  We prove that temporal control of the strengths of springs connecting $N$
harmonic oscillators in a chain provides complete access to all Gaussian states
of $N-1$ collective modes. The proof relies on the construction of a suitable
basis of cradle modes for the system. An iterative algorithm to reach any
desired Gaussian state requires at most $3N(N-1)/2$ operations. We illustrate
this capability by engineering squeezed pseudo-phonon states - highly
non-local, strongly correlated states that may result from various nonlinear
processes. Tunable chains of coupled harmonic oscillators can be implemented by
a number of current state-of-the-art experimental platforms, including cold
atoms in lattice potentials, arrays of mechanical micro-oscillators, and
coupled optical waveguides.
