Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 10(-17) in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.

Pulsed rotating supersonic source for merged molecular beams Rev. Sci. Instrum. 83, 064102 (2012) An atomic beam source for fast loading of a magneto-optical trap under high vacuum Rev. Sci. Instrum. 83, 055102 (2012) A low phase noise microwave source for atomic spin squeezing experiments in 87Rb Rev. Sci. Instrum. 83, 044701 (2012) Ultra-sensitive high-precision spectroscopy of a fast molecular ion beam Micromotion of ions in Paul traps has several adverse effects, including alterations of atomic transition line shapes, significant second-order Doppler shifts in high-accuracy studies, and limited confinement time in the absence of cooling. The ac electric field that causes the micromotion may also induce significant Stark shifts in atomic transitions. We describe three methods of detecting micromotion. The first relies on the change of the average ion position as the trap potentials are changed. The second monitors the amplitude of the sidebands of a narrow atomic transition, caused by the first-order Doppler shift due to the micromotion. The last technique detects the Doppler shift induced modulation of the fluorescence rate of a broad atomic transition. We discuss the detection sensitivity of each method to Doppler and Stark shifts, and show experimental results using the last technique. ͓S0021-8979͑98͒05610-2͔

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We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.

Measurements of internal energy states of atomic ions confined in traps can be used to illustrate fundamental properties of quantum systems, because long relaxation times and observation times are available. In the experiments described here, a single ion or a few identical ions were prepared in well-defined superpositions of two internal energy eigenstates. The populations of the energy levels were then measured. For an individual ion, the outcome of the measurement is uncertain, unless the amplitude for one of the two eigenstates is zero, and is completely uncertain when the magnitudes of the two amplitudes are equal. In one experiment, a single Hg+ ion, confined in a linear rf trap, was prepared in various superpositions of two hyperfine states. In another experiment, groups of Be+ ions, ranging in size from about 5 to about 400 ions, were confined in a Penning trap and prepared in various superposition states. The measured population fluctuations were greater when the state amplitudes were equal than when one of the amplitudes was nearly zero, in agreement with the predictions of quantum mechanics. These fluctuations, which we call quantum projection noise, are the fundamental source of noise for population measurements with a fixed number of atoms. These fluctuations are of practical importance, since they contribute to the errors of atomic frequency standards.

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We present a high bandwidth piezoelectric-actuated mirror for length stabilization of an optical cavity. The actuator displays a transfer function with a flat amplitude response and greater than 135 • phase margin up to 200 kHz, allowing a 180 kHz unity gain frequency to be achieved in a closed servo loop. To the best of our knowledge, this actuator has achieved the largest servo bandwidth for a piezoelectric transducer (PZT). The actuator should be very useful in a wide variety of applications requiring precision control of optical lengths, including laser frequency stabilization, optical interferometers, and optical communications.

Dehmelt had proposed this optical double-resonance scheme (terming it electron shelving) as an amplification mechanism to detect a weak transition in singleatom spectroscopy. 5 This technique has been used for several years in high-resolution spectroscopic studies of samples of many laser-cooled ions, achieving quantum amplifications of 10 and higher. In 1981, electron-shelving amplification was used to perform optical-optical double resonance in a single, lasercooled, trapped ion. While the signal-to-noise ratio in that experiment was not sufficient to see quantum jumps directly, the fact that the atomic fluorescence would be bistable was noted. More recently, the statistics of quantum switching in a single atom have been theoretically treated in some detail first by Cook and Kimble7 and subsequently by several other authors. s '3 In this Letter we report the clear experimental demonstration of quantum jumps in a single laser-cooled '9sHg+ ion stored in a miniature radio-frequency trap.The basic idea for quantum switching and the associated statistics is illustrated with the three-level system shown in Fig. 1 is also admitted, then the atom will occasionally be driven into the metastable state and the fluorescence from the strong transition will abruptly disappear. The cessation of the scattering of many photons on the strong transition for one photon absorbed on the weak transition permits unit detection efficiency of the transition to the metastable state. 6' Some time later, the atom returns spontaneously or is driven out of the D state back to the ground state, which causes a sudden return of the fluorescence on the strong transition.