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Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands

Rabi flopping between Bloch bands induced by a weak ac resonant field is a coherent effect involving interband transitions. Here we consider the fundamental processes of emission/absorption of quanta and Rabi oscillations in non-Hermitian two-band lattices exhibiting unbalanced non-Hermitian skin effect, and unveil an unprecedented scenario of Rabi flopping. The effective dipole moment of the transition - usually considered a bulk property - is however strongly dependent on boundary conditions, being greatly enhanced with increased Rabi frequency only when open boundaries are present. As the field strength is increased, Rabi oscillations rapidly become anharmonic, and transitions cease to be vertical in the energy-momentum plane until the system enters into an unstable regime (complex quasi-energy spectrum) due to secular amplification channels. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how the competition between non-Hermitian, non-local and Floquet influences can result in significant enhancements of physically measurable quantities.