Decoherence of tripartite states - a trapped ion coupled to an optical cavity

We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.Comment: Revised version, errors corrected and references added. 12 pages, 6 figures, Presented at ICSSUR May 2005, Besancon, Franc

Focusing a deterministic single-ion beam

We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an einzel-lens. Starting from a segmented linear Paul trap, we have implemented a procedure which allows us to deterministically load a predetermined number of ions by using the potential shaping capabilities of our segmented ion trap. For single-ion loading, an efficiency of 96.7(7)% has been achieved. These ions are then deterministically extracted out of the trap and focused down to a 1sigma-spot radius of (4.6 \pm 1.3)mum at a distance of 257mm from the trap center. Compared to former measurements without ion optics, the einzel-lens is focusing down the single-ion beam by a factor of 12. Due to the small beam divergence and narrow velocity distribution of our ion source, chromatic and spherical aberration at the einzel-lens is vastly reduced, presenting a promising starting point for focusing single ions on their way to a substrate.Comment: 16 pages, 7 figure

Nature of the Darwin term and (Zα)4m3/M2{(Z\alpha)^4 m^3/M^2} contribution to the Lamb shift for an arbitrary spin of the nucleus

The contact Darwin term is demonstrated to be of the same origin as the spin-orbit interaction. The $(Z\alpha)^4 m^3/M^2$ correction to the Lamb shift, generated by the Darwin term, is found for an arbitrary nonvanishing spin of the nucleus, both half-integer and integer. There is also a contribution of the same nature to the nuclear quadrupole moment.Comment: 9 pages, latex, no figure

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

Controlling fast transport of cold trapped ions

We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10^4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 micro meter in 3.6 micro seconds). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10 $\pm$ 0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.Comment: 5 pages, 4 figure

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

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. The decoherence-free subspace is left neither during gate operations nor during the transport of quantum information.Comment: 6 pages, 6 figure