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Optical finite representation of the Lorentz group
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abstract
We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to design a $\mathcal{PT}$-symmetric optical structure. Thus, the array of coupled waveguides may keep or break $\mathcal{PT}$-symmetry, leading to a device that behaves like an oscillator or directional amplifier, respectively. We show that the so-called linear $\mathcal{PT}$-symmetric dimer belongs to this class of photonic lattices.
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Cited by 1 Pith paper
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$\mathcal{PT}$-symmetry from Lindblad dynamics in an optomechanical system
The strong-to-weak coupling transition in optomechanical state transfer is interpreted as a passive PT-symmetry breaking transition, with exact Lindblad/non-Hermitian agreement only in the single-excitation subspace.
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