Dynamics and control of fast ion crystal splitting in segmented Paul traps

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.Comment: 23 pages, 9 figure

Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.Comment: 5 pages, 4 figures, supplemental material (mathematica and matlab files) available upon reques

Controlling the transport of an ion: Classical and quantum mechanical solutions

We investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time

Cryogenic setup for trapped ion quantum computing

We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120~dB reduction of 50~Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than $\pm$20~nm over 2~s. In addition to the cryogenic apparatus, we describe the setup required for an operation with $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ and $^{\mathrm{88}}$Sr$^{\mathrm{+}}$ ions. The instability of the laser manipulating the optical qubits in $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ is characterized yielding a minimum of its Allan deviation of 2.4$\cdot$10$^{\mathrm{-15}}$ at 0.33~s. To evaluate the performance of the apparatus, we trapped $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ ions, obtaining a heating rate of 2.14(16)~phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8)~ms

Theoretical model for ultracold molecule formation via adaptive feedback control

We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to unshaped pulses at the respective optimal pump-dump delay time. Since our model yields directly the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments

Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 \mu m above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schr\"odinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.Comment: 20 pages, 13 figure

A trapped-ion local field probe

We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is confined in a segmented Paul trap and shuttled around to reach different probing sites. By the use of a single atom probe, it becomes possible characterizing fields with spatial resolution of a few nm within an extensive region of millimeters. We demonstrate the scheme by accurately investigating the electric fields providing the confinement for the ion. For this we present all theoretical and practical methods necessary to generate these potentials. We find sub-percent agreement between measured and calculated electric field values

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