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

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2020-12
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American Physical Society
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Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling 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 wave guides and (ii) we design the state transfer from one coupled oscillator to another.
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Tobalina, A., Torrontegui, E., Lizuain, I., Palmero, M. & Muga, J. G. (2020). Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators. Physical Review A, 102(6).