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arXiv:1505.04942 · New Journal of Physics

Fast separation of two trapped ions

M Palmero, S. Martínez-Garaot, U G Poschinger, A Ruschhaupt, Juan Gonzalo Muga

Published Sep 18, 2015• 30 citations
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Abstract

We design fast protocols to separate or recombine two ions in a segmented Paul trap. By inverse engineering the time evolution of the trapping potential composed of a harmonic and a quartic term, it is possible to perform these processes in a few microseconds without final excitation. These times are much shorter than the ones reported so far experimentally. The design is based on dynamical invariants and dynamical normal modes. Anharmonicities beyond the harmonic approximation at potential minima are taken into account perturbatively. The stability versus an unknown potential bias is also studied.

DOI
10.1088/1367-2630/17/9/093031

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We design fast protocols to separate or recombine two ions in a segmented Paul trap. By inverse engineering the time evolution of the trapping potential composed of a harmonic and a quartic term, it is possible to perform these processes in a few microseconds without final excitation. These times are much shorter than the ones reported so far experimentally. The design is based on dynamical invariants and dynamical normal modes. Anharmonicities beyond the harmonic approximation at potential minima are taken into account perturbatively. The stability versus an unknown potential bias is also studied.
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.
Abstract We inverse engineer fast rotations of a transversally tight, linear trap with two ions for a predetermined rotation angle and time, avoiding final excitation. Different approaches are analyzed and compared when the ions are of the same species or of different species. The separability into dynamical normal modes for equal ions in a harmonic trap, or for different ions in non-harmonic traps with up to quartic terms allows for simpler computations of the rotation protocols. For non-separable scenarios, in particular for different ions in harmonic traps, rotation protocols are also found using more costly numerical optimisations.
We investigate the dynamics of mixed-species ion crystals during transport between spatially distinct locations in a linear Paul trap in the diabatic regime. In a general mixed-species crystal, all degrees of freedom along the direction of transport are excited by an accelerating well, so unlike the case of same-species ions, where only the center-of-mass mode is excited, several degrees of freedom have to be simultaneously controlled by the transport protocol. We design protocols that lead to low final excitations in the diabatic regime using invariant-based inverse engineering for two different-species ions and also show how to extend this approach to longer mixed-species ion strings. Fast transport of mixed-species ion strings can significantly reduce the operation time in certain architectures for scalable quantum-information processing with trapped ions.
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.