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

• URL: http://arxiv.org/abs/2007.15055v1
• Date: Wed, 29 Jul 2020 18:57:14 GMT
• Title: Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
• Authors: A. Tobalina, E. Torrontegui, I. Lizuain, M. Palmero, and J. G. Muga
• Abstract summary: 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. For these "coupled systems" 2D invariants may still guide the Hamiltonian design.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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