wave superfluid phases and Majorana zero modes of fermionic atoms in RF absorption
We study the superfluid phases of quasi-2D atomic Fermi gases interacting via
a p-wave Feshbach resonance. We calculate the absorption spectra of these
phases under a hyperfine transition, for both non-rotating and rotating
superfluids. We show that one can identify the different phases of the p-wave
superfluid from the absorption spectrum. The absorption spectrum shows clear
signatures of the existence of Majorana zero modes at the cores of vortices of
the weakly-pairing phase
Adiabatic continuity between Hofstadter and Chern insulator states
We show that the topologically nontrivial bands of Chern insulators are
adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate
adiabatic connection also between several familiar fractional quantum Hall
states on Hofstadter lattices and the fractional Chern insulator states in
partially filled Chern bands, which implies that they are in fact different
manifestations of the same phase. This adiabatic path provides a way of
generating many more fractional Chern insulator states and helps clarify that
nonuniformity in the distribution of the Berry curvature is responsible for
weakening or altogether destroying fractional topological states
Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution
We consider Bloch electrons on the honeycomb lattice under a uniform magnetic
field with flux per cell. It is shown that the problem factorizes
to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl
group and by the use of its irreducible representation on the space of theta
functions, we find a nested set of Bethe equations, which determine the
eigenstates and energy spectrum. The Bethe equations have simple form which
allows to consider them further in the limit by the technique
of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational
flux.Comment: 7 pages, 2 figures, Revte
Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
One-dimensional quasiperiodic systems, such as the Harper model and the
Fibonacci quasicrystal, have long been the focus of extensive theoretical and
experimental research. Recently, the Harper model was found to be topologically
nontrivial. Here, we derive a general model that embodies a continuous
deformation between these seemingly unrelated models. We show that this
deformation does not close any bulk gaps, and thus prove that these models are
in fact topologically equivalent. Remarkably, they are equivalent regardless of
whether the quasiperiodicity appears as an on-site or hopping modulation. This
proves that these different models share the same boundary phenomena and
explains past measurements. We generalize this equivalence to any
Fibonacci-like quasicrystal, i.e., a cut and project in any irrational angle.Comment: 7 pages, 2 figures, minor change
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal)
conductance of a two dimensional electron system placed in a strong
perpendicular magnetic field, and subjected to periodic modulations and/or
disorder potentials. The scattering problem is recast as a set of
inhomogeneous, coupled linear equations, allowing us to find the transmission
probabilities from a finite-size system computation; the results are exact for
non-interacting electrons. Our method fully accounts for the effects of the
disorder and the periodic modulation, irrespective of their relative strength,
as long as Landau level mixing is negligible. In particular, we focus on the
interplay between the effects of the periodic modulation and those of the
disorder. This appears to be the relevant regime to understand recent
experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)],
and our numerical results are in qualitative agreement with these experimental
results. The numerical techniques we develop can be generalized
straightforwardly to many-terminal geometries, as well as other multi-channel
scattering problems.Comment: 13 pages, 11 figure
Spontaneous radiation of a finite-size dipole emitter in hyperbolic media
We study the radiative decay rate and Purcell effect for a finite-size dipole
emitter placed in a homogeneous uniaxial medium. We demonstrate that the
radiative rate is strongly enhanced when the signs of the longitudinal and
transverse dielectric constants of the medium are opposite, and the
isofrequency contour has a hyperbolic shape. We reveal that the Purcell
enhancement factor remains finite even in the absence of losses, and it depends
on the emitter size.Comment: 6 pages, 3 figure
Violation of the entropic area law for Fermions
We investigate the scaling of the entanglement entropy in an infinite
translational invariant Fermionic system of any spatial dimension. The states
under consideration are ground states and excitations of tight-binding
Hamiltonians with arbitrary interactions. We show that the entropy of a finite
region typically scales with the area of the surface times a logarithmic
correction. Thus, in contrast to analogous Bosonic systems, the entropic area
law is violated for Fermions. The relation between the entanglement entropy and
the structure of the Fermi surface is discussed, and it is proven, that the
presented scaling law holds whenever the Fermi surface is finite. This is in
particular true for all ground states of Hamiltonians with finite range
interactions.Comment: 5 pages, 1 figur
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