Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
7 pags., 3 figs., 1 tab. ; 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. ; This work was supported by the Basque Country Government (Grant No. IT986-16), and by PGC2018-101355- B-I00 (MCIU/AEI/FEDER,UE). E.T. acknowledges support from PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER No. S2018/TCS- 4342 (QUITEMAD-CM).