An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this "strong coupling regime" of cavity quantum electrodynamics 1,2 (cQED) has been the subject of spectacular experimental advances, and great efforts have been made to control the coupling rate by trapping 3,4 and cooling the atom 5,6 towards the motional ground state, which has been achieved in one dimension so far 5 . For N atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einstein condensates (BECs) 7 , but although first experiments combining BECs and optical cavities have been reported recently 8,9 , coupling BECs to strong-coupling cavities has remained an elusive goal. Here we report such an experiment, which is made possible by combining a new type of fibre-based cavity 10 with atom chip technology 11 . This allows single-atom cQED experiments with a simplified setup and realizes the new situation of N atoms in a cavity each of which is identically and strongly coupled to the cavity mode 12 . Moreover, the BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field. This gives rise to a controlled, tunable coupling rate, as we confirm experimentally. We study the heating rate caused by a cavity transmission measurement as a function of the coupling rate and find no measurable heating for strongly coupled BECs. The spectrum of the coupled atoms-cavity system, which we map out over a wide range of atom numbers and cavity-atom detunings, shows vacuum Rabi splittings exceeding 20 gigahertz, as well as an unpredicted additional splitting which we attribute to the atomic hyperfine structure. The system is suitable as a light-matter quantum interface for quantum information 13 . 2 The interaction of an ensemble of N atoms with a single mode of radiation has been a recurrent theme in quantum optics at least since the work of Dicke 14 , who showed that under certain conditions the atoms interact with the radiation collectively, giving rise to new effects such as superradiance. Recently, collective interactions with weak fields, with and without a cavity, have become a focus of theoretical and experimental investigations, especially since it became clear that they can turn the ensemble into a quantum memory 13,15 . Such a memory would become a key element for processing quantum information 13,16 if realized with near-unit conversion efficiency and long storage time. The figure of merit determining the probability of converting an atomic excitation into a cavity photon (a "memory qubit" into a "flying qubit") is the between the ensemble and the field, 2 is the cavity photon decay rate and 2 the atomic spontaneous emission rate. (Up to a factor of order 1, C N is the single-pass optical depth of the atomic sample multiplied by the cavity finesse .) For weak excitation, to which we restrict oursel...

We have realized a fiber-based Fabry-Perot cavity with CO 2 lasermachined mirrors. It combines very small size, high finesse F ≥ 130000, small waist and mode volume, and good mode matching between the fiber and cavity modes. This combination of features is a major advance for cavity quantum electrodynamics (CQED), as shown in recent CQED experiments with Bose-Einstein condensates enabled by this cavity [Y. Colombe et al., Nature 450, 272 (2007)]. It should also be suitable for a wide range of other applications, including coupling to solid-state emitters, gas detection at the single-particle level, fiber-coupled single-photon sources and high-resolution optical filters with large stopband.

Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light.1, 2 Similar control is difficult to achieve with radio frequency or microwave radiation because the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms' motion. 2, 3 The field gradients are negligible at these frequencies for freely propagating fields; however, stronger gradients can be generated in the near-field of microwave currents in structures smaller than the free-space wavelength. 4,5 In the experiments reported here, we coherently manipulate the internal quantum states of the ions on time scales of 20 ns. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation 4, 6-8 suitable for general quantum computation. 9 We implement both operations through the magnetic fields from 1 arXiv:1104.3573v3 [quant-ph]