Trapped ions coupled to optical cavities can be used to build up quantum interfaces between stationary and flying qubits in a quantum network. Shared entangled states between different network nodes have proven to be an essential resource for various applications of a quantum network, such as distributed quantum computation. At a first quantum network node, we have trapped ions in a linear Paul trap and coupled them to an optical cavity two centimeter in length. We have demonstrated entanglement of a single ion with a single photon, and used this high-fidelity operation to entangle two ions in a heralded fashion [1,2]. However, the speed of these operations is intrinsically limited by the ion-cavity coupling strength, which is predetermined by the length of the optical cavity.
Fiber-based optical cavities have been coupled to single ions and it has been shown that these microscopic cavities allow access to the strong coupling regime .
Operating in this regime would enable quantum communication protocols to be carried out over long distances with enhanced fidelity and efficiency. With this goal, we have designed and constructed a novel ion-cavity system which incorporates a fiber cavity. In my talk, I will introduce basic building blocks of quantum networks based on trapped ions coupled to optical cavities and will present recent results, including simulation and characterization of our fiber-based ion-cavity system.
 A. Stute et al., Nature. 485, 482 (2012)
 B. Casabone et al., Phys. Rev. Lett. 111, 100505 (2013)
 H. Takahashi et al., arXiv:1808.04031 (2018)
Quantum measurement is based on the interaction between a quantum object and a meter entangled with the object. While information about the object is being extracted by the interaction, the quantum fluctuations of the object are imprinted onto the meter as a form of decoherence. Here, we study the nondestructive reconstruction of the photon number in an optical cavity, harnessing the quantum decoherence. We consider a single 40Ca+ ion that is dispersively coupled to a high-finesse cavity. While the cavity is populated with weak coherent states, Ramsey spectroscopy is performed on the qubit transition to identify the shift and the broadening of the atomic energy levels. The shift is due to the ac Stark effect induced by cavity photons, and the broadening is attributed to the photon-number fluctuations of the cavity field. We show theoretically that photon-number distributions of the intracavity fields can be reconstructed in a basis of up to eleven Fock states with the maximum likelihood method. Furthermore, we show that the photon number of each polarization component can also be reconstructed, taking advantage of the rich energy-level structure of the ion. In combination with currently available mirror-coating technology, quantum non-demolition (QND) measurement of cavity photons will make it possible to create and manipulate nonclassical cavity-field states in the optical domain.
Trapped ions are a promising platform for local quantum information processing. In order to distribute this quantum information over long distances, we can take advantage of optical cavities, which ofier a coherent interface between matter and light, enabling the transfer of quantum information from stationary qubits such as ions onto photons. We demonstrate such an interface by coupling trapped ions to a cavity and have recently shown that a quantum state can be faithfully transferred from a single ion onto a single photon. In particular, this transfer can be improved by taking advantage of a collective effect between multiple ions, namely, superradiant emission into the cavity. In this proof-of-principle experiment, we tune the phase of a two-ion entangled state between sub- and superradiance. The superradiant coupling is then used to enhance the transfer of quantum information onto a photon from a logical qubit encoded in the two ions. Finally, prospects for linking together distant ions in cavities via a quantum network are discussed. Toward this goal, we outline a fiber-based ion-cavity experiment which allows access to the single-ion strong-coupling regime.