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## Observation of Defect States in PT-Symmetric Optical Lattices

Alois Regensburger, Mohammad-Ali Miri, Christoph Bersch, Jakob Näger, Georgy Onishchukov, Demetrios N. Christodoulides, Ulf Peschel

We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.

http://arxiv.org/abs/1301.1455
Optics (physics.optics); Quantum Physics (quant-ph)

## Topologically protected midgap states in complex photonic lattices

Henning Schomerus

One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Drawing on the concepts of band-structure topology, I here describe the formation of exponentially localized, topologically protected midgap states in photonic systems with spatially distributed gain and loss. When gain and loss are suitably arranged these states maintain their topological protection and then acquire a selectively tunable amplification rate. This finds applications in the beam dynamics along a photonic lattice and in the lasing of quasi-one-dimensional photonic crystals.

http://arxiv.org/abs/1301.0777
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

## Non-Hermitian Oscillator and R-deformed Heisenberg Algebra

Rajkumar Roychoudhury, Barnana Roy, Partha Pratim Dube

A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.

http://arxiv.org/abs/1301.0716
Mathematical Physics (math-ph); Quantum Physics (quant-ph)

## Analytic and Algebraic Methods XI: Registration now open

The 11th Analytic and Algebraic Methods in Physics conference will be held at Villa Lanna, Prague, CZ between 30 October 2013 and 1 November 2013.

Details of the conference and registration may be found on:
http://gemma.ujf.cas.cz/~znojil/conf/micromeetingjedenact.html

## PT-Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions

O. Yesiltas

In this article, we have introduced a $$\mathcal{PT}$$-symmetric non-Hermitian Hamiltonian model which is given as $$\hat{\mathcal{H}}=\omega (\hat{b}^{\dagger}\hat{b}+1/2)+ \alpha (\hat{b}^{2}-(\hat{b}^{\dagger})^{2})$$ where $$\omega$$ and $$\alpha$$ are real constants, $$\hat{b}$$ and $$\hat{b^{\dagger}}$$ are first order differential operators. The Hermitian form of the Hamiltonian $$\mathcal{\hat{H}}$$ is obtained by suitable mappings and it is interrelated to the time independent one dimensional Dirac equation in the presence of position dependent mass. Then, Dirac equation is reduced to a Schr\”{o}dinger-like equation and two new complex non-$$\mathcal{PT}$$-symmetric vector potentials are generated. We have obtained real spectrum for these new complex vector potentials using shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.

http://arxiv.org/abs/1301.0205
Mathematical Physics (math-ph); Quantum Physics (quant-ph)

## Non-Hermitian quantum mechanics viewed from quantum mechanics

Yan-Gang Miao, Zhen-Ming Xu

Real eigenvalues of some non-Hermitian (pseudo-Hermitian or PT-symmetric) Hamiltonians can be determined by solving operator quantum equations of motion rather than Schroedinger equations within the framework of quantum mechanics. This method is in particular applicable for the class of models which are closely related to the harmonic oscillator. In this way, a new application of quantum mechanics is thus given.

http://arxiv.org/abs/1212.6705
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)