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Trapped atomic ions embedded in optical cavities are a promising platform to enable long-distance quantum networks and their most far-reaching applications. Here we achieve and analyze photon indistinguishability in a telecom-converted ion-cavity system. First, two-photon interference of cavity photons at their ion-resonant wavelength is observed and found to reach the limits set by spontaneous emission. Second, this limit is shown to be preserved after a two-step frequency conversion replicating a distributed scenario, in which the cavity photons are converted to the telecom C band and then back to the original wavelength. The achieved interference visibility and photon efficiency would allow for the distribution and practical verification of entanglement between ion-qubit registers separated by several tens of kilometers.

We describe a novel method to measure the surface charge densities on optical fibers placed in the vicinity of a trapped ion, where the ion itself acts as the probe. Surface charges distort the trapping potential, and when the fibers are displaced, the ion's equilibrium position and secular motional frequencies are altered. We measure the latter quantities for different positions of the fibers and compare these measurements to simulations in which unknown charge densities on the fibers are adjustable parameters. Values ranging from −10 to +50 e/µm 2 were determined. Our results will benefit the design and simulation of miniaturized experimental systems combining ion traps and integrated optics, for example, in the fields of quantum computation, communication and metrology. Furthermore, our method can be applied to any setup in which a dielectric element can be displaced relative to a trapped charge-sensitive particle.

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We dispersively couple a single trapped ion to an optical cavity to extract information about the cavity photon-number distribution in a nondestructive way. The photon-number-dependent AC-Stark shift experienced by the ion is measured via Ramsey spectroscopy. We use these measurements first to obtain the ion-cavity interaction strength. Next, we reconstruct the cavity photon-number distribution for coherent states and for a state with mixed thermal-coherent statistics, finding overlaps above 99% with the calibrated states.Cavity quantum electrodynamics (cavity QED) provides a conceptually simple and powerful platform for probing the quantized interaction between light and matter [1]. Early experiments opened a window into the dynamics of coherent atom-photon interactions, first through observations of collective Rabi oscillations and vacuum Rabi splittings [2][3][4][5] and later at the single-atom level [6][7][8][9][10][11]. More recently, building on measurements of the cavity field via the atomic phase [12,13], cavity photon statistics have been analyzed in experiments with Rydberg atoms or superconducting qubits in microwave resonators [14][15][16][17], culminating in the generation and stabilization of nonclassical cavity field states [18][19][20][21][22][23][24]. These experiments operate in a dispersive regime, in which information about the cavity field can be extracted via the qubits with minimal disturbance to the field [1].In parallel, it was pointed out that the Jaynes-Cummings Hamiltonian that describes cavity QED also describes the interaction of light and ions in a harmonic trapping potential [25]. This interaction underpins the generation of nonclassical states of motion [26][27][28][29] and the implementation of gates between trapped ions [30]. In analogy to the phase shifts experienced by qubits due to the cavity field, ions experience quantized AC-Stark shifts due to their coupling to the harmonic trap potential [31]. These shifts have been characterized using techniques similar to those introduced in Ref. [12]. Here, we have transferred the principle of dispersive measurement to an ion qubit coupled to a cavity. In contrast to experiments with flying Rydberg atoms, the ion is strongly confined; in contrast to both Rydberg and superconducting-qubit experiments, our cavity operates in the optical regime.We employ a single trapped 40 Ca + ion as a quantum sensor [32] to extract information about cavity photons without destroying them. Via Ramsey spectroscopy of the ion, we measure the phase shift and dephasing of the ion's state, both of which result from the interaction of the ion with the cavity field. The phase shift is induced by the mean number of cavity photons due to the AC-Stark effect, and the dephasing is caused by uncertainties in the cavity photon number. Reconstructing the cavity photon-number distribution from these measurements allows us to determine the mean and the width of the distribution and thus to distinguish between states with coherent photon statistics and mixed thermal-co...