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.
@article{arxiv.1710.03145,
title = {Controllability in tunable chains of coupled harmonic oscillators},
author = {L. F. Buchmann and K. Mølmer and D. Petrosyan},
journal= {arXiv preprint arXiv:1710.03145},
year = {2018}
}