December 2012
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Day December 22, 2012

Optical Resonator Analog of a Two-Dimensional Topological Insulator

G. Q. Liang, Y. D. Chong

A lattice of optical ring resonators can exhibit a topological insulator phase, with the direction of rotation in the resonators playing the role of spin. This occurs when the inter-resonator coupling is sufficiently large, and the synthetic magnetic vector potential set up by the couplers is zero. Using the transfer matrix method, we derive the band structure, phase diagram, and the projected band diagram showing the existence of spin-polarized edge states. When PT (parity/time-reversal) symmetric gain and loss are introduced, the system functions as an optical diode which does not require optical nonlinearities.

http://arxiv.org/abs/1212.5034
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

Resources needed for non-unitary quantum operations

Raam Uzdin

Non-unitary operations generated by an effective non-Hermitian Hamiltonian can be used to create quantum state manipulations which are impossible in Hermitian quantum mechanics. These operations include state preparation (or cooling) and non-orthogonal state discrimination. In this work we put a lower bound on the resources needed for the construction of some given non-unitary evolution. Passive systems are studied in detail and a general feature of such a system is derived. After interpreting our results using the singular value decomposition, several examples are studied analytically. In particular, we put a lower bound on the resources needed for non-Hermitian state preparation and non-orthogonal state discrimination.

http://arxiv.org/abs/1212.4584
Quantum Physics (quant-ph)