D. Kolbe

We demonstrate excitation of a single trapped cold $^{40}$Ca$^+$ ion to Rydberg levels by laser radiation in the vacuum-ultraviolet at 122 nm wavelength. Observed resonances are identified as 3d$^2$D$_{3/2}$ to 51 F, 52 F and 3d$^2$D$_{5/2}$ to 64F. We model the lineshape and our results imply a large state-dependent coupling to the trapping potential. Rydberg ions are of great interest for future applications in quantum computing and simulation, in which large dipolar interactions are combined with the superb experimental control offered by Paul traps.

We present studies of mixed Coulomb crystals of 40Ca+ and 40Ca2+ ions in a linear Paul trap. Doubly charged ions are produced by photoionisation of trapped 40Ca+ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled 40Ca+ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with 40Ca2+ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al., Phys. Rev. A 87, (2013) 052304 and Phys. Rev. Lett 108, (2012) 023003 using ions excited to Rydberg states.

We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss anticipated theoretical and experimental challenges on the way towards its realization.