  We treat control of several two-level atoms interacting with one mode of the
electromagnetic field in a cavity. This provides a useful model to study
pertinent aspects of quantum control in infinite dimensions via the emergence
of infinite-dimensional system algebras. Hence we address problems arising with
infinite-dimensional Lie algebras and those of unbounded operators. For the
models considered, these problems can be solved by splitting the set of control
Hamiltonians into two subsets: The first obeys an abelian symmetry and can be
treated in terms of infinite-dimensional Lie algebras and strongly closed
subgroups of the unitary group of the system Hilbert space. The second breaks
this symmetry, and its discussion introduces new arguments. Yet, full
controllability can be achieved in a strong sense: e.g., in a time dependent
Jaynes-Cummings model we show that, by tuning coupling constants appropriately,
every unitary of the coupled system (atoms and cavity) can be approximated with
arbitrarily small error.
