A single ion as a shot noise limited magnetic field gradient probe

It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of \Delta B/B_0 ~ 5*10^{-7} over a test distance of 140 \micro m, which can be extended to the mm range, still with sub \micro m resolution. A fast experimental sequence is presented, facilitating its use as a magnetic field gradient calibration routine, and it is demonstrated that the main limitation is the quantum shot noise.Comment: 5 pages, 3 figure

Colloquium: Trapped ions as quantum bits -- essential numerical tools

Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of the wavepacket dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wavefunctions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material (http://kilian-singer.de/ent).Comment: accepted for publication in Review of Modern Physics 201

Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap

Miniaturized ion trap arrays with many trap segments present a promising architecture for scalable quantum information processing. The miniaturization of segmented linear Paul traps allows partitioning the microtrap in different storage and processing zones. The individual position control of many ions - each of them carrying qubit information in its long-lived electronic levels - by the external trap control voltages is important for the implementation of next generation large-scale quantum algorithms. We present a novel scalable microchip multi-segmented ion trap with two different adjacent zones, one for the storage and another dedicated for the processing of quantum information using single ions and linear ion crystals: A pair of radio-frequency driven electrodes and 62 independently controlled DC electrodes allows shuttling of single ions or linear ion crystals with numerically designed axial potentials at axial and radial trap frequencies of a few MHz. We characterize and optimize the microtrap using sideband spectroscopy on the narrow S1/2 D5/2 qubit transition of the 40Ca+ ion, demonstrate coherent single qubit Rabi rotations and optical cooling methods. We determine the heating rate using sideband cooling measurements to the vibrational ground state which is necessary for subsequent two-qubit quantum logic operations. The applicability for scalable quantum information processing is proven.Comment: 17 pages, 11 figure

Quantum State Manipulation and Dynamics in Micro Ion Traps

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