Implicit Lyapunov control of closed quantum systems

Abstract

In this paper, we investigate the state convergence problem for closed quantum systems under degenerate cases. An implicit Lyapunov-based control strategy is proposed for the convergence analysis of finite dimensional bilinear Schrödinger equations. The degenerate cases that the systems do not satisfy the strong regular condition [17] and the condition 〈φ i|H1|φj〉 ≠ 0, i, j ≠ k for eigenstates φi, φj of H0 different from target state φk, are considered. First the Lyapunov function is defined by the implicit function and the existence is guaranteed by a fixed point theorem. Then the convergence analysis is investigated by the LaSalle invariance principle. Finally, an example is provided to show the effectiveness of proposed results. ©2009 IEEE.