Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
Quantum Physics
2021-01-04 v1
Abstract
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these "coupled systems" 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic waveguides; and (ii) we design the state transfer from one coupled oscillator to another.
Keywords
Cite
@article{arxiv.2007.15055,
title = {Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators},
author = {A. Tobalina and E. Torrontegui and I. Lizuain and M. Palmero and J. G. Muga},
journal= {arXiv preprint arXiv:2007.15055},
year = {2021}
}