Related papers: Optical simulation of Majorana physics
We present several second-order linear differential equations that are associated to a particular Riccati equation with only one constant parameter in its coefficients through the technique of supersymmetric factorizations and through a…
A new computational method to solve the hyperbolic (Vlasov) equation and the elliptic (Poisson-like) equation at the polar axis is proposed. It is shown that the value of a scalar function at the polar axis can be predicted by its…
This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square…
A full density-matrix simulation is performed for optical deflection of a barium monofluoride ($^{138}$Ba$^{19}$F) beam using the bichromatic force, which employs pairs of counter-propagating laser beams that are offset in frequency. We…
We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two and three dimensions and their one dimensional superlattice. We calculate the long wavelength limit of the dynamical polarization…
A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation where the spinor field $(\psi)$ is by definition equal to its charge-conjugate field $(\psi_c)$. Here, we…
Photonic molecules, i.e. artificial structures composed of coherently coupled optical cavities, are paradigmatic systems for investigating fundamental phenomena across photonics, quantum optics and topological physics. In recent years,…
In a Majorana basis, the Dirac equation for a free spin one-half particle is a 4x4 real matrix differential equation. The solution can be a Majorana spinor, a 4x1 real column matrix, whose entries are real functions of the space-time. Can a…
We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement,…
Cold atoms in an optical lattice with brick-wall geometry have been used to mimic graphene, a two-dimensional material with characteristic Dirac excitations. Here we propose to bring such artificial graphene into the proximity of a second…
In the N=1 supersymmetric extension of the Standard Model, neutralinos associated in supermultiplets with the neutral electroweak gauge and Higgs bosons are, as well as gluinos, Majorana fermions. They can be paired with the Majorana…
We present the results of low lying excitation of coupled optical cavity arrays. We derive the Dirac equation for this system and explain the existence of Majorana fermion mode in the system. We present quite a few analytical relations…
We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably Li(Fe$_{1-x}$Co$_x$)As. A key ingredient of this proposal are the 3D Dirac cones recently…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
We study families of solitons in a two-dimensional (2D) model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum…
With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is,…
At photonic Dirac points, electromagnetic waves are governed by the same equations as two-component massless relativistic fermions. However, photonic Dirac points are known to occur in pairs in "photonic graphene" and other similar photonic…
We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By…
Dirac energy-dispersions are responsible of the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting…