Pseudo Hermitian interactions in the Dirac Equation

We consider $(2+1)$ dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states and the Dirac Hamiltonians are $\eta$-pseudo Hermitian. Some examples have been explicitly worked out.Comment: 8 pages, NO figure

(1+1)(1+1) dimensional Dirac equation with non Hermitian interaction

We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.Comment: 9 page

Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems

A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-hermitian operators, which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetryComment: 11 pages, LaTeX, no figure

(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib) (an inversely linear plus linear, leading to a PT-symmetric oscillator model), and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an $\eta$-weak-pseudo-Hermiticity generator are presented and a complexified PT-symmetric periodic-type model is used as an illustrative example.Comment: 11 pages, no figures, revise

Pseudo-Hermitian Interactions in Dirac Theory: Examples

We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both the cases we show that the energy spectrum is real and all the other features of non-relativistic pseudo-Hermitian formulation are present. Using the spectral method the positive definite metric operator ($\eta$) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.Comment: 13 pages, Latex, No figs, Revised version to appear in MPL

Photonic Dirac Waveguides

The Dirac equation is a paradigmatic model that describes a range of intriguing properties of relativistic spin-1/2 particles, from the existence of antiparticles to Klein tunneling. However, the Dirac-like equations have found application far beyond its original scope, and has been used to comprehend the properties of graphene and topological phases of matter. In the field of photonics, the opportunity to emulate Dirac physics has also enabled topological photonic insulators. In this paper, we demonstrate that judiciously engineered synthetic potentials in photonic Dirac systems can offer physical properties beyond both the elementary and quasi-particles, and topological realms. Specifically, we introduce a new class of optical Dirac waveguides, whose guided electromagnetic modes are endowed with pseudo-spin degree of freedom. Pseudo-spin coupled with the ability to engineer synthetic gauge potentials acting on it, enables control over the guided modes which is unattainable in conventional optical waveguides. In particular, we use a silicon nanophotonic metasurface that supports pseudo-spin degree of freedom as a testing platform to predict and experimentally confirm a spin-full nature of the Dirac waveguides. We also demonstrate that, for suitable trapping potentials, the guided modes exhibit spin-dependent field distributions, which gives rise to their distinct transport and radiative properties. Thereby, the Dirac waveguides manifest spin-dependent radiative lifetimes - the non-Hermitian spin-Hall effect - and open new avenues for spin-multiplexing, controlling characteristics of guided optical modes, and tuning light-matter interactions with photonic pseudo-spins.Comment: 16 pages, 5 figure