Ander Tobalina

We inverse engineer fast rotations of a linear trap with two ions for a predetermined rotation angle and time, avoiding final excitation. Different approaches are analyzed and compared when the ions are of the same species or of different species. The separability into dynamical normal modes for equal ions in a common harmonic trap, or for different ions in non-harmonic traps with up to quartic terms allows for simpler computations of the rotation protocols. For non-separable scenarios, in particular for different ions in a harmonic trap, rotation protocols are also found using more costly numerical optimisations.

We assess the energy cost of shortcuts to adiabatic expansions or compressions of a harmonic oscillator, the power strokes of a quantum Otto engine. Difficulties to identify the cost stem from the interplay between different parts of the total system (the primary system -the particle-, and the control system) and definitions of work (exclusive and inclusive). While attention is usually paid to the inclusive work of the primary system, we identify the energy cost as the exclusive work of the total system, which, for a clearcut scale disparity between primary and control systems, coincides with the exclusive work for the control system. This energy cost makes the efficiency of the engine zero. For an ion in a Paul trap, the Paul trap fixes the gauge for the primary system, resulting in a counterintuitive evolution of its inclusive power and internal energy. Conditions for which inclusive power of the primary system and exclusive power control system are proportional are found.