Chaos and $\mathcal{P}\mathcal{T}$-symmetry breaking transitions in a driven, nonlinear dimer with balanced gain and loss

Dynamics of a simple system, such as a two-state (dimer) model, are dramatically changed in the presence of interactions and external driving, and the resultant unitary dynamics show both regular and chaotic regions. We investigate the non-unitary dynamics of such a dimer in the presence of balanced gain and loss for the two states, i.e. a $\mathcal{P}\mathcal{T}$ symmetric dimer. We find that at low and high driving frequencies, the $\mathcal{P}\mathcal{T}$-symmetric dimer motion continues to be regular, and the system is in the $\mathcal{P}\mathcal{T}$-symmetric state. On that other hand, for intermediate driving frequency, the system shows chaotic motion, and is usually in the $\mathcal{P}\mathcal{T}$-symmetry broken state. Our results elucidate the interplay between the $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and regular-chaotic transitions in an experimentally accessible toy model.