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arXiv · 2007.15055

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

A. Tobalina·E. Torrontegui·I. Lizuain·M. Palmero·J. G. Muga
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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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A. Tobalina, E. Torrontegui, I. Lizuain, M. Palmero, J. G. Muga. 2020-07-29. Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators. https://doi.org/10.1103/physreva.102.063112

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