Identification of dynamical Lie algebras for finite-level quantum control systems

Abstract

The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the dynamical Lie algebra for an N-level system with equally spaced energy levels and uniform transition dipole moments, is a subalgebra for $so(N)$ if $N=2\ell +1$, and a subalgebra of $sp(\ell )$ if $N=2\ell$. General conditions for obtaining either $so(2\ell +1)$ or $sp(\ell )$ are established.

IoP LaTeX, ca. 14 pages

References in corpus (1)

• Complete controllability of finite-level quantum systems

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