TY - JOUR

T1 - Dynamical recurrence and the quantum control of coupled oscillators

AU - Genoni, Marco G.

AU - Serafini, Alessio

AU - Kim, M. S.

AU - Burgarth, Daniel

PY - 2012

Y1 - 2012

N2 - Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.

AB - Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.

UR - http://www.scopus.com/inward/record.url?scp=84859595344&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.108.150501

DO - 10.1103/PhysRevLett.108.150501

M3 - Article

C2 - 22587236

SN - 0031-9007

VL - 108

SP - 150501-1-150501-5

JO - Physical Review Letters

JF - Physical Review Letters

IS - 15

M1 - 150501

ER -