14,393 research outputs found
Urn Models and Beta-splines
Some insight into the properties of beta-splines is gained by applying the techniques of urn models. Urn models are used to construct beta-spline basis functions and to derive the basic properties of these blending functions and the corresponding beta-spline curves. Only the simple notion of linear geometric continuity and with the most elementary beta parameter are outlined. Non-linear geometric continuity leads to additional beta parameters and to more complicated basis functions. Whether urn models can give us any insight into these higher order concepts still remains to be investigated
Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
Driving a quantum system periodically in time can profoundly alter its
long-time dynamics and trigger topological order. Such schemes are particularly
promising for generating non-trivial energy bands and gauge structures in
quantum-matter systems. Here, we develop a general formalism that captures the
essential features ruling the dynamics: the effective Hamiltonian, but also the
effects related to the initial phase of the modulation and the micro-motion.
This framework allows for the identification of driving schemes, based on
general N-step modulations, which lead to configurations relevant for quantum
simulation. In particular, we explore methods to generate synthetic spin-orbit
couplings and magnetic fields in cold-atom setups.Comment: 25 pages, 6 figures, includes Appendices (A-K). An erroneous factor
of two has been corrected in the last term of Eq. C10 (Appendix C); this typo
had no impact on the rest of the articl
Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates
Shaking optical lattices in a resonant manner offers an efficient and
versatile method to devise artificial gauge fields and topological band
structures for ultracold atomic gases. This was recently demonstrated through
the experimental realization of the Harper-Hofstadter model, which combined
optical superlattices and resonant time-modulations. Adding inter-particle
interactions to these engineered band systems is expected to lead to
strongly-correlated states with topological features, such as fractional Chern
insulators. However, the interplay between interactions and external
time-periodic drives typically triggers violent instabilities and
uncontrollable heating, hence potentially ruling out the possibility of
accessing such intriguing states of matter in experiments. In this work, we
study the early-stage parametric instabilities that occur in systems of
resonantly-driven Bose-Einstein condensates in optical lattices. We apply and
extend an approach based on Bogoliubov theory [PRX 7, 021015 (2017)] to a
variety of resonantly-driven band models, from a simple shaken Wannier-Stark
ladder to the more intriguing driven-induced Harper-Hofstadter model. In
particular, we provide ab initio numerical and analytical predictions for the
stability properties of these topical models. This work sheds light on general
features that could guide current experiments to stable regimes of operation.Comment: 15 pages, 6 figures, one appendi
Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
We study the transport of cold fermionic atoms trapped in optical lattices in
the presence of artificial Abelian or non-Abelian gauge potentials. Such
external potentials can be created in optical lattices in which atom tunneling
is laser assisted and described by commutative or non-commutative tunneling
operators. We show that the Hall-like transverse conductivity of such systems
is quantized by relating the transverse conductivity to topological invariants
known as Chern numbers. We show that this quantization is robust in non-Abelian
potentials. The different integer values of this conductivity are explicitly
computed for a specific non-Abelian system which leads to a fractal phase
diagram.Comment: 6 pages, 2 figure
Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
Realizing strongly-correlated topological phases of ultracold gases is a
central goal for ongoing experiments. And while fractional quantum Hall states
could soon be implemented in small atomic ensembles, detecting their signatures
in few-particle settings remains a fundamental challenge. In this work, we
numerically analyze the center-of-mass Hall drift of a small ensemble of
hardcore bosons, initially prepared in the ground state of the
Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall
drift upon release, for a wide range of magnetic flux values, we identify an
emergent Hall plateau compatible with a fractional Chern insulator state: the
extracted Hall conductivity approaches a fractional value determined by the
many-body Chern number, while the width of the plateau agrees with the spectral
and topological properties of the prepared ground state. Besides, a direct
application of Streda's formula indicates that such Hall plateaus can also be
directly obtained from static density-profile measurements. Our calculations
suggest that fractional Chern insulators can be detected in cold-atom
experiments, using available detection methods.Comment: 13 pages, 11 figures; extended version accepted for publicatio
Buneman instability in a magnetized current-carrying plasma with velocity shear
Buneman instability is often driven in magnetic reconnection. Understanding
how velocity shear in the beams driving the Buneman instability affects the
growth and saturation of waves is relevant to turbulence, heating, and
diffusion in magnetic reconnection. Using a Mathieu-equation analysis for weak
cosine velocity shear together with Vlasov simulations, the effects of shear on
the kinetic Buneman instability are studied in a plasma consisting of strongly
magnetized electrons and cold unmagnetized ions. In the linearly unstable
phase, shear enhances the coupling between oblique waves and the sheared
electron beam, resulting in a wider range of unstable eigenmodes with common
lower growth rates. The wave couplings generate new features of the electric
fields in space, which can persist into the nonlinear phase when electron holes
form. Lower hybrid instabilities simultaneously occur at
with a much lower growth
rate, and are not affected by the velocity shear.Comment: Accepted by Physics of Plasm
Periodically-driven quantum matter: the case of resonant modulations
Quantum systems can show qualitatively new forms of behavior when they are
driven by fast time-periodic modulations. In the limit of large driving
frequency, the long-time dynamics of such systems can often be described by a
time-independent effective Hamiltonian, which is generally identified through a
perturbative treatment. Here, we present a general formalism that describes
time-modulated physical systems, in which the driving frequency is large, but
resonant with respect to energy spacings inherent to the system at rest. Such a
situation is currently exploited in optical-lattice setups, where superlattice
(or Wannier-Stark-ladder) potentials are resonantly modulated so as to control
the tunneling matrix elements between lattice sites, offering a powerful method
to generate artificial fluxes for cold-atom systems. The formalism developed in
this work identifies the basic ingredients needed to generate interesting flux
patterns and band structures using resonant modulations. Additionally, our
approach allows for a simple description of the micro-motion underlying the
dynamics; we illustrate its characteristics based on diverse dynamic-lattice
configurations. It is shown that the impact of the micro-motion on physical
observables strongly depends on the implemented scheme, suggesting that a
theoretical description in terms of the effective Hamiltonian alone is
generally not sufficient to capture the full time-evolution of the system.Comment: 16 pages, 3 figures; includes a new Section III dedicated to the
strong-driving regim
- …