Growing the $\mathcal{PT}$ transition threshold by strong coupling to neutral chains. (arXiv:1802.00854v1 [quant-ph])

The $\mathcal{PT}$ symmetry breaking threshold in discrete realizations of
systems with balanced gain and loss is determined by the effective coupling
between the gain and loss sites. In one dimensional chains, this threshold is
maximum when the two sites are closest to each other or the farthest. We
investigate the fate of this threshold in the presence of parallel, strongly
coupled, Hermitian (neutral) chains, and find that it is increased by a factor
proportional to the number of neutral chains. We present numerical results and
analytical arguments for this enhancement. We then consider the effects of
adding neutral sites to $\mathcal{PT}$ symmetric dimer and trimer
configurations and show that the threshold is more than doubled, or tripled by
their presence. Our results provide a surprising way to engineer the
$\mathcal{PT}$ threshold in experimentally accessible samples.

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