Exact dynamics and qubit inversion of non-Hermitian driven two-level systems

The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric structure of the problem can be unequivocally ap- appreciated. Performing a spectral analysis of an auxiliary stationary Schrödinger-like equation, complex time-dependent driving functions are obtained for which the corresponding (time-dependent) Schrödinger equation can be straightforwardly solved. Such complex drivings are seen to produce transitions in the qubit state in different, however interesting, manners. We believe that the results reported here will be of interest for designing and carrying out various experiments in laboratories specializing in nuclear magnetic resonance or in optics with gain and loss materials.