  We study the ground state of a bilayer system of dipolar bosons with dipoles
oriented by an external field perpendicularly to the two parallel planes. By
decreasing the interlayer distance, for a fixed value of the strength of the
dipolar interaction, the system undergoes a quantum phase transition from an
atomic to a pair superfluid. We investigate the excitation spectrum across this
transition by using microscopic approaches. Quantum Monte Carlo methods are
employed to obtain the static structure factors and intermediate scattering
functions in imaginary time. The dynamic response is calculated using both the
correlated basis functions (CBF) method and the approximate inversion of the
Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic
phase, both density and spin excitations are gapless. However, in the
pair-superfluid phase a gap opens in the excitation energy of the spin mode.
For small separation between layers, the minimal spin excitation energy equals
the binding energy of a dimer and is twice the gap value.
