## Landau-Zener-Stückelberg interferometry in $$\mathcal P \mathcal T$$-symmetric optical waveguides.(English)Zbl 1275.78006

The authors investigate theoretically the non-adiabatic transitions in an $$\mathcal{PT}$$-symmetric lattice subject to a strong ac-force. In an optical realization of the lattice, the curvature of the waveguides along the paraxial propagation direction plays the role of the external periodic force necessary to drive the system through an avoided level crossing. Analytical expressions for the transition probabilities after multiple passages are obtained within an effective two-mode approximation. It is shown that gain and losses of the light beam, as well as the relative occupation probabilities of the bands involved in the transitions, can be accurately managed upon tuning the parameters of the system and are particularly sensitive to the amplitude of the non-Hermitian component of the lattice. Numerical simulations for the complete system are found to agree very well with the approximate analytical results.

### MSC:

 78A50 Antennas, waveguides in optics and electromagnetic theory 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 78A10 Physical optics 78A40 Waves and radiation in optics and electromagnetic theory 81V80 Quantum optics 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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