2,413 research outputs found
Short Range Interactions in the Hydrogen Atom
In calculating the energy corrections to the hydrogen levels we can identify
two different types of modifications of the Coulomb potential , with one
of them being the standard quantum electrodynamics corrections, ,
satisfying over the whole range of
the radial variable . The other possible addition to is a potential
arising due to the finite size of the atomic nucleus and as a matter of fact,
can be larger than in a very short range. We focus here on the latter
and show that the electric potential of the proton displays some undesirable
features. Among others, the energy content of the electric field associated
with this potential is very close to the threshold of pair production.
We contrast this large electric field of the Maxwell theory with one emerging
from the non-linear Euler-Heisenberg theory and show how in this theory the
short range electric field becomes smaller and is well below the pair
production threshold
Wilson Fermions and Axion Electrodynamics in Optical Lattices
The formulation of massless relativistic fermions in lattice gauge theories
is hampered by the fundamental problem of species doubling, namely, the rise of
spurious fermions modifying the underlying physics. A suitable tailoring of the
fermion masses prevents such abundance of species, and leads to the so-called
Wilson fermions. Here we show that ultracold atoms provide us with the first
controllable realization of these paradigmatic fermions, thus generating a
quantum simulator of fermionic lattice gauge theories. We describe a novel
scheme that exploits laser-assisted tunneling in a cubic optical superlattice
to design the Wilson fermion masses. The high versatility of this proposal
allows us to explore a variety of interesting phases in three-dimensional
topological insulators, and to test the remarkable predictions of axion
electrodynamics.Comment: RevTex4 file, color figures, slightly longer than the published
versio
Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
Topological insulators are a broad class of unconventional materials that are
insulating in the interior but conduct along the edges. This edge transport is
topologically protected and dissipationless. Until recently, all existing
topological insulators, known as quantum Hall states, violated time-reversal
symmetry. However, the discovery of the quantum spin Hall effect demonstrated
the existence of novel topological states not rooted in time-reversal
violations. Here, we lay out an experiment to realize time-reversal topological
insulators in ultra-cold atomic gases subjected to synthetic gauge fields in
the near-field of an atom-chip. In particular, we introduce a feasible scheme
to engineer sharp boundaries where the "edge states" are localized. Besides,
this multi-band system has a large parameter space exhibiting a variety of
quantum phase transitions between topological and normal insulating phases. Due
to their unprecedented controllability, cold-atom systems are ideally suited to
realize topological states of matter and drive the development of topological
quantum computing.Comment: 11 pages, 6 figure
Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
Ultracold fermions trapped in a honeycomb optical lattice constitute a
versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett.
61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be
engineered through laser-induced methods, explicitly breaking time-reversal
symmetry. This potentially opens a bulk gap in the energy spectrum, which is
associated with a non-trivial topological order, i.e., a non-zero Chern number.
