Optical Frequency Measurements Research Articles

Optical frequency standards and measurements

We describe the performance characteristics and frequency measurements of two high-accuracy high-stability laser-cooled atomic frequency standards. One is a 657-nm (456-THz) reference using magneto-optically trapped Ca atoms, and the other is a 282-nm (1064-THz) reference based on a single Hg/sup +/ ion confined in an RF-Paul trap. A femtosecond mode-locked laser combined with a nonlinear microstructure fiber produces a broad and stable comb of optical modes that is used to measure the frequencies of the reference lasers locked to the atomic standards. The measurement system is referenced to the primary frequency standard NIST F-1, a Cs atomic fountain clock. Both optical standards demonstrate exceptional short-term instability (/spl ap/5/spl times/10/sup -15/ at 1 s), as well as excellent reproducibility over time. In light of our expectations for the future of optical frequency standards, we consider the present performance of the femtosecond optical frequency comb, along with its limitations and future requirements.

Absolute frequency measurement of the 4355-nm ^171Yb^+-clock transition with a Kerr-lens mode-locked femtosecond laser

We have measured the frequency of the $6s^2S_{1/2} - 5d^2D_{3/2}$ electric-quadrupole transition of $^{171}$Yb$^+$ with a relative uncertainty of $1\times 10^{-14}$, $\nu_{Yb}$ = 688 358 979 309 312 Hz $\pm$ 6 Hz. A femtosecond frequency comb generator was used to phase-coherently link the optical frequency derived from a single trapped ion to a cesium fountain controlled hydrogen maser. This measurement is one of the most accurate measurements of optical frequencies ever reported, and it represents a contribution to the development of optical clocks based on an $^{171}$Yb$^+$ ion standard.

Direct RF to optical frequency measurements with a femtosecond laser comb

By spanning an optical octave (>300 THz) with a broadened femtosecond laser frequency comb, we directly measure the frequencies of optical standards at 1064/532 nm, 633 nm and 778 nm in terms of the microwave frequency that controls the comb spacing. This microwave frequency can be linked directly to the cesium standard.

A New Era of Frequency Standards and Optical Frequency Measurement

A New Era of Frequency Standards and Optical Frequency Measurement

Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb

With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of 2x10(-13) in 5 s , to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the Hg(+) clock transition with an improvement in accuracy of ~10(5) compared with its best previous measurement.

Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb

Femtosecond laser-frequency comb techniques are vastly simplifying the measurement and synthesis of optical frequencies. A single mode-locked femtosecond laser, with its spectrum broadened by self-phase modulation in a microstructured or tapered nonlinear fiber, can produce millions of sharp laser lines in a precise evenly spaced grid spanning much of the visible and near-infrared spectrum. The absolute frequency of each line is determined by two observable radio-frequency signals. The pulse repetition rate gives the spacing of the comb lines and the rate at which the phase of the lightwave slips, relative to the intensity envelope from pulse to pulse determines the offset frequency by which each line is displaced from a precise integral multiple of the repetition frequency. This offset frequency can be measured most easily if the comb spans more than an optical octave so that one can observe a radio frequency beat note between the second harmonic of the infrared comb lines with the corresponding comb lines at the blue end. Such an optical-frequency synthesizer makes optical oscillations readily countable and provides the long-awaited compact optical clockwork for an all-optical clock.

Ultrasensitive spectroscopy, the ultrastable lasers, the ultrafast lasers, and the seriously nonlinear fiber: a new alliance for physics and metrology

We now appreciate the fruit of decades of development in the independent fields of ultrasensitive spectroscopy, ultrastable lasers, ultrafast lasers, and nonlinear optics. But a new feature of the past two or three years is the explosion of interconnectedness between these fields, opening remarkable and unexpected progress in each, due to advances in the other fields. For brevity, we here focus mainly on the new possibilities in the field of optical frequency measurement.

Optical frequency measurement: 40 years of technology revolutions

The past forty years have witnessed spectacular progress in precision measurements, beginning with the first coherent optical source, the HeNe CW laser. Almost immediately, the pioneers of the stable laser epoch introduced optical heterodyne techniques to explore the stability of the laser's optical frequency, expecting the few milliHertz linewidth predicted by the Schawlow-Townes formula for phase diffusion, and instead finding myriad physical processes that broaden and jiggle optical frequencies far beyond that narrow range. After a huge time and learning effort, most of these technical limitations can now be overcome. The paper is intended to offer a bystander/sometimes-participant's view into the advances in laser tools and the exciting scientific/technical worlds that were opened by them. Roughly one "zillion" further clever inventions and techniques have added capability to the laser and have enabled many bursts of productive research. Now, after nearly forty years of incremental progress, the astonishing reality is that within the past one year - absolute optical frequency measurements have suddenly become feasible, simple - even routine. This welcome and unexpected progress is based on the merger of techniques from the ultrastable lasers and the ultrafast lasers research communities. In a very real sense, these research objectives seem to be the exact opposites - the most unchanging versus the most quickly changing.

