We prepare a maximally entangled state of two ions and couple both ions to the mode of an optical cavity. The phase of the entangled state determines the collective interaction of the ions with the cavity mode, that is, whether the emission of a single photon into the cavity is suppressed or enhanced. By adjusting this phase, we tune the ion-cavity system from sub-to superradiance. We then encode a single qubit in the two-ion superradiant state and show that this encoding enhances the transfer of quantum information onto a photon.Sub-and superradiance are fundamental effects in quantum optics arising in systems that are symmetric under the interchange of any pair of particles [1][2][3]. Superradiance has been widely studied in many-atom systems, in which effects such as a phase transition [4,5] and narrow-linewidth lasing [6] have recently been observed. For few-atom systems, each atom's state and position can be precisely controlled, and thus collective emission effects such as Rydberg blockade [7] and the Lamb shift [8] can be tailored. In a pioneering experiment using two trapped ions, variation of the ions' separation allowed both sub-and superradiance to be observed, with the excited-state lifetime extended or reduced by up to 1.5% [9]. The contrast was limited because spontaneous emission from the ions was not indistinguishable, as the ions' separation was on the order of the wavelength of the emitted radiation. This limitation can be overcome by observing preferential emission into a single mode, such as the mode defined by incident radiation [1] or by an optical cavity. In a cavity setting, indistinguishability is guaranteed when the emitters are equally coupled to the mode, even if they are spatially separated. Subradiance corresponds to a suppressed interaction of the joint state of the emitters with the cavity mode, while for the superradiant state, the interaction is enhanced.In the context of quantum networks [10,11], superradiance can improve a quantum interface when one logical qubit is encoded across N physical qubits. In the DLCZ protocol for heralded remote entanglement, efficient retrieval of stored photons is based on superradiance [12,13]. Superradiance can also improve the performance of a deterministic, cavity-based interface, which enables the direct transmission of quantum information between network nodes [14]. If a qubit is encoded in the state.. ↓ N , the coupling rate to the cavity is enhanced from the single-qubit rate g to the effective rate g √ N , relaxing the technical requirements for strong coupling between light and matter [15]. This state corresponds to the first step in the superradiant cascade described by Dicke [1]. In contrast, subradiant states are antisymmetrized, resulting in suppressed emission. From a quantum-information perspective, subradiant states are interesting because they span a decoherence-free subspace [16][17][18]. A subradiant state of two superconducting qubits coupled to a cavity has recently been prepared [19].Here, we generate collective states of tw...

We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Optical profilometry allows us to determine the radii of curvature and ellipticities of the fiber mirrors. From finesse measurements, we infer a single-atom cooperativity of up to 12 for FFPCs longer than 200 μm in length; comparison to cavities constructed with reference substrate mirrors produced in the same coating run indicates that our FFPCs have similar scattering losses. We characterize the birefringence of our fiber mirrors, finding that careful fiber-mirror selection enables us to construct FFPCs with degenerate polarization modes. As FFPCs are novel devices, we describe procedures developed for handling, aligning, and cleaning them. We discuss experiments to anneal fiber mirrors and explore the influence of the atmosphere under which annealing occurs on coating losses, finding that annealing under vacuum increases the losses for our reference substrate mirrors. X-ray photoelectron spectroscopy measurements indicate that these losses may be attributable to oxygen depletion in the mirror coating. Special design considerations enable us to introduce a FFPC into a trapped ion setup. Our unique linear Paul trap design provides clearance for such a cavity and is miniaturized to shield trapped ions from the dielectric fiber mirrors. We numerically calculate the trap potential in the absence of fibers. In the experiment additional electrodes can be used to compensate distortions of the potential due to the fibers. Home-built fiber feedthroughs connect the FFPC to external optics, and an integrated nanopositioning system affords the possibility of retracting or realigning the cavity without breaking vacuum.

We demonstrate precise control of the coupling of each of two trapped ions to the mode of an optical resonator. When both ions are coupled with near-maximum strength, we generate ion-ion entanglement heralded by the detection of two orthogonally polarized cavity photons. The entanglement fidelity with respect to the Bell state Ψ+ reaches F≥(91.9±2.5)%. This result represents an important step toward distributed quantum computing with cavities linking remote atom-based registers.

We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can be operated at cavity lengths as large as 1.5 mm without significant deterioration of the finesse. This is achieved by using a laser dot machining technique to shape spherical mirrors with ultralow roughness and employing single-mode fibers with large mode area for good mode matching to the cavity. Additionally, in contrast to previous FFPs, these cavities can be used over an octave-spanning frequency range with adequate coatings. We also show directly that shape deviations caused by the fiber's index profile lead to a finesse decrease as observed in earlier attempts to build long FFP cavities, and show a way to overcome this problem.

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