In this work, we consider the possibility of producing and identifying such a
robust Chern insulator in the laser-coupled honeycomb lattice. We explore a
large parameter space spanned by experimentally controllable parameters and
obtain a variety of phase diagrams, clearly identifying the accessible
topologically non-trivial regimes. We discuss the signatures of Chern
insulators in cold-atom systems, considering available detection methods. We
also highlight the existence of topological semi-metals in this system, which
are gapless phases characterized by non-zero winding numbers, not present in
Haldane's original model.Comment: 30 pages, 12 figures, 4 Appendice
Interaction-dependent photon-assisted tunneling in optical lattices: a quantum simulator of strongly-correlated electrons and dynamical gauge fields
We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling parameters, we can also obtain a t-J model with independently controllable tunneling t, super-exchange interaction J, and even a Heisenberg-Ising anisotropy. Hence, the full phase diagram of this paradigmatic model becomes accessible to cold-atom experiments, departing from the region t _ J allowed by standard single-band Hubbard Hamiltonians in the strong-repulsion limit. We finally show that, by generalizing the photon-assisted tunneling scheme, the quantum simulator yields models of dynamical Gauge fields, where atoms of a given electronic state dress the tunneling of the atoms with a different internal state, leading to Peierls phases that mimic a dynamical magnetic field
Non-relativistic limit in the 2+1 Dirac Oscillator: A Ramsey Interferometry Effect
We study the non-relativistic limit of a paradigmatic model in Relativistic
Quantum Mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a
novel kind of Zitterbewegung which persists in this non-relativistic regime,
and leads to an observable deformation of the particle orbit. This effect can
be interpreted in terms of a Ramsey Interferometric phenomenon, allowing an
insightful connection between Relativistic Quantum Mechanics and Quantum
Optics. Furthermore, subsequent corrections to the non-relativistic limit,
which account for the usual spin-orbit Zitterbewegung, can be neatly understood
in terms of a Mach-Zehnder interferometer.Comment: RevTex4 file, color figures, submitted for publicatio
Edge states and topological orders in the spin liquid phases of star lattice
A group of novel materials can be mapped to the star lattice, which exhibits
some novel physical properties. We give the bulk-edge correspondence theory of
the star lattice and study the edge states and their topological orders in
different spin liquid phases. The bulk and edge-state energy structures and
Chern number depend on the spin liquid phases and hopping parameters because
the local spontaneous magnetic flux in the spin liquid phase breaks the time
reversal and space inversion symmetries. We give the characteristics of bulk
and edge energy structures and their corresponding Chern numbers in the
uniform, nematic and chiral spin liquids. In particular, we obtain analytically
the phase diagram of the topological orders for the chiral spin liquid states
SL[\phi,\phi,-2\phi], where \phi is the magnetic flux in two triangles and a
dodecagon in the unit cell. Moreover, we find the topological invariance for
the spin liquid phases, SL[\phi_{1},\phi_{2},-(\phi_{1}+\phi_{2})] and
SL[\phi_{2},\phi_{1},-(\phi_{1}+\phi_{2})]. The results reveal the relationship
between the energy-band and edge-state structures and their topological orders
of the star lattice.Comment: 7 pages, 8 figures, 1 tabl
Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
We study the adiabatic dynamics of Majorana fermions across a quantum phase
transition. We show that the Kibble-Zurek scaling, which describes the density
of bulk defects produced during the critical point crossing, is not valid for
edge Majorana fermions. Therefore, the dynamics governing an edge state quench
is nonuniversal and depends on the topological features of the system. Besides,
we show that the localization of Majorana fermions is a necessary ingredient to
guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in
Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M.
Cazalilla, M. Rigol. New references and some typos correcte
Identifying topological edge states in 2D optical lattices using light scattering
We recently proposed in a Letter [Physical Review Letters 108 255303] a novel
scheme to detect topological edge states in an optical lattice, based on a
generalization of Bragg spectroscopy. The scope of the present article is to
provide a more detailed and pedagogical description of the system - the
Hofstadter optical lattice - and probing method. We first show the existence of
topological edge states, in an ultra-cold gas trapped in a 2D optical lattice
and subjected to a synthetic magnetic field. The remarkable robustness of the
edge states is verified for a variety of external confining potentials. Then,
we describe a specific laser probe, made from two lasers in Laguerre-Gaussian
modes, which captures unambiguous signatures of these edge states. In
particular, the resulting Bragg spectra provide the dispersion relation of the
edge states, establishing their chiral nature. In order to make the Bragg
signal experimentally detectable, we introduce a "shelving method", which
simultaneously transfers angular momentum and changes the internal atomic
state. This scheme allows to directly visualize the selected edge states on a
dark background, offering an instructive view on topological insulating phases,
not accessible in solid-state experiments.Comment: 17 pages, 10 figures. Revised and extended version, to appear in EJP
Special Topic for the special issue on "Novel Quantum Phases and Mesoscopic
Physics in Quantum Gases". Extended version of arXiv:1203.124
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