Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators

TL;DR

This paper develops an invariant-based inverse engineering method for controlling the dynamics of coupled, time-dependent harmonic oscillators, enabling precise wave packet manipulation and state transfer in non-separable systems.

Contribution

It introduces a novel invariant-based approach for inverse Hamiltonian engineering applicable to coupled oscillators that are not separable by point transformations.

Findings

Controlled wave packet deflection in harmonic waveguides

Designed state transfer between coupled oscillators

Demonstrated effectiveness in non-separable systems

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.