We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO 2 laser-machined, high-finesse optical Fabry-Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections to the paraxial resonator theory is in excellent agreement with the measurements, showing that geometric effects are the main source of the frequency splitting of polarization modes for the type of microscopic cavity studied here. By rotating one of the mirrors around the cavity axis, the splitting can be tuned. In the case of an identical differential phase shift per mirror, it can even be eliminated, despite a nonvanishing eccentricity of each mirror. We expect our results to have important implications for many experiments in cavity quantum electrodynamics, where Fabry-Perot cavities with small mode volumes are required. [33,34] to applications in quantum information processing, such as the efficient and coherent coupling of atomic states to the polarization of single photons [35]. The latter requires degeneracy of the polarization eigenmodes, which has been achieved for Fabry-Perot cavities built from superpolished mirror substrates [36]. Microfabricated cavities, however, can have increased frequency splittings between polarization eigenmodes, as was first observed in CO 2 laser-machined resonators [10,20]. If the splitting is on the order of the linewidth of the cavity, there can be detrimental effects on all kinds of experiments [37][38][39]. There are two strategies for dealing with the splitting in cavities: to minimize it until it becomes negligible, or to increase it such that the two polarization modes are well separated [38]. In either case, it is necessary to understand and control this splitting.Two potential sources of the splitting of polarization eigenmodes in a Fabry-Perot cavity can be distinguished. The first one is birefringence of the mirror materials, usually attributed to mechanical stress [39,40]. Combined with a finite penetration depth, this leads to a polarization-dependent phase shift upon reflection. The second source is directly related to the cavity geometry. Its existence is not evident from the usual paraxial resonator theory, in which the cavity field and its resonances are described by a scalar mode function that is independent of the polarization. The paraxial theory does describe the polarization-independent splitting of higher-order transverse modes of equal order in a cavity with elliptical mirrors, but it cannot account for an additional splitting of each of these modes into a doublet via the polarization degree of freedom. Any splitting of the polarization modes thus has to originat...

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Quantum repeaters promise to enable quantum networks over global distances by circumventing the exponential decrease in success probability inherent in direct photon transmission. We propose a realistic, functionally integrated quantum-repeater implementation based on single atoms in optical cavities. Entanglement is directly generated between the single-atom quantum memory and a photon at telecom wavelength. The latter is collected with high efficiency and adjustable temporal and spectral properties into a spatially well-defined cavity mode. It is heralded by a near-infrared photon emitted from a second, orthogonal cavity. Entanglement between two remote quantum memories can be generated via an optical Bell-state measurement, while we propose entanglement swapping based on a highly efficient, cavity-assisted atom-atom gate. Our quantum-repeater scheme eliminates any requirement for wavelength conversion such that only a single system is needed at each node. We investigate a particular implementation with rubidium and realistic parameters for Fabry-Perot cavities based on CO 2 laser-machined optical fibers. We show that the scheme enables the implementation of a rather simple quantum repeater that outperforms direct entanglement generation over large distances and does not require any improvements in technology beyond the state of the art.

We demonstrate semiconductor terahertz (THz) resonators with sub-wavelength dimensions in all three dimensions of space. The maximum confinement is obtained for resonators with a diameter of 13 lm, which operate at a wavelength of %272 lm. This corresponds to a k eff /6 confinement, where k eff is the wavelength inside the material (or k/20, if the free space wavelength is considered). These highly sub-wavelength devices operate on the fundamental magnetic resonance, which corresponds to the fundamental oscillation mode of split-ring resonators and is usually inactive in purely optical resonators. In this respect, these resonators are another step towards the hybridization of optics and electronics at THz frequencies. As a proof of principle for cavity quantum electrodynamics experiments, we apply these resonators to THz intersubband polaritons.

We present a rack-mounted ultra-low-noise laser system for Sr lattice clocks, with spectral purity transfer stability of 4×10−18@1s and 2×10−19@100s. We realize a system stability of 5×10-16@1s, representing state-of-the-art performance for rack-mounted commercial systems.

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We present a fully phase-locked comb-disciplined-laser system, conceived to operate the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100). Via phase-locking to the comb, four ECDLs and a Ti:Sapphire laser inherit the stability of an ultra-stable laser.