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

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

2002-03-20

arxiv.org/abs/quant-ph/0203104v1

J. Phys. A, 35 (2002), 2327

Physics

Quantum Physics

IoP LaTeX, ca. 14 pages

Scientific paper

10.1088/0305-4470/35/9/319

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.

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