Accuracy comparison of absolute optical frequency measurement between harmonic-generation synthesis and a frequency-division femtosecond comb

Using an iodine-stabilized He-Ne laser as a transfer oscillator, we compare absolute measurements of the optical frequency from a traditional frequency synthesis chain based on harmonic generation and from the frequency division technique of an ultrawide bandwidth femtosecond frequency comb. The agreement between these two measurements, both linked to the Cs standard, is 220+/-770 Hz, yielding a measurement accuracy of 1.6x10(-12). We report 473 612 353 604.8+/-1.2 kHz as a preliminary updated value of the absolute frequency of the " f" component for the He-Ne laser international standard at 633 nm.

Metrology of the hydrogen and deuterium atoms: Determination of the Rydberg constant and Lamb shifts

We present a detailed description of several experiments which have been previously reported in several letters: the determination of the 1S Lamb shift in hydrogen by a comparison of the frequencies of the 1S-3S and 2S-6S or 2S-6D two-photon transitions, and the measurement of the 2S-8S/D and 2S-12D optical frequencies. Following a complete study of the lineshape of the two-photon transitions, we provide the updated values of these frequencies which have been used in the 1998 adjustment of the fundamental constants. From an analysis taking into account these results and several other precise measurements by other authors, we show that the optical frequency measurements have superseded the microwave determination of the 2S Lamb shift and we deduce optimized values for the Rydberg constant, = 109 737.315 685 50(84) cm-1 (relative uncertainty of ) and for the 1S and 2S Lamb shifts L(1S) = 8 172.840(22) MHz and L(2S-2P) = 1 057.8450(29) MHz (respectively, 8 183.970(22) MHz and 1 059.2341(29) MHz for deuterium). These are now the most accurate values available.

Absolute optical frequency measurement of the cesiumD2line

We have performed an absolute optical frequency measurement of the cesium ${D}_{2}$ line at 352 THz (852 nm). This frequency is an important scaling parameter in atomic interferometry. The ${D}_{2}$ line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at $88.4 \mathrm{THz}$ $(3.39 \ensuremath{\mu}\mathrm{m}).$ A frequency mismatch of $1.78 \mathrm{THz}$ between $4\ifmmode\times\else\texttimes\fi{}88.4 \mathrm{THz}=354 \mathrm{THz}$ and the ${D}_{2}$ line was bridged with an optical frequency comb generator. We find ${f}_{D2}=351725718.50(11) \mathrm{MHz}$ for the hyperfine centroid, improving previous results by almost two orders of magnitude.

Method Developed for Ultraprecise Optical Frequency Measurements

Method Developed for Ultraprecise Optical Frequency Measurements

Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb

We demonstrate a great simplification in the long-standing problem of measuring optical frequencies in terms of the cesium primary standard. An air-silica microstructure optical fiber broadens the frequency comb of a femtosecond laser to span the optical octave from 1064 to 532 nm, enabling us to measure the 282 THz frequency of an iodine-stabilized Nd:YAG laser directly in terms of the microwave frequency that controls the comb spacing. Additional measurements of established optical frequencies at 633 and 778 nm using the same femtosecond comb confirm the accepted uncertainties for these standards.

Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis

We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which we used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.

Sub-systems for optical frequency measurements: application to the 282-nm /sup 199/Hg/sup +/ transition and the 657-nm Ca line

We are developing laser frequency measurement technologies that should allow us to construct an optical frequency synthesis system capable of measuring optical frequencies with a precision limited by the atomic frequency standards. The system will be used to interconnect and compare new advanced optical-frequency references (such as Ca, Hg(+ ), and others) and eventually to connect these references to the Cs primary frequency standard. The approach we are taking is to subdivide optical frequency intervals into smaller and smaller pieces until we are able to use standard electronic-frequency-measurement technology to measure the smallest interval.

Optical frequency measurement across a 104-THz gap with a femtosecond laser frequency comb

The frequency-domain mode comb of a Ti:sapphire femtosecond laser centered at 350 THz is broadened to 150 THz (full width at -30 dBc) by self-phase modulation in a single-mode optical fiber. By phase locking continuous-wave lasers to elements of the comb near 1064 and 778 nm, we measure the 104-THz frequency gap between these two lasers with a relative uncertainty of 2.7 x 10(-11) in 1 s.

Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation

The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented.

Optical Frequency Measurement of the2S−12DTransitions in Hydrogen and Deuterium: Rydberg Constant and Lamb Shift Determinations

We have performed a pure optical frequency measurement of the $2S\ensuremath{-}12D$ two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, ${R}_{\ensuremath{\infty}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}109737.31568516(84){\mathrm{cm}}^{\ensuremath{-}1}$ (relative uncertainty of $7.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$) and for the $1S$ and $2S$ Lamb shifts ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8172.837(22)\mathrm{MHz}$ and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1057.8446(29)\mathrm{MHz}$ [respectively, ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8183.966(22)\mathrm{MHz}$, and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1059.2337(29)\mathrm{MHz}$ for deuterium]. These are now the most accurate values available.

Accurate measurement of the frequency of the 6S–8S two-photon transitions in cesium

Accurate optical frequency measurement is realized on the hyperfine components of the 6S–8S two-photon transition in cesium with an uncertainty of 3×10 −10. Light shift and pressure shift are studied. These measurements show that these transitions can be used for the realization of an optical standard at 822 nm, in order to provide new optical frequency references in the visible range.

光周波数計測と通信網への応用

光周波数計測と通信網への応用