Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped 199 Hg ϩ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 ϫ 10 Ϫ15 is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.

We present a microfabricated optical cavity, which combines a very small mode volume with high finesse. In contrast to other micro-resonators, such as microspheres, the structure we have built gives atoms and molecules direct access to the high-intensity part of the field mode, enabling them to interact strongly with photons in the cavity for the purposes of detection and quantum-coherent manipulation. Light couples directly in and out of the resonator through an optical fiber, avoiding the need for sensitive coupling optics. This renders the cavity particularly attractive as a component of a lab-on-a-chip, and as a node in a quantum network. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2132066͔ High-finesse optical cavities are central to many techniques and devices in atomic physics, 1 optoelectronics, 2 chemistry, 3 and biosensing. 4 As well as selecting spectral and spatial distributions of the classical electromagnetic field, optical cavities make it possible to harness quantum effects for applications in quantum information science. 1,5 For example, it is possible to produce single photons on demand using atoms 6,7 or ions 8 inside a cavity and to create entanglement between those that share a cavity photon. 9-11 Similar ideas are being pursued with quantum dots. 12,13 Microscopic cavities are of particular interest 14 because small volume gives the photon a large field and because they offer the possibility of integration with micro-opto-electro-mechanical systems 15 and atom chips. [16][17][18] Here we present a simple and innovative method for fabricating microscopic, broadly-tuneable, high-finesse cavities. These have the significant new feature that their structure is open, giving an atom, molecule or quantum dot direct access to an antinode of the cavity mode. This structure is therefore ideally suited for detecting small numbers of particles, 19 and miniaturizing quantum devices based on strong dipole-cavity coupling.We have made high-finesse, open optical cavities that operate in length at a range of approximately 20-200 m. Each cavity is formed by a concave micro-mirror and the plane tip of an optical fiber, both coated for reflection, as illustrated in Fig. 1͑a͒. Arrays of concave mirrors are fabricated in silicon by wet-etching isotropically through circular apertures in a lithographic mask using a mixture of HF and HNO 3 in acetic acid. The etch bath in which the wafer is immersed undergoes continuous agitation during the etching process, resulting in an approximately spherical surface profile, as shown in Fig. 1͑b͒. The etch rate and the final morphology of the silicon surface are highly dependent on the agitation and on the concentration of each component in the etchant. 20 Precise control over these factors gives us repeatable surface profiles in the silicon with 6 nm rms roughness. In our first experiment, gold is sputtered onto an array of mirror templates to form a layer 100 nm thick with a surface roughness of 10 nm. The plane mirror of the cavity is a dielectric multilayer, w...

Objectives Previous studies suggest that high systemic bone mineral density (BMD) is associated with incident knee OA defined by osteophytes, but not with joint space narrowing (JSN), and are inconsistent regarding BMD and progression of existing OA. We tested the association of BMD with incident and progressive tibiofemoral OA in a large, prospective study of men and women ages 50–79 with, or at risk for, knee OA. Methods Baseline and 30-month weight-bearing PA and lateral knee x-rays were scored for K–L grade, JSN and osteophytes. Incident OA was defined as the development of K–L grade ≥2 at follow-up. All knees were classified for increases in grade of JSN and osteophytes from baseline. The association of gender-specific quartiles of baseline BMD with risk of incident and progressive OA was analyzed using logistic regression, adjusting for covariates. Results The mean age of 1,754 subjects was 63.2 (SD, 7.8) and BMI 29.9 (SD, 5.4). In knees without baseline OA, higher femoral neck and whole body BMD were associated with an increased risk of incident OA and increases in grade of JSN and osteophytes (p < 0.01 for trends); adjusted odds were 2.3 to 2.9-fold greater in the highest vs. the lowest BMD quartiles. In knees with existing OA, progression was not significantly related to BMD. Conclusions In knees without OA, higher systemic BMD was associated with a greater risk of the onset of JSN and K–L grade ≥2. The role of systemic BMD in early knee OA pathogenesis warrants further investigation.

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg + and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be fHg = 1 064 721 609 899 143(10) Hz and fCa = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg + and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of |(∂fCa/∂t)/fCa| ≤ 8 × 10 −14 yr −1 , and |(∂fHg/∂t)/fHg| ≤ 30 × 10 −14 yr −1 .Optical standards based on a single ion or a collection of laser-cooled atoms are emerging as the most stable and accurate frequency sources of any sort [1,2,3,4,5]. However, because of their high frequencies (∼ 500 THz), it has proven difficult to count cycles as required for building an optical clock and comparing to the cesium microwave standard. Only recently, a reliable and convenient optical clockwork fast enough to count optical oscillations has been realized [6,7,8]. Here, we report an optical clockwork based on a single femtosecond laser that phase coherently divides down the visible radiation of the Hg + and Ca optical frequency standards to a countable radio frequency. By this means we determine the absolute frequencies of these optical transitions with unparalleled precision in terms of the SI second as realized at NIST [9]. Indeed, for the Hg + standard, the statistical uncertainty in the measurement is essentially limited by our knowledge of the SI second at ∼ 2 × 10 −15 . The high precision and high demonstrated stability of the standards [1,4] combined with the straightforward femtosecond-laser-based clockwork suggest Hg + and Ca as excellent references for future all-optical clocks. Additionally, the comparison of atomic frequencies over time provides constraints on the possible time variation of fundamental constants. When combined with previous measurements, the current level of precision allows us to place the tightest constraint yet on the possible variation of optical frequencies with respect to the cesium standard.The Hg + and Ca systems have recently been described elsewhere [1,4,10,11], so we summarize only the basic features. The heart of the mercury optical frequency standard is a single, laser-cooled 199 Hg + ion that is stored in a cryogenic, radio frequency spherical Paul trap. The 2 S 1/2 (F = 0, M F = 0) ↔ 2 D 5/2 (F = 2, M F = 0) electric-quadrupole transition at 282 nm [ Fig. 1(a)] provides the reference for the optical standard [1]. We lock the frequency-doubled output of a well-stabilized 563 nm dye laser to the center of the quadrupole resonance by irradiating the Hg + ion alternately at two frequencies near the maximum slope of the resonance signal and on opposite sides of its center. Transitions to the metastable 2 D 5/2 state are detected with near unit ...