Matthias Keller

Control over the internal states of trapped ions makes them the ideal system to generate single and two-photon states. Coupling a single ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape, phase and frequency. Using the long coherence time of the ion's internal states and employing a scheme to protect the coherence of the ion-cavity interaction, we demonstrate the generation of a two-photon entangled state with full control over the phase. Initially, ion-photon entanglement is generated. A second photon is subsequently generated, mapping the ion's state onto the second photon. By adjusting the drive field the phase of the entangled state can be fully controlled. We implement this scheme in the most resource efficient way by utilizing a single $^{40}$Ca$^+$ ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.

We report on the sympathetic cooling and Coulomb crystallization of xenon highly charged ions (HCIs) with laser-cooled Ca$^+$ ions. The HCIs are produced in a compact electron beam ion trap, then charge selected, decelerated, and finally injected into a cryogenic linear Paul trap. There, they are captured into $^{40}$Ca$^+$ Coulomb crystals, and co-crystallized within them, causing dark voids in their fluorescence images. Fine control over the number of trapped ions and HCIs allows us to realize mixed-species crystals with arbitrary ordering patterns. By investigating Xe$^{q+}$--Ca$^+$ strings, we confirm the HCI charge states, measure their lifetime and characterize the mixed-species motional modes. Our system effectively combines the established quantum control toolbox for Ca$^+$ with the rich set of atomic properties of Xe highly charged ions, providing a resourceful platform for optical frequency metrology, searches for signatures of new physics, and quantum information science.

We present a novel, single-ion trap with integrated optical fibers directly embedded within the trap structure to deliver laser light as well as collect the ion's fluorescence. This eliminates the need for optical windows. We characterise the system's performance and measure signal-to-background ratios in the ion's fluorescence on the order of 50, which allows us to perform state readout with a fidelity over 99% in 600 $μ$s. We test the system's resilience to thermal variations in the range between 22°C and 53°C, and the system's vibration resilience at 34 Hz and 300 Hz and find no effect on its performance. The combination of compactness and robustness of our fiber-coupled trap makes it well suited for applications in, as well as outside, research laboratory environments and in particular for highly compact portable optical atomic clocks. While our system is designed for trapping $^{40}$Ca$^{+}$ ions the fundamental design principles can be applied to other ion species.

Incorporating optical cavities in ion traps is becoming increasingly important in the development of photonic quantum networks. However, the presence of the cavity can hamper efficient laser cooling of ions because of geometric constraints that the cavity imposes and an unfavourable Purcell effect that can modify the cooling dynamics substantially. On the other hand the coupling of the ion to the cavity can also be exploited to provide a mechanism to efficiently cool the ion. In this paper we demonstrate experimentally how cavity cooling can be implemented to improve the localisation of the ion and thus its coupling to the cavity. By using cavity cooling we obtain an enhanced ion-cavity coupling of $2π\times (16.7\pm 0.1)$ MHz, compared with $2π\times (15.2\pm 0.1)$ MHz when using only Doppler cooling.

We investigate schemes for generating indistinguishable single photons, a key feature of quantum networks, from a trapped ion coupled to an optical cavity. Through selection of the initial state in a cavity-assisted Raman transition, we suppress the detrimental effect of spontaneous emission present in previously demonstrated schemes in similar systems. We measure a visibility of 72(2)% without correction for background counts in a Hong-Ou-Mandel interference measurement for the new scheme, with 51(2)% for a commonly-used scheme with similar parameters. Schemes such as the one demonstrated here have applications in distributed quantum computing and communications, where high fidelities are vital, and depend on the mutual indistinguishability of single photons.

Strong coupling between an atom and an electromagnetic resonator is an important condition in cavity quantum electrodynamics (QED). While strong coupling in various physical systems has been achieved so far, it remained elusive for single atomic ions. In this paper we demonstrate for the first time the coupling of a single ion to an optical cavity with a coupling strength exceeding both atomic and cavity decay rates. We use cavity assisted Raman spectroscopy to precisely characterize the ion-cavity coupling strength and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Our work paves the way towards new applications of cavity QED utilizing single trapped ions in the strong coupling regime for quantum optics and quantum technologies.

