15.10.Iv Ions: vibrational states

Fabrication of a segmented micro Penning trap and numerical investigations of versatile ion positioning protocols


M. Hellwig, A. Bautista-Salvador, K. Singer, G. Werth, F. Schmidt-Kaler
New Journal of Physics 12 065019 (2010)

We describe a versatile planar Penning trap structure, which allows to dynamically modify the trapping configuration almost arbitrarily. The trap consists of 37 hexagonal electrodes, each of 300 mikron diameter, fabricated in a gold-on-sapphire lithographic technique. Every hexagon can be addressed individually, thus shaping the electric potential. The fabrication of such a device with clean room methods is demonstrated.

A trapped-ion local field probe


G. Huber, F. Ziesel, U.G. Poschinger, K. Singer, F. Schmidt-Kaler
Applied Physics B: Lasers and Optics 100, 725 (2010)

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.

Quantum gate in the decoherence-free subspace of trapped-ion qubits


P. Ivanov, U.G. Poschinger, K. Singer, F. Schmidt-Kaler
Europhysics Letters 92, 30006 (2010)

We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground-state and two physical qubits to make up one logical qubit with ultra long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing.

Quantum zigzag transition in interacting atom chains


E. Shimshoni, G. Morigi and S. Fishman

A string of trapped interacting ions at zero temperature ($T=0$) exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. The transition is driven by transverse, short wavelength vibrational modes. We propose a quantum field--theoretical description of this transition by the one dimensional Ising model in a transverse field.

Trapped ions as quantum bits: Essential numerical tools (Colloquium)


K. Singer, U. Poschinger, M. Murphy, P. Ivanov, F. Ziesel, T. Calarco, F. Schmidt-Kaler


Rev. Mod. Phys. 82, 2609 (2010)

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, 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 are presented.

Correcting errors in a quantum gate with pushed ions via optimal control


U. V. Poulsen, S. Sklarz, D. Tannor, T. Calarco


Phys. Rev. A 82, 012339 (2010).

We analyze in detail the so-called pushing gate for trapped ions, introducing a time-dependent harmonic approximation for the external motion. We show how to extract the average fidelity for the gate from the resulting semiclassical simulations. We characterize and quantify precisely all types of errors coming from the quantum dynamics and reveal that slight nonlinearities in the ion-pushing force can have a dramatic effect on the adiabaticity of gate operation.

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