A. Tobalina

We present a unitary quantum control scheme that produces a highly monochromatic ion beam from a Paul trap. Our protocol is implementable by supplying the segmented electrodes with voltages of the order of Volts, which mitigates the impact of fluctuating voltages in previous designs and leads to a low-dispersion beam of ions. Moreover, our proposal does not rely on sympathetically cooling the ions, which bypasses the need of loading different species in the trap -- namely, the propelled ion and, e.g., a $^{40}$Ca$^+$ atom able to exert sympathetic cooling -- incrementing the repetition rate of the launching procedure. Our scheme is based on an invariant operator linear in position and momentum, which enables us to control the average extraction energy and the outgoing momentum spread. In addition, we propose a sequential operation to tailor the transversal properties of the beam before the ejection to minimize the impact spot and to increase the lateral resolution of the implantation.

There is recent interest in determining energy costs of shortcuts to adiabaticity (STA), but different definitions of "cost" have been used. We demonstrate the importance of taking into account the Control System (CS) for a fair assessment of energy flows and consumptions. We model the energy consumption and power to transport an ion by a STA protocol in a multisegmented Paul trap. The ion is driven by an externally controlled, moving harmonic oscillator. Even if no net ion- energy is gained at destination, setting the time-dependent control parameters is a macroscopic operation that costs energy and results in energy dissipation for the short time scales implied by the intrinsically fast STA processes. The potential minimum is displaced by modulating the voltages on control (dc) electrodes. A secondary effect of the modulation, usually ignored as it does not affect the ion dynamics, is the time- dependent energy shift of the potential minimum. The non trivial part of the energy consumption is due to the electromotive forces to set the electrode voltages through the low-pass filters required to preserve the electronic noise from decohering the ion's motion. The results for the macroscopic CS (the Paul trap) are compared to the microscopic power and energy of the ion alone. Similarities are found -and may be used quantitatively to minimize costs- only when the CS-dependent energy shift of the harmonic oscillator is included in the ion energy.

By applying invariant-based inverse engineering in the small-oscillations regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length), to transport a load between two positions at different heights with minimal final energy excitation for a microcanonical ensemble of initial conditions. The analogies between ion transport in multisegmented traps or neutral atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.