We report a novel miniature Paul ion trap design with an integrated optical fibre cavity which can serve as a building block for a fibre-linked quantum network. In such cavity quantum electrodynamic set-ups, the optimal coupling of the ions to the cavity mode is of vital importance and this is achieved by moving the ion relative to the cavity mode. The trap presented herein features an endcap-style design complemented with extra electrodes on which additional radiofrequency voltages are applied to fully control the pseudopotential minimum in three dimensions. This method lifts the need to use three-dimensional translation stages for moving the fibre cavity with respect to the ion and achieves high integrability, mechanical rigidity and scalability. Not based on modifying the capacitive load of the trap, this method leads to precise control of the pseudopotential minimum allowing the ion to be moved with precisions limited only by the ion's position spread. We demonstrate this by coupling the ion to the fibre cavity and probing the cavity mode profile.

Trapped atomic ions are ideal single photon emitters with long lived internal states which can be entangled with emitted photons. Coupling the ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape. These features are key for quantum information processing and quantum communication. However, the photons emitted by these systems are unsuitable for long-distance transmission due to their wavelengths. Here we report the transmission of single photons from a single $^{40}\text{Ca}^{+}$ ion coupled to an optical cavity over a 10 km optical fibre via frequency conversion from 866 nm to the telecom C-band at 1,530 nm. We observe non-classical photon statistics of the direct cavity emission, the converted photons and the 10 km transmitted photons, as well as the preservation of the photons' temporal shape throughout. This telecommunication ready system can be a key component for long-distance quantum communication as well as future cloud quantum computation.

We report on the alteration of photon emission properties of a single trapped ion coupled to a high finesse optical fiber cavity. We show that the vacuum field of the cavity can simultaneously affect the emissions in both the infrared (IR) and ultraviolet (UV) branches of the $Λ-$type level system of $^{40}\mathrm{Ca}^+$ despite the cavity coupling only to the IR transition. The cavity induces strong emission in the IR transition through the Purcell effect resulting in a simultaneous suppression of the UV fluorescence. The measured suppression of this fluorescence is as large as 66% compared with the case without the cavity. Through analysis of the measurement results, we have obtained an ion-cavity coupling of $\bar{g}_0 = 2π\cdot (5.3 \pm 0.1)$ MHz, the largest ever reported so far for a single ion in the IR domain.

The Mølmer-Sørensen gate is a state-of-the-art entangling gate in the ion trap quantum computing where the gate fidelity can exceed 99\%. Here we propose an analogous implementation in the setting of cavity QED. The cavity photon mode acts as the bosonic degree of freedom in the gate in contrast of that played by a phonon mode in ion traps. This is made possible by utilising cavity assisted Raman transitions interconnecting the logical qubit states embedded in a four-level energy structure, making the "anti-Jaynes-Cummings" (AJC) term available under the rotating-wave approximation. We identify practical sources of infidelity and discuss their effects on the gate performance. Our proposal not only demonstrates an alternative entangling gate scheme but also sheds new light on the relationship between ion traps and cavity QED, in the sense that many techniques developed in the former are transferable to the latter through our framework.

We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential. We aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors for different mirror orientations with respect to the trapping electrodes, as well as for mirror misalignment. We also analyze the effect of the mirror material properties such as dielectric constants and surface conductivity, and study the effect of surface charges on the mirrors. The smallest trapping potential distortions are found if the cavities are aligned along the major symmetry axis of the electrode geometries. These cavity configurations also appear to be the most stable with respect to any mirror misalignment.

Recent technological advances in cavity quantum electrodynamics (CQED) are paving the way to utilise multiple quantum emitters confined in a single optical cavity. In such systems it is crucially important to control the quantum mechanical coupling of individual emitters to the cavity mode. In this regard, combining ion trap technologies with CQED provides a particularly promising approach due to the well-established motional control over trapped ions. Here we experimentally demonstrate coupling of up to five trapped ions in a string to a high-finesse optical cavity. By changing the axial position and spacing of the ions in a fully deterministic manner, we systematically characterise their coupling to the cavity mode through visibility measurements of the cavity emission. In good agreement with the theoretical model, the results demonstrate that the geometrical configuration of multiple trapped ions can be manipulated to obtain optimal cavity coupling. Our system presents a new ground to explore CQED with multiple quantum emitters, enabled by the highly controllable collective light-matter interaction.

We present a mass spectrometric technique for identifying the masses and relative abundances of Coulomb-crystallized ions held in a linear Paul trap. A digital radiofrequency waveform is employed to generate the trapping potential, as this can be cleanly switched off, and static dipolar fields subsequently applied to the trap electrodes for ion ejection. Excellent detection efficiency is demonstrated for Ca+ and CaF+ ions from bi-component Ca+/CaF+ Coulomb crystals prepared by reaction of Ca+ with CH3F. A quantitative linear relationship is observed between ion number and the corresponding integrated TOF peak, independent of the ionic species. The technique is applicable to a diverse range of multi-component Coulomb crystals - demonstrated here for Ca+/NH3+/NH4+ and Ca+/CaOH+/CaOD+ crystals - and will facilitate the measurement of ion-molecule reaction rates and branching ratios in complicated reaction systems.

