Controllability in tunable chains of coupled harmonic oscillators

TL;DR

This paper demonstrates that controlling spring strengths in a chain of harmonic oscillators enables complete manipulation of all Gaussian states of the system, with an efficient algorithm for state preparation applicable across various experimental platforms.

Contribution

It introduces a method to achieve full Gaussian state controllability in coupled harmonic oscillators and provides an efficient algorithm for state engineering.

Findings

Complete Gaussian state controllability via spring strength control

An iterative algorithm with at most 3N(N-1)/2 operations

Feasibility demonstrated in multiple experimental platforms

Abstract

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.