Engineered Diabatic Transition under Arbitrarily Slow Evolution via Phase-Difference Manipulation

The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here, we show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, instantaneous transition accumulation and instantaneous transition probability, to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new phase-difference manipulation method, we control instantaneous transition probability and instantaneous transition accumulation to induce adiabaticity violation in a Landau-Zener process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow Landau-Zener process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.