Abstract
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.
Highlights
Several papers [1,2,3,4,5,6,7,8,9,10,11,12] have studied the ‘energy cost’ or ‘energy consumption’ of shortcuts to adiabaticity (STA) [13, 14], fast track routes to the results of slow adiabatic processes
The power for the primary system, and any definition of energy consumption that depends on the energy of the PS, depend on the control system through f (t)
As new quantum technologies unfold from laboratory prototypes to commercially available devices, energetic costs of processes may become more and more relevant
Summary
Several papers [1,2,3,4,5,6,7,8,9,10,11,12] have studied the ‘energy cost’ or ‘energy consumption’ of shortcuts to adiabaticity (STA) [13, 14], fast track routes to the results of slow adiabatic processes. Often the primary system (PS), whose state is of interest for the application at hand, is microscopic while the control system (CS) is macroscopic, so that the PS is described as governed by a semiclassical Hamiltonian with (classical) external time-dependent control parameters. Different STA are commonly formulated by specifying the protocol, i.e., the time dependences of the parameters that induce fast state changes of the PS. There, the energy flow with the outer world is studied for an enlarged system that includes the PS and the CS required to change the time-dependent parameters that drive the PS. The divide between the enlarged system PS+CS and the outer world should be drawn such that the energy flow through that boundary can be translated into actual fuel or electric power consumption. Related discussions of the need to include a CS along with the PS, see e.g. [16], where the energy required to manipulate a mesoscopic quantum system in the presence of noise is examined, or [17], where fundamental limits of quantum refrigeration are discussed
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