Rydberg excitation of trapped cold ions: a detailed case study

Abstract

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.

Rydberg Excitation of a Single Trapped Ion

“…This results in giant dipolar interactions between Rydberg atoms [3] which enable the formation of ultralong-range molecules [4], quantum logic gate operations between two neutral atoms [5,6], and the control of the state of transmitted light through a Rydberg sample at the single photon level [7]. A completely new approach to this field of research is the Rydberg excitation of trapped ions [8,9,10], which aims to combine the long-range Rydberg-blockade mechanism, demonstrated in the case of neutral atoms confined in optical lattices [11,12,13], with the superb level of control over single ions achieved in Paul traps [14,15]. Rydberg ions in Coulomb crystals will allow for shaping localized vibrational modes for quantum simulation and fast parallel execution of quantum gates [16,17].…”

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

“…1, described in detail in [11]) consisting of four cylindrical electrodes (diameter 2.5 mm) and two endcaps (distance 10 mm) with holes (diameter 1 mm) to provide axial optical access to the ions. The Paul trap is operated with an rf-amplitude of U rf = 100 V -200 V at a frequency Ω/(2π) = 10.66 MHz.…”

“…A detailed description of this laser can be found in [17,11]. Coherent VUV radiation at 121.26 nm is produced by triple resonant four-wave mixing in mercury with three fun-damental waves at 254 nm, 408 nm and 540 nm (see Fig.…”

“…The idea of mode shaping has the potential to drastically simplify this approach since the complexity of the mode spectrum can be significantly reduced. Such tailoring of vibrational modes may be possible employing the unique properties of Rydberg states [10], where the polarizability of the ion is strongly enhanced leading to significant modifications of the radial trapping potential [11,12].…”

The Production and Study of Cold Antiprotons and Antihydrogen

“…Starting in the Hänsch Laboratory in Garching, and then moving to the Walz Laboratory in Mainz, our collaborators continue to improve a source of Lyman alpha radiation suitable for laser cooling and for 1s-2p spectrosocpy [46,47,48,49,50,51,52,53,54,55]. Four-wave mixing is used to generate continuous, coherent Lyman alpha radiation at 121.5 nm.…”