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arXiv:0912.2527 · Journal of the Optical Society of America B

Feedback-optimized operations with linear ion crystals

J. F. Eble, Stefan Ulm, Peter V. Zahariev, Ferdinand Schmidt‐Kaler, Kilian Singer

Published Apr 27, 2010• 11 citations
arXivHTMLPDF

Abstract

We report transport operations with linear crystals of 40Ca+ ions performed by applying complex electric time-dependent potentials. For their control we use the information obtained from the ions’ fluorescence. We demonstrate that by means of this feedback technique, we can transport a predefined number of ions and also split and unify ion crystals. The feedback control allows for a robust scheme, compensating for experimental errors, as it does not rely on a precisely known electrical modeling of the electric potentials in the ion trap beforehand. Our method allows us to generate a self-learning voltage ramp for the required process. With an experimental demonstration of a transport with more than 99.8% success probability, this technique may facilitate the operation of a future ion-based quantum processor.

DOI
10.1364/josab.27.000a99

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arXiv:quant-ph/0702175•Feb 16, 2007•2 citations
We report transport operations with linear crystals of 40Ca+ ions performed by applying complex electric time-dependent potentials. For their control we use the information obtained from the ions’ fluorescence. We demonstrate that by means of this feedback technique, we can transport a predefined number of ions and also split and unify ion crystals. The feedback control allows for a robust scheme, compensating for experimental errors, as it does not rely on a precisely known electrical modeling of the electric potentials in the ion trap beforehand. Our method allows us to generate a self-learning voltage ramp for the required process. With an experimental demonstration of a transport with more than 99.8% success probability, this technique may facilitate the operation of a future ion-based quantum processor.
Coherence effects in a Lambda system of a 40Ca+ ion are investigated. Zeeman sublevels are utilized to evoke electromagnetically induced transparencies. The characteristic dark resonance and line shape alterations are analyzed for varying light field intensities. New features arise by avoiding all coherences in a Lambda-system. This is achieved by exposing the ion to only one single laser light field, going the spectroscopy. Pulsed light sequences ensure stable cooling and spectroscopy. A quantum mechanical description of the process is given, revealing the dark-resonance-free shape of the spectrum. This enables the determination of the Rabi frequency of the applied laser light field as well as the photon collection efficiency of the imaging system. In many cases in QIPC, it is important to precisely determine the position of the ions, for this information obtained from the ions" fluorescence is utilized. The capability of the segmented Paul trap to create custom electric potentials is utilized to form time dependent potentials with multiple trapping wells. The application of feedback control allows purposeful movement of a predefined number of ions and position regulation by altering the trapping voltages. Ion transport over 1 mm with more than 99.8 % success probability is accomplished without any knowledge of the potentials. By means of the feedback control this allows automated dividing of a linear ion crystal into two distinct potentials as well as the opposite process of merging. In order to perform these experiments, several novel techniques for the operation of an ion trap have been developed. A technique for automatic compensation is introduced to minimize the RF driven micromotion of the ion crystal. Additionally, a precise method for simultaneous measuring the oscillation frequencies for individual ions in an ion crystal is presented. Hereby, the oscillation modes of multi-species ion crystals can be analyzed for the determination of dopant isotopes.
Quantum processors based on linear arrays of trapped ions have achieved exceptional performance, but scaling to large qubit numbers requires realizing two-dimensional ion arrays as envisioned in the quantum charge-coupled device (QCCD) architecture. Here, we present a scalable method for the control of ion crystals in a grid-based surface-electrode Paul trap and characterize it in the context of transport operations that sort and reorder multispecies crystals. By combining cowiring of control electrodes at translationally symmetric locations in each grid site with the sitewise ability to exchange the voltages applied to two special electrodes gated by a binary input, site-dependent operations can be achieved using only a fixed number of analog voltage signals and a single digital input per site. In two separate experimental systems containing nominally identical grid traps, one using Yb + 171 − Ba + 138 crystals and the other Ba + 137 − Sr + 88 , we demonstrate this method by characterizing the conditional intrasite crystal reorder and the conditional exchange of ions between adjacent sites on the grid. Averaged across a multisite region of interest, we measure subquanta motional excitation in the axial in-phase and out-of-phase modes of the crystals following these operations at exchange rates of 2.5 kHz. In this initial demonstration, the logic controlling the voltage exchange occurs in software, but the applied signals mimic a proposed hardware implementation using crossover switches. These techniques can be further extended to implement other conditional operations in the QCCD architecture such as gates, initialization, and measurement. Published by the American Physical Society 2024
The manipulation of trapped charged particles by electric fields is an accurate, robust, and reliable technique for many applications or experiments in high-precision spectroscopy. The transfer of an ion sample between multiple traps allows the use of a tailored environment in quantum information, cold chemistry, or frequency metrology experiments. In this article, we experimentally study the transport of ion clouds of up to 8000080\phantom{\rule{0.16em}{0ex}}00080000 ions over a distance of 20 mm inside a linear radio-frequency trap. Ion transport is controlled by a transfer function, which is designed taking into account the local electric potentials. We observe that the ion response is very sensitive to the details of the description of the electric potential. Nevertheless, we show that fast transport---with a total duration of 100 $\ensuremath{\mu}s$---results in transport efficiencies attaining values higher than 90% of the ion number, even with large ion clouds. For clouds smaller than 2000 ions, a 100% transfer efficiency is observed. Transport induced heating, which depends on the transport duration, is also analyzed.
A feedback control method for producing an equidistant ion string in a surface-electrode ion trap has been experimentally demonstrated. This method features three advantages: (i) The optimal voltage can be constrained within the specified reachable range. (ii) The height of trapped ions from the trap surface can be maintained at the same value when strings with different number of ions or with different ion spacings are to be trapped. (iii) This method is resistant to a stray electric field near the trap. By this method, the asymmetry of the ion string caused by a stray field is minimized. The robustness of trapping a variable number of ions at the same potential and the dependency of the axial frequency on the number of ions are also investigated experimentally. This work would be a practical method to create a linear ion string with a large number of ions and may find applications in large-scale quantum computing, quantum simulation, and phase transition studies utilizing homogeneous ion strings.
We have developed fast and accurate protocols for ion shuttling in a surface-electrode ion trap, which allows efficient splitting and merging of two ions. These protocols are based on innovative improvements in the driving potential field model, where voltage is introduced as a variable parameter. This enhancement specifically addresses the issue of increased control errors that occur with larger inter-ion distances. We have devised a general model-solving procedure that uses a parameterized model to describe the total potential energy of the two ions and ions oscillating eigenfrequency in a dynamical normal modes. By employing optimization techniques, we determine optimal voltage ramps for the dynamic potential field, enabling accurate control of physical quantities during the splitting process. In additionally, through simulating the classical dynamics of the theoretical scheme, we decouple the ion oscillations by employing discrete Fourier transform (DFT) and nonlinear fitting techniques. Two ions are separated into individual potential wells with a distance of 200 μ𝑚 within 50 μs. The ion position drift is only 0.01%. During the splitting process, the frequency fluctuation of the center-of-mass mode of the ions is less than 0.69%, and the minimum average excitation of a single ion is 0.02 phonon. Accurate and fast ion shuttling technology facilitates the development of large-scale trapped-ion quantum computing. Maintaining the ions oscillating eigenfrequency constant during the shuttling operation alleviates the problem of decoherence of quantum information.
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.