A complete classification of operator controllability for closed three-level quantum systems driven by a single control

Abstract:In this work, we study operator controllability of finite-dimensional closed quantum systems driven by a single coherent control. Two general Lie-algebraic results on controllability of such systems are proved. The first gives sufficient conditions under which controllability of the system is preserved when controlled energy-level shifts are added. The second gives a sufficient basis-element condition under which the dynamical Lie algebra contains $\mathfrak{su}(N)$ and the system is therefore operator controllable. These results, together with known controllability conditions, are applied to obtain a complete classification of operator controllability of all three-level quantum systems in terms of their free and interaction Hamiltonian matrix elements. This classification covers all combinations of energy-level and level-spacing degeneracies, two or three allowed transitions, as well as the presence or absence of controlled energy-level shifts, and gives necessary and sufficient conditions for operator controllability in each case.

arXiv:2610.14938 [quant-ph]

(or arXiv:2610.14938v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.14938 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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