Inverse engineering of fast state transfer among coupled oscillators

We design faster-than-adiabatic state transfers (switching of quantum numbers) in time-dependent coupled-oscillator Hamiltonians. The manipulation to drive the process is found using a two-dimensional invariant recently proposed S. Simsek and F. Mintert, Quantum 5 (2021) 409, involves both rotation transient scaling principal axes potential Cartesian representation. Importantly, this degenerate except for subspace spanned by its ground state. Such degeneracy, general, allows infidelities final states with respect ideal target eigenstates. However, value single control parameter can be chosen so that switching perfect arbitrary (not necessarily known) initial Additional 2D linear invariants are used find easily values needed provide generic expressions energies. In particular we transformations harmonic trap particle (such as an ion or neutral atom) rotated one, eigenstates converted into replicas at time, some time angle.