We present a novel method of machining optical fiber surfaces with a CO${}_2$ laser for use in Fiber-based Fabry-Perot Cavities (FFPCs). Previously FFPCs were prone to large birefringence and limited to relatively short cavity lengths ($\le$ 200 $μ$m). These characteristics hinder their use in some applications such as cavity quantum electrodynamics with trapped ions. We optimized the laser machining process to produce large, uniform surface structures. This enables the cavities to achieve high finesse even for long cavity lengths. By rotating the fibers around their axis during the laser machining process the asymmetry resulting from the laser's transverse mode profile is eliminated. Consequently we are able to fabricate fiber mirrors with a high degree of rotational symmetry, leading to remarkably low birefringence. Through measurements of the cavity finesse over a range of cavity lengths and the polarization dependence of the cavity linewidth, we confirmed the quality of the produced fiber mirrors for use in low-birefringence FFPCs.

In this paper we present a technique for the precise measurement of electric dipole allowed transitions in trapped ions. By applying a probe and a cooling laser in quick succession, the full transition can be probed without causing distortion from heating the ion. In addition, two probes can be utilized to measure a dispersion-like signal, which is well suited to stabilizing the laser to the transition. We have fully characterized the parameters for the measurement and find that it is possible to measure the transition frequency to better than 100kHz with an interrogation time of 30s. The long-term stability of the spectroscopy signal is determined by employing two independent ion trap systems. The first ion trap is used to stabilize the spectroscopy laser. The second ion trap is then employed to measure the stability by continuously probing the transition at two frequencies. From the Allan variance a frequency instability of better than 10$^{-10}$ is obtained for an interrogation time of 1000s.

We have developed a novel all-optical broadband scheme for exciting, amplifying and measuring the secular motion of ions in a radio frequency trap. Oscillation induced by optical excitation has been coherently amplified to precisely control and measure the ion's secular motion. Requiring only laser line-of-sight, we have shown that the ion's oscillation amplitude can be precisely controlled. Our excitation scheme can generate coherent motion which is robust against variations in the secular frequency. Therefore, our scheme is ideal to excite the desired level of oscillatory motion under conditions where the secular frequency is evolving in time. Measuring the oscillation amplitude through Doppler velocimetry, we have characterized the experimental parameters and compared them with a molecular dynamics simulation which provides a complete description of the system.

We have developed a novel scheme to measure the secular motion of trapped ions. Employing pulsed excitation and analysis of the fluorescence of laser cooled ions, we have measured the centre-of-mass mode frequency of single as well as entire ion crystals with a frequency precision better than 5e-4 within an interrogation time on the order of seconds, limited only by the fluorescence collection efficiency and the background noise. We have used this method to measure the mass of ions and observed charge exchange collisions between trapped calcium isotopes.

We have investigated the all-optical generation of ions by photo-ionisation of atoms generated by pulsed laser ablation. A direct comparison between a resistively heated oven source and pulsed laser ablation is reported. Pulsed laser ablation with 10 ns Nd:YAG laser pulses is shown to produce large calcium flux, corresponding to atomic beams produced with oven temperatures greater than 650 K. For an equivalent atomic flux, pulsed laser ablation is shown to produce a thermal load more than one order of magnitude smaller than the oven source. The atomic beam distributions obey Maxwell-Boltzmann statistics with most probable speeds corresponding to temperatures greater than 2200 K. Below a threshold pulse fluence between 280 mJ/cm^2 and 330 mJ/cm^2, the atomic beam is composed exclusively of ground state atoms. For higher fluences ions and excited atoms are generated.

We have realized a compact system to efficiently couple the fluorescent light emitted by a single trapped ion to two opposing optical fibers. The fibers are tightly integrated in the center electrodes of a miniature endcap trap. They capture light from the ion with a numerical aperture of 0.34 each, corresponding to 6% of the solid angle in total. The high collection efficiency and high signal-to-background ratio make the setup an ideal quantum light source. We have observed strong antibunching of the photons emitted from the two fibers. The system has a range of applications from single-ion state detection in quantum information processing to strong coupling cavity-QED with ions.