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July 13, 2026
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On Controllability of Λ- and V-Atoms and Other Three-Level Systems with Two Allowed Transitions

Lobachevskii Journal of Mathematics. 2023. Vol. 44. P. 2101–2108.
Kuznetsov S. A., Pechen A. N.

A three-level Λ-atom (resp., V-atom) is a three-level quantum system with a forbidden direct transition between the two lowest (resp., highest) energy states. These systems are particular examples of three-level systems with only two allowed transitions and are important in quantum optics, e.g., for modeling electromagnetically induced transparency, etc. For generality, we consider not only Λ- and V-atoms, but all other types of three-level systems with only two allowed transitions between basis states. For the most general case of arbitrary non-zero complex values of the interaction Hamiltonian, we combine in a unified way the description of the structure of the dynamical Lie algebra as well as controllability properties for such systems. It turns out that for non-degenerate transition frequencies the system is completely controllable for any non-zero interaction Hamiltonian, while for the degenerate case the system is either uncontrollable or controllable, depending on the exact values of matrix elements of the free and interaction Hamiltonians.

Research target: Physics Mathematics
Language: English
DOI
Keywords: controllabilityquantum controlthree-level systemΛ-atomV-atom
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