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arXiv:1208.3986 · New Journal of Physics

Quantum control of the motional states of trapped ions through fast switching of trapping potentials

Joseba Alonso, Florian Leupold, B. C. Keitch, Jonathan Home

Published Feb 1, 2013• 42 citations
arXivHTMLPDF

Abstract

We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the precision required for a number of important control parameters. We also consider the possibilities and limitations for generating motional state squeezing using these techniques, which could be used as a basis for the investigation of Gaussian-state entanglement.

DOI
10.1088/1367-2630/15/2/023001

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We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the precision required for a number of important control parameters. We also consider the possibilities and limitations for generating motional state squeezing using these techniques, which could be used as a basis for the investigation of Gaussian-state entanglement.
The outstanding degree of control over trapped ions in Paul traps gives rise to the development of novel quantum manipulation techniques. Optical transitions can be used for precise manipulation of internal and external states. This way, non-classical states can be created which are a key component of quantum algorithms based on quantum logic operations. This powerful optical toolbox enabled the trapped ion system to assume leadership in the field of quantum computation. This thesis addresses two major challenges in the field of micro ion trap quantum optics. The temperature dependence of the heating rate from the ion trap surface is analysed in a novel cryogenic micro ion trap. Furthermore segmented traps allow state manipulations by time dependent electrical potentials, generated by the control voltages. These electrical fields provide a fast and reliable control handle to the ions external degrees of freedom. Quantum computation in Paul trap arrays is based on a combination of ion crystal transport, splitting and merging operations, while laser driven quantum state manipulations are mainly carried out on small ion crystals. Within this thesis a basic building block was realised by performing transport operations with a single ground-state cooled ion. As a highlight of experimental achievements, shuttling in the non-adiabatic regime, on the timescale of the motional period was demonstrated with low residual energy transfer. For his endeavour a specialised low noise arbitrary function generator was designed and manufactured during this thesis. Arbitrary voltage ramps at a sampling rate of up to 2.5 MS/s on up to 12 channels allow the study of a novel excitation method by directly manipulating the ion using electrical forces. Accurate numerical simulations in combination with the fast high resolution voltage supply allow deterministic quantum manipulations via momentum kicks. I report the first experimental demonstration of displaced number states with trapped ions.
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.
Scalable trapped-ion quantum computing requires fast and reliable transport of ions through complex, segmented radiofrequency trap architectures without inducing excessive motional excitation. We present a numerical toolchain for the systematic generation of time-dependent electrode voltages enabling fast, low-excitation ion shuttling in segmented radiofrequency traps. Based on a model of the trap electrode geometry, the framework combines an electrostatic field solver, efficient unconstrained optimization, waveform postprocessing, and dynamical simulations of ion motion to compute voltage waveforms that realize prescribed transport trajectories while respecting experimental constraints such as voltage limits and bandwidth. The toolchain supports arbitrary trap geometries, including junctions and multi-zone layouts, and allows for the flexible incorporation of optimization objectives. We provide a detailed assessment of the accuracy of the framework by investigating its numerical stability and by comparing measured and predicted secular frequencies. The framework is optimized for numerical performance, enabling rapid numerical prototyping of trap architectures of increasing complexity. As application examples, we apply the framework to the transport of a potential well along a linear, uniformly segmented trap, and we compute a solution for shuttling a potential well around the corner of an X-type trap junction. The presented approach provides an extensible and highly efficient numerical foundation for designing and validating transport protocols in current and next-generation trapped-ion processors.
Current classical computing methods are unable to simulate quantum many-body interactions efficiently.Analog quantum simulators with even small numbers of quantum degrees of freedom are expected to enable the investigation of systems not fully accessible in traditional computing such as condensed-matter systems, quantum chemistry, and material science.Two-dimensional lattices of trapped ions are a good candidate to realize an analog quantum simulator for their addressability, individual control and individual detection.Here, we report on multiple unique lattice surface ion trap designs, microfabricated at Sandia National Laboratories, capable of trapping and interacting up to 4 ions.Ions are held in close proximity in individual all radio-frequency potential minima and interact via their Coulomb repulsion.The Coulomb coupling between ions allows for simulation of spin-spin interactions 1-6 .Control electrodes of the trap can be used to adjust principal axes of the ion's motion and thus enable individual control over the interaction between ions.The lattice trap array architecture tested in this work can be scaled to larger two-dimensional lattices of trapped ions.
Abstract Shuttling ions at high speed and with low motional excitation is essential for realizing fast and high-fidelity algorithms in many trapped-ion-based quantum computing architectures. Achieving such performance is challenging due to the sensitivity of an ion to electric fields and the unknown and imperfect environmental and control variables that create them. Here we implement a closed-loop optimization of the voltage waveforms that control the trajectory and axial frequency of an ion during transport in order to minimize the final motional excitation. The resulting waveforms realize fast round-trip transport of a trapped ion across multiple electrodes at speeds of 0.5 electrodes per microsecond (35 m·s −1 for a one-way transport of 210 μm in 6 μs) with a maximum of 0.36 ± 0.08 mean quanta gain. This sub-quanta gain is independent of the phase of the secular motion at the distal location, obviating the need for an electric field impulse or time delay to eliminate the coherent motion.
Scalable trapped-ion quantum computing requires fast and reliable transport of ions through complex, segmented radiofrequency trap architectures without inducing excessive motional excitation. We present a numerical toolchain for the systematic generation of time-dependent electrode voltages enabling fast, low-excitation ion shuttling in segmented radiofrequency traps. Based on a model of the trap electrode geometry, the framework combines an electrostatic field solver, efficient unconstrained optimization, waveform postprocessing, and dynamical simulations of ion motion to compute voltage waveforms that realize prescribed transport trajectories while respecting experimental constraints, such as voltage limits and bandwidth. The toolchain supports arbitrary trap geometries, including junctions and multi-zone layouts, and allows for the flexible incorporation of optimization objectives. We provide a detailed assessment of the accuracy of the framework by investigating its numerical stability and by comparing measured and predicted secular frequencies. The framework is optimized for numerical performance, enabling rapid numerical prototyping of trap architectures of increasing complexity. As application examples, we apply the framework to the transport of a potential well along a linear, uniformly segmented trap, and we compute a solution for shuttling a potential well around the corner of an X-type trap junction. The presented approach provides an extensible and highly efficient numerical foundation for designing and validating transport protocols in current and next-generation trapped-ion processors.