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 $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$, satisfying $\left|\delta V\right|\ll\left|V_{C}\right|$ over the whole range of the radial variable $r$. The other possible addition to $V_{C}$ is a potential arising due to the finite size of the atomic nucleus and as a matter of fact, can be larger than $V_{C}$ 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 $e^+e^-$ 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