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 <sup>40</sup>Ca<sup>+</sup> 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.