Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Bloch band theory and bulk-boundary correspondence in non-Hermitian systems are attracting great attention in different areas of science. Interband transitions and Rabi flopping induced by emission or absorption of field quanta are fundamental and well-understood processes in Hermitian systems. However, they are challenged in a non-Hermitian system, where band theory is affected by system boundaries. Here we consider Rabi oscillations in non-Hermitian 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. Rabi oscillations become anharmonic and transitions cease to be vertical in the energy-momentum plane in systems with open boundaries. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how competition between non-Hermitian, non-local and Floquet effects can result in significant enhancements of physically measurable quantities.