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arXiv:1802.08571 · New Journal of Physics

Energy consumption for ion-transport in a segmented Paul trap

Ander Tobalina, Joseba Alonso, Juan Gonzalo Muga

Published May 21, 2018• 23 citations
arXivHTMLPDF

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 CSdependent energy shift of the harmonic oscillator is included in the ion-energy.

DOI
10.1088/1367-2630/aac685

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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 CSdependent energy shift of the harmonic oscillator is included in the ion-energy.
Abstract It was recently proposed to use small groups of trapped ions as qubit carriers in miniaturized electrode arrays that comprise a large number of individual trapping zones, between which ions could be moved [1,2] This approach might be scalable for quantum information processing with a large numbers of qubits. Processing of quantum information is achieved by transporting ions to and from separate memory and qubit manipulation zones in between quantum logic operations. The transport of ion groups in this scheme plays a major role and requires precise experimental control and fast transport times. In this paper we introduce a theoretical framework to study ion transport in external potentials that might be created by typical miniaturized Paul trap electrode arrays. In particular we discuss the relationship between classical and quantum descriptions of the transport and study the energy transfer to the oscillatory motion during near‐adiabatic transport. Based on our findings we suggest a numerical method to find electrode potentials as a function of time to optimize the local potential an ion experiences during transport. We demonstrate this method for one specific electrode geometry that should closely represent the situation encountered in realistic trap arrays.
We experimentally demonstrate fast separation of a two-ion crystal in a microstructured segmented Paul trap. By the use of spectroscopic calibration routines for the electrostatic trap potentials, we achieve the required precise control of the ion trajectories near the critical point, where the harmonic confinement by the external potential vanishes. The separation procedure can be controlled by three parameters: a static potential tilt, a voltage offset at the critical point, and the total duration of the process. We show how to optimize the control parameters by measurements of ion distances, trap frequencies, and the final motional excitation. We extend the standard measurement technique for motional excitation to allow for discriminating thermal and oscillatory states, and to cover a dynamic range covering more than 4 orders of magnitude in energy. It is shown that for fast separation times, oscillatory motion is excited, while a predominantly thermal state is obtained for long times. At a separation duration of $80\phantom{\rule{0.222222em}{0ex}}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$, a minimum mean excitation of n‾=4.16(0.16)\overline{n}=4.16(0.16)n=4.16(0.16) vibrational quanta per ion is achieved, which is consistent with the adiabatic limit given by our particular trap. The presented technique does not rely on specific trap geometry parameters and can therefore be adopted for different segmented traps.
\n\nWe 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 microscopic primary system, we identify the energy cost as the exclusive work of the total system, which, for a clear-cut scale disparity between a microscopic primary system and a macroscopic control system, coincides with the exclusive work for the control system alone. We redefine the “engine efficiency” taking into account this cost. Our working horse model is an engine based on an ion in a Paul trap with power strokes designed via shortcuts to adiabaticity. Opposite to the paradigm of slow-cycle reversible engines with vanishing power and maximal efficiency, this fast-cycle engine increases the microscopic power at the price of a vanishing efficiency. 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.\n
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 microscopic primary system, we identify the energy cost as the exclusive work of the total system, which, for a clear-cut scale disparity between a microscopic primary system and a macroscopic control system, coincides with the exclusive work for the control system alone.We redefine the "engine efficiency" taking into account this cost.Our working horse model is an engine based on an ion in a Paul trap with power strokes designed via shortcuts to adiabaticity.Opposite to the paradigm of slow-cycle reversible engines with vanishing power and maximal efficiency, this fast-cycle engine increases the microscopic power at the price of a vanishing efficiency.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.focus article
We theoretically investigate the process of splitting two-ion crystals in segmented Paul traps, i.e. the structural transition from two ions confined in a common well to ions confined in separate wells. The precise control of this process by application of suitable voltage ramps to the trap segments is non-trivial, as the harmonic confinement transiently vanishes during the process. This makes the ions strongly susceptible to background electric field noise, and to static offset fields in the direction of the trap axis. We analyze the reasons why large energy transfers can occur, which are impulsive acceleration, the presence of residual background fields and enhanced anomalous heating. For the impulsive acceleration, we identify the diabatic and adiabatic regimes, which are characterized by different scaling behavior of the energy transfer with respect to time. We propose a suitable control scheme based on experimentally accessible parameters. Simulations are used to verify both the high sensitivity of the splitting result and the performance of our control scheme. Finally, we analyze the impact of trap geometry parameters on the crystal splitting process.
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, nonadiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies (or times) for given times (or energies), and discuss their realizability by means of Dirac impulses or otherwise.