Arezoo Mokhberi

We present a method for measuring the polarizability of Rydberg ions confined in the harmonic potential of a Paul trap. For a highly excited electronic state, the coupling between the electronic wave function and the trapping field modifies the excitation probability depending on the motional state of the ion. This interaction strongly depends on the polarizability of the excited state and manifests itself in the state-dependent secular frequencies of the ion. We initialize a single trapped $^{40}$Ca$^+$ ion from the motional ground state into coherent states with $|α|$ up to 12 using electric voltages on the trap segments. The internal state, firstly initialised in the long-lived 3D$_{5/2}$ state, is excited to a Rydberg S$_{1/2}$-state via the 5P$_{3/2}$ state in a two-photon process. We probe the depletion of the 3D$_{5/2}$ state owing to the Rydberg excitation followed by a decay into the internal ground 4S$_{1/2}$ state. By analysing the obtained spectra we extract the polarizability of Rydberg states which agree with numerical calculations. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers. An accurate value of the state polarizability is needed for quantum gate operations with Rydberg ion crystals.

A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ and for $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ ion. From a nonlinear regression to resonance frequencies, we determined the ionization energy of 2 870 575.582(15) GHz, measured 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of $δ_{S_{1/2}}=1.802995(5)$ and $δ_{D_{5/2}}=0.626888(9)$ for $nS_{1/2}$ and $nD_{5/2}$ states respectively, which allow for unambiguous addressing of Rydberg levels of Ca$^+$ ions.

In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions feature several important properties, unique in their combination: they are tightly bound in a harmonic potential of a Paul trap, in which their internal and external degrees of freedom can be controlled in a precise fashion. High fidelity state preparation of both internal and motional states of the ions has been demonstrated, and the internal states have been employed to store and manipulate qubit information. Furthermore, strong dipolar interactions can be realised between ions in Rydberg states and be explored for investigating correlated many-body systems. By laser coupling to Rydberg states, the polarisability of the ions can be both enhanced and tuned. This can be used to control the interactions with the trapping fields in a Paul trap as well as dipolar interactions between the ions. Thus, trapped Rydberg ions present an attractive alternative for fast entangling operations as compared to those mediated by normal modes of trapped ions, which are advantageous for a future quantum computer or a quantum simulator.

We present an experimental investigation of the Rydberg 23 P$_{1/2}$ state of laser-cooled $^{40}$Ca$^+$ ions in a radiofrequency ion trap. Using micromotion sideband spectroscopy on a narrow quadrupole transition, the oscillating electric field at the ion position was precisely characterised, and the modulation of the Rydberg transition due to this field was minimised. From a correlated fit to this P line and previously measured P and F level energies of Ca II, we have determined the ionization energy of 95 751.916(32) $\rm {cm}^{-1}$, in agreement with the accepted value, and the quantum defect for the $n$ P$_{1/2}$ states.

We discuss the design and optimisation of two types of junctions between surface-electrode radiofrequency ion-trap arrays that enable the integration of experiments with sympathetically cooled molecular ions on a monolithic chip device. A detailed description of a multi-objective optimisation procedure applicable to an arbitrary planar junction is presented, and the results for a cross junction between four quadrupoles as well as a quadrupole-to-octupole junction are discussed. Based on these optimised functional elements, we propose a multi-functional ion-trap chip for experiments with translationally cold molecular ions at temperatures in the millikelvin range. This study opens the door to extending complex chip-based trapping techniques to Coulomb-crystallised molecular ions with potential applications in mass spectrometry, spectroscopy, controlled chemistry and quantum technology.