  We investigate the synthesis of continuous-variable two-mode unitary gates in
the setting where two modes A and B are coupled by a fixed quadratic
Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed
by Hamiltonian H interspaced by local phase shifts applied to A and B. We
concentrate on protocols that require the minimum necessary number of steps and
we show how to implement the beam splitter and the two-mode squeezer in just
three steps. Particular attention is paid to the Hamiltonian x_A p_B that
describes the effective off-resonant interaction of light with the collective
atomic spin.
