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.

Dual-comb spectroscopy is an emerging new spectroscopic tool that exploits the frequency resolution, frequency accuracy, broad bandwidth, and brightness of frequency combs for ultrahigh-resolution, high-sensitivity broadband spectroscopy. By using two coherent frequency combs, dual-comb spectroscopy allows a sample's spectral response to be measured on a comb tooth-by-tooth basis rapidly and without the size constraints or instrument response limitations of conventional spectrometers. This review describes dual-comb spectroscopy and summarizes the current state of the art. As frequency comb technology progresses, dual-comb spectroscopy will continue to mature and could surpass conventional broadband spectroscopy for a wide range of laboratory and field applications.

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We have produced a very cold sample of spin-polarized trapped atoms. The technique used dramatically simplifies the production of laser-cooled atoms. In this experiment, 1.8x10' neutral cesium atoms were optically captured directly from a low-pressure vapor in a small glass cell. We then cooled the & 1-mm' cloud of trapped atoms and loaded it into a low-field magnetic trap in the same cell. The magnetically trapped atoms had an eAective temperature as low as 1.1+ 0.2 pK, which is the lowest kinetic temperature ever observed and far colder than any previous sample of trapped atoms. Such an optically trapped sample is useful for many applications, but it has some inherent limitations; the atomic spins are randomly oriented, perturbing light fields must be present, and it is di%cult to achieve temperatures lower than 300 pK. We have overcome these limitations by loading the optically trapped atoms into a magnetostatic trap. Because the atoms are very cold when first loaded, we can trap them with relatively small magnetic fields. By properly cooling the atoms before turning on the magnetic trap we have produced a sample which is more than 100 times colder than any previously trapped neutral atoms.In where the steady-state number N, is given by N, =Rr =(1/J6)(V . /o')v, (m/2kT) .

The broadband, coherent nature of narrow-linewidth fiber frequency combs is exploited to measure the full complex spectrum of a molecular gas through multiheterodyne spectroscopy. We measure the absorption and phase shift experienced by each of 155 000 individual frequency-comb lines, spaced by 100 MHz and spanning from 1495 to 1620 nm, after passing through hydrogen cyanide gas. The measured phase spectrum agrees with the Kramers-Kronig transformation of the absorption spectrum. This technique can provide a full complex spectrum rapidly, over wide bandwidths, and with hertz-level accuracy.

We present theoretical predictions and experimental measurements for the achievable phase noise, timing jitter, and frequency stability in the coherent transport of an optical frequency over a fiber-optic link. Both technical and fundamental limitations to the coherent transfer are discussed. Measurements of the coherent transfer of an optical carrier over links ranging from 38 to 251 km demonstrate good agreement with theory. With appropriate experimental design and bidirectional transfer on a single optical fiber, the frequency instability at short times can reach the fundamental limit imposed by delay-unsuppressed phase noise from the fiber link, yielding a frequency instability that scales as link length to the 3 / 2 power. For two-way transfer on separate outgoing and return fibers, the instability is severely limited by differential fiber noise.

The transfer of high-quality time-frequency signals between remote locations underpins a broad range of applications including precision navigation and timing, the new field of clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and the future redefinition of the second [1-7]. However, present microwave-based time-frequency transfer [8-10] is inadequate for state-of-the-art optical clocks and oscillators [1,11-15] that have femtosecond-level timing jitter and accuracies below 1E-17; as such, commensurate optically-based transfer methods are needed. While fiber-based optical links have proven suitable [16,17], they are limited to comparisons between fixed sites connected by a specialized bidirectional fiber link. With the exception of tests of the fundamental constants, most applications instead require more flexible connections between remote and possibly portable optical clocks and oscillators. Here we demonstrate optical time-frequency transfer over free-space via a two-way exchange between coherent frequency combs, each phase-locked to the local optical clock or oscillator. We achieve femtosecond-scale timing deviation, a residual instability below 1E-18 at 1000 s and systematic offsets below 4E-19, despite frequent signal fading due to atmospheric turbulence or obstructions across the 2-km link. This free-space transfer would already enable terrestrial links to support clock-based geodesy. If combined with satellite-based free-space optical communications, it provides a path toward global-scale geodesy, high-accuracy time-frequency distribution, satellite-based relativity experiments, and "optical GPS" for precision navigation

We demonstrate coherent dual frequency-comb spectroscopy for detecting variations in greenhouse gases. High signal-to-noise spectra are acquired spanning 5990 to 6260 cm -1 (1600 to 1670 nm) covering ~700 absorption features from CO 2 , CH 4 , H 2 O, HDO, and 13 CO 2 , across a 2-km open-air path. The transmission of each frequency comb tooth is resolved, leading to spectra with <1 kHz frequency accuracy, no instrument lineshape, and a 0.0033-cm -1 point spacing. The fitted path-averaged concentrations and temperature yield dry-air mole fractions. These are compared with a point sensor under well-mixed conditions to evaluate current absorption models for real atmospheres. In heterogeneous conditions, timeresolved data demonstrate tracking of strong variations in mole fractions. A precision of <1 ppm for CO 2 and <3 ppb for CH 4 is achieved in 5 minutes in this initial demonstration. Future portable systems could support regional emissions monitoring and validation of the spectral databases critical to global satellitebased trace gas monitoring.