Quantum system driven by incoherent a.c fields: Multi-crossing Landau Zener dynamics

The paper investigates the multi-crossing dynamics of a Landau-Zener (LZ) system driven by two sinusoidal a.c fields applying the Dynamic Matrix approach (DMA). The system is shown to follow one-crossing and multi-crossing dynamics for low and high frequency regime respectively. It is shown that in low frequency regime, the resonance phenomenon occurs and leads to the decoupling of basis states; the effective gap vanishes and then the complete blockage of the system. For high frequency, the system achieves multi-crossing dynamics with two fictitious crossings; the system models a Landau-Zener-Stückelberg (LZS) interferometer with critical parameters that tailor probabilities. The system is then shown to depend only on the phase that permits the easiest control with possible application in implementing logic gates.