Adiabatic state conversion for (a)cyclic non-Hermitian quantum Hamiltonians of generalized functional form - Nicholas S. Nye; Nikolaos V. Kantartzis (APL Quantum)
In the present paper, we aim to firmly establish the adiabatic properties of two-level non-Hermitian quantum structures evolving along generalized (open/acyclic or closed/cyclic) paths in parameter space. Analytical solutions in terms of Airy and modified Bessel functions have been retrieved for linear and hyperbolic temporal dependencies in parity-time-symmetric-like systems, which were subsequently studied in the slowly varying limit to show conversion to one of the instantaneous eigenstates. Such a mode switching behavior is found to be an identifying feature of dissipative quantum settings, whether they evolve along cyclic or acyclic trajectories, and this has been proven in our paper by separately analyzing the dynamics of (i) the ratio of the state vector components, via a variant of the Möbius transformation, and (ii) the complex probability amplitudes, through a systematic inspection of the mode population equations. In the latter instance, it was furthermore shown that the identity of the eigenstate, to which the quantum arrangement transitions, depends highly on the magnitude of the adiabatic rate β. Along these lines, the concepts of the instantaneous (D) and averagely (Dav) dominant eigenstates are brought forth, while a reconfigurable photonic switch is also proposed, which can convert either to the D or to the Dav modes based on the total period of evolution. Finally, we apply our findings in the case of closed parametric paths to demystify the recently reported symmetric and asymmetric state conversion effects and additionally demonstrate that operation at or near exceptional points does not qualitatively affect the conclusions of the current investigation.