We systematically investigate the non-Hermitian generalizations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"uckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behavior is analyzed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulas for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasized. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time
(PT) reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualized through the beam intensity profile and the transition probabilities measured by the center of mass of the profile.
Abstract The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett . 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor . 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N , transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.