August 2012
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## Antisymmetric PT-photonic structures with balanced positive and negative index materials

Li Ge, H. E. Tureci

In this Letter we study a new class of synthetic materials in which the refractive index satisfies a special symmetry, $$n(-x)=-n^*(x)$$, which we term antisymmetric parity-time (APT) systems. Unlike PT-symmetric systems which require balanced gain and loss, i.e. $$n(-x)=n^*(x)$$, APT systems consist of balanced positive and negative index materials (NIMs). Despite the seemingly PT-symmetric optical potential $$V(x)\equiv n(x)^2\omega^2/c^2$$, such systems are not invariant under combined PT operation due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.

http://arxiv.org/abs/1208.4644
Optics (physics.optics)

## Quantum search using non-Hermitian adiabatic evolution

Alexander I. Nesterov, Gennady P. Berman

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover’s problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.

http://arxiv.org/abs/1208.4642
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph)