Frequency Standards and Metrology

The following sections are included:

• Preface

• CONTENTS

I would like to begin the week here in St. Andrews by welcoming you all to this Symposium on Frequency Standards and Metrology. The Symposium is the sixth in a series of Symposia stretching back over 30 years. The first was organised by Jacques Vanier in 1971 at Forét Montmorency in Quebec. It was followed by Copper Mountain (1976), Aussois (1981), Ancona (1988) and Woods Hole (1995). Copper Mountain was the responsibility of Helmut Hellwig, who sadly died last year. Over the last 30 years, Helmut has been a driving force for the shape and scope of the Symposia, and Michael Garvey will shortly offer a tribute to him…

I'd like to thank the Symposium organizers for the opportunity to speak for a few minutes about Helmut Hellwig. As most of you know Helmut died last July. Today I want to look retrospectively at Helmut's career and at the many contributions that made him so important to many of us in the time and frequency community…

This brief review of the history of atomic frequency standards includes: atomic beam magnetic resonance, microwave absorption and optical pumping, atomic masers, lasers, laser cooling and laser cooled atoms and ions at optical frequencies.

The accuracy of atomic clocks, in the microwave or in the optical domain, is now such that a new theoretical framework [1] is required, which includes: 1 - A fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold atom interferometric devices use atoms in "free fall" in a fountain geometry), 2 - An account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones, 3 - A second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties, 4 - A covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines, is presented, using both an exact propagator of atom waves in gravito-inertial fields [2] and a covariant Dirac equation in the presence of weak gravitational fields [3]. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source can be discussed in the context of present and future microwave and optical clocks.

We analyse a novel class of non-degenerate, doubly (DRO) or triply (TRO) resonant optical parametric oscillators (OPOs) producing signal and idler waves that are sub-harmonics of the pump frequency (3ω → 2ω, ω), and subject to an additional resonant coupling via the second-harmonic generation (SHG) of the idler wave (ω + ω → 2ω). At exact 3 ÷ 2 ÷ 1 non-degeneracy, self phase-locking among the three waves is theoretically predicted, freezing the well-known quantum phase diffusion noise in conventional oscillators. Three possible phase states corresponding to the same intensity state emerge. When slightly detuned from the 3 ÷ 2 ÷ 1 point, and under some specific conditions, the OPO:SHG cascading is expected to lead to a passively mode-locked cw-OPO providing two frequency combs peaked around the signal and idler frequencies. We report our attempt to observe both types of self-phase-locked (SPL) operation in a single-grating (OPO-only section) periodically poled lithium niobate (PPLN) oscillator, under the very weak self injection-locking by non-phase matched spontaneous idler SHG.

We review the development of continuous-wave optical parametric oscillators (OPOs) at the University of Konstanz as coherent light sources for high resolution spectroscopy. We describe various implementations of such devices covering a wide range of wavelengths (550 – 4000 nm), discuss their performance and present first applications to Doppler-free spectroscopy of methane at 3.39 µm and molecular iodine at 580 nm.

The results of investigations of the frequency shifts of a transportable He-Ne/CH₄ laser standard depending on various factors are presented. The experiments were performed in the telescopic laser with different optical schemes. The frequency reproducibility of the methane standard estimated as 5 · 10^-14.

We discuss the present performance and limits of our Cs and Rb fountains. The BNM/LPTF operates three cold atom clocks: two Cs fountains and a dual Cs-Rb fountain. By using an ultra-stable cryogenic sapphire oscillator to interrogate the atoms the frequency stability reaches 3.6 × 10^-14τ^-1/2. The accuracy of our fountains is now near 10^-15. We discuss here the problems to be solved to reach a 10^-16 accuracy. For instance this implies a continuous monitoring of the collisional frequency shift at the percent level in Cs. In contrast, ⁸⁷Rb cold atom clocks exhibit a collisional shift ~ 100 times smaller than Cs which should lead to a better ultimate accuracy. Comparing the hyperfine energies of atoms with different atomic numbers Z, one can search for a possible violation of the Einstein Equivalence Principle. When interpreted as a test of the stability of the fine structure constant (α = e²/4πϵ₀ħc), measurements of the ratio ν_Rb/ν_Cs spread over a two year interval show no change of α at the 7 × 10^-15/year level.

At the Physikalisch-Technische Bundesanstalt (PTB) the atomic caesium fountain CSF1 is used as a primary frequency standard for the measurement of the scale unit of the International Atomic Time scale, TAI (Temps Atomique International), since July 2000. In total seven measurements were performed up to now and reported to the Bureau International des Poids et Mesures (BIPM). In routine operation the total relative uncertainty of CSF1 is u_B = 1.0 × 10^-15 and its frequency instability is σ_y = 2 × 10^-13(τ/s)^-1/2, currently limited by the detected atom number of 4 · 10⁴. The main uncertainty limitation is due to the collisional shift, which has been carefully evaluated.

We present results from NIST-F1, the NIST primary frequency standard, a Cesium atomic fountain. In particular we give the results of the latest frequency evaluation which has a combined standard fractional frequency uncertainty of 1.3 × 10^-15 in the laboratory and a total uncertainty of 1.5 × 10^-15 including the time transfer to the Bureau International des Poids et Mesures (BIPM) international atomic time scale (TAI). We also present results that demonstrate the attainment of the quantum projection noise limit in this fountain.

We have performed an initial characterization of the stability of the U.S. Naval Observatory (USNO) cesium fountain atomic clock. This device has a short-term fractional frequency stability of up to 1.5 × 10^-13τ^-1/2. This short-term performance enables us to measure hydrogen maser behavior over the short to medium term. We have recently implemented real time-steering of a hydrogen maser with the fountain. Over a period of roughly 9 days of continuous operation, we have steered out the drift of a cavity-tuned maser.

Techniques for comparing frequency standards at the 1 × 10^-15 level are examined, including the impact of displacements in time and space. The additional uncertainties contributing to the comparison process using current technologies in stable frequency references and in long-distance frequency-transfer techniques are quantified. As an example, the results of two frequency comparisons between a pair of cesium-fountain primary frequency standards are given.

We have developed an optical clock based on a laser whose frequency is locked to a single, laser-cooled ¹⁹⁹Hg⁺ ion and that uses a femtosecond laser and microstructure fiber to phase-coherently divide the optical frequency to a countable microwave frequency. The measured short-term stability in the optical domain is about an order of magnitude higher than the best cesium-fountain clock. The estimated value of the electric-quadrupole frequency shift of the ²S_1/2 (F = 0, m_F = 0) - ²D_5/2 (F = 2, m_F = 0) clock transition is given.

A single laser cooled ion in a radiofrequency trap can serve as a reference for a highly stable optical frequency standard. We present recent results of our work with single indium ions, using the 5s^{2 1}S₀ - 5s5p ³P₀ transition at a wavelength of 237 nm as the clock transition. This resonance has a linewidth of only 0.8 Hz where systematic shifts should be controllable at the mHz level. A single In⁺ ion is stored in a miniature Paul-Straubel trap and laser cooled to a temperature of about 100 µK. The clock transition is excited using a frequency quadrupled Nd:YAG laser emitting at 946 nm. A fractional resolution of 1.3 × 10^-13 has been achieved so far (linewidth of 170 Hz at 1267 THz), limited by the frequency instability of the Nd:YAG laser. The absolute frequency of the clock transition has been measured with an uncertainty of 2 × 10^-13 using a phase-coherent frequency chain and a methane-stabilized HeNe laser as a reference, that was calibrated against an atomic cesium fountain clock.

The ²S_1/2–²F_7/2 octupole transition in ¹⁷¹Yb⁺ is probed using the quantum jump technique and a spectrum of the carrier on the (F = 0, m_F = 0)-(F = 3, m_F = 0) component is observed with linewidth of 4.5 kHz. Measurements are made of the second-order Zeeman shift and the AC Stark shift for this transition and show good agreement with theory.

Femtosecond laser frequency comb techniques are vastly simplifying the art of measuring the frequency of light. A single mode-locked femtosecond laser is now sufficient to synthesize hundreds of thousands of evenly spaced spectral lines, spanning much of the visible and near infrared region. The mode frequencies are absolutely known in terms of the pulse repetition rate and the carrier-envelope phase slippage rate, which are both accessible to radio frequency counters. Such a universal optical frequency comb synthesizer can serve as a clockwork in atomic clocks, based on atoms, ions or molecules oscillating at optical frequencies.

We introduce a novel concept for optical frequency measurement which employs a Kerr-lens mode-locked laser as a transfer oscillator whose noise properties do not enter the measurement process. We experimentally demonstrate, that this method opens up the route to phase-link oscillators with arbitrary frequencies in the optical range.

This paper reports absolute frequency measurements of trapped ion and HeNe/I₂ systems using the NPL femtosecond comb. Two transition frequencies in laser-cooled single trapped ions have been measured: the ⁸⁸Sr⁺ 5s ²S_1/2 - 4d ²D_5/2 electric quadrupole transition at 674 nm and the ¹⁷¹Yb⁺ 4f¹⁴6s ²S_1/2 (F = 0) - 4f¹³6s^{2 2}F_7/2 (F = 3) electric octupole transition at 467 nm. In addition, the frequency of the helium-neon laser NPL-S stabilised to four hyperfine components of the ¹²⁷I₂ 11-5 R(127) line at 633 nm has been measured.

The paper summarizes the relative advantages and disadvantages of Coherent Population Trapping (CPT) and Intensity Optical Pumping (IOP) for the implementation of a passive atomic frequency standard. The paper outlines the basic principles common to both CPT and IOP when using laser optical pumping, and makes explicit their similarities and their differences. The paper describes recent experimental results obtained in the same cell on the characteristics of the CPT and IOP ⁸⁷Rb-hyperfme resonance line.

A simple, compact and low-power microwave frequency reference based on CPT resonances in Cs vapor is described. The 14 cm³ physics package exhibits a resonance width of 620 Hz at 4.6 GHz, a short-term fractional frequency instability of , and dissipates less than 30 mW, not including temperature control. We discuss the prospects for extreme miniaturization to sub-millimeter dimensions.

Coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms under coherent population trapping. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble is taken into account. Moreover, relevant density and propagation effects are described. The case of alkali-metal atoms submitted to a Λ excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas.

An all-optical RF standard based on dark states of ⁸⁵Rb atoms has been developed. With this system we were able to measure ultra-narrow optically induced hyperfine dark resonances below 20 Hz (Q-value > 1.5 × 10⁸). The frequency of a signal generator was stabilized to the dark resonance giving a relative frequency stability (square root of Allan variance) of 3.5 × 10^-11τ^-1/2 (1S < t < 2000s). The best stability reached at an integration time of t = 2000s was 6.4 × 10^-13, which is sufficient for many high-precision applications. The frequency shifts caused by various experimental parameters were also studied.

Using an atom interferometer method based on adiabatic transfer between atomic states, we measure the recoil velocity of cesium due to the coherent scattering of a photon. The value of ħ/M_Cs is used to obtain a preliminary new value for the fine structure constant. The current experimental uncertainty in α is 7.4 ppb.

We demonstrate a Rb fountain clock which has a small cold collision shift that is cancelled by detuning the microwave cavity. We also demonstrate a juggling Rb clock and propose a novel quantum atom-optics precision scattering measurement for a juggling atomic clock. Finally we describe the design concept for RACE, a microgravity Rb clock for the ISS.

We present the most recent optical frequency measurements in hydrogen and deuterium. From an analysis taking into account the scaling law of the Lamb shifts, 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 and for the 1S and 2S Lamb shifts. We report also the recent improvement of our 1S-3S experiment and the development of a new method to deduce the second order Doppler effect.

Preliminary results of a new frequency measurement of the 2³P₀ - 2³P₁ fine structure interval of Helium atom are presented. An accuracy improvement of about a factor of two with respect to the previous measurement ¹ is obtained. A detail description of the improvements in the experimental set-up is done. Two times better precision and three times better reproducibility of Helium transitions at 1083 nm are allowed with these changes. Implications and limits of this measurement to yield a 1.8 × 10^-8 accurate value of the fine structure constant are discussed. Finally, the same experiment opens, for the first time, the possibility of absolute frequency measurements of the 1083 nm Helium transitions with accuracies of a few parts in 10¹¹.

The interest of space environment for cold atom clocks is outlined. We discuss the scientific objectives of the European space mission ACES which will fly onboard the international space station in 2005-2007 with a cold atom clock, PHARAO.

This paper describes progress toward the development of a Primary Atomic Reference Clock in Space (PARCS) and reviews the scientific and technical objectives of the PARCS mission. PARCS is a collaborative effort involving the National Institute of Standards and Technology (NIST), the University of Colorado, the Jet Propulsion Laboratory (JPL), the Harvard Smithsonian Center for Astrophysics (SAO) and the Politecnico di Torino. Space systems for this experiment include a laser-cooled cesium atomic clock and a GPS frequency-comparison and orbit determination system, along with a hydrogen maser that serves as both a local oscillator for the cesium clock and a reference against which certain tests of gravitational theory can be made. In the microgravity environment of the International Space Station (ISS), cesium atoms can be launched more slowly through the clock's microwave cavity, thus significantly reducing a number of troubling effects (including several critical systematic effects), so clock performance can be substantially improved beyond that achieved on earth.

Secondary frequency standards based on spherical microwave resonators are proposed for new accurate Michelson Morley (MM) experiments. We identify a set of near degenerate modes (which we dub Whispering Spheroid modes) that propagate over the spheres surface in different directions. Amongst this set we identify two modes that have orthogonal propagation directions. The first is the well-known Whispering Gallery mode, which propagates approximately like a ray along the equator of the sphere. The second we dub the Whispering Longitude mode, which propagates as wave fronts along the azimuth, in the longitudinal direction. If the beat frequency between the modes is measured as the experiment is rotated, we show how to choose the axis of rotation in the laboratory frame to obtain maximum sensitivity to violations of Special Relativity (SR).

We describe a primary fountain frequency standard operating with a continuous beam of laser-cooled Cs atoms. In such a device, aliasing effects, which may degrade the short-term stability in pulsed fountains, are removed and atomic-noise limited stability can be achieved with a state-of-the art, but commercially available, local oscillator. The present experimental short-term stability is measured to be 2.5 · 10^-13τ^-1/2. Another feature of the continuous fountain is the reduced atomic density and higher beam temperature which reduces the collisional shift of the atomic frequency below the 10^-15 level. The light-shift is an undesirable characteristic of the continuous operation. Without a light-trap, a light-shift of the order of 10^-12 has been measured. The shift is stable enough not to affect the frequency stability to 10⁴ seconds (2.5 · 10^-15). A rotating light-trap has been constructed and tested to bring the light-shift and the corresponding uncertainty to a negligible level. Various contributions to the accuracy are studied.

Clouds of cold atoms, collected and refrigerated by laser light, can be cooled to nanoKelvin temperatures. This has created the new field of atom optics where cold atoms are manipulated, much as photons are controlled in traditional optics using mirrors, lenses, and gratings. It is also becoming possible to confine and manipulate atoms in extremely small traps and waveguides, which give access to de Broglie wave physical optics. Atoms flowing in such structures could provide a new technology based on the flow and quantum interactions of neutral atoms. Atom "chips" could lead to integrated atom interferometers and even possibly to a quantum information processor.

Atomic multiple beam interferometers with a high finesse were discussed on Ramsey geometry and optical Ramsey geometry. Also, the atomic polarized beam interferometers with three states and two resonance light fields were discussed.

We report the first operation of a microwave frequency standard based on the 12.6 GHz ground-state hyperfine transition in a cloud of laser-cooled ¹⁷¹Yb⁺ ions, with a preliminary measurement of the transition frequency. We obtain 12 642 812 118.468 5(7)(6) Hz, where the first uncertainty combines statistical uncertainty and the uncertainty of the systematic shifts in the transition frequency due to the trap environment, and the second is that of a comparison between a reference hydrogen maser and the SI second. This value is in agreement with earlier measurements obtained for buffer gas-cooled ions where the second-order Doppler shift is 180 times larger. A full evaluation of systematic shifts is still pending, but the dominant effects are discussed. Motional second-order Doppler shifts are determined within an uncertainty of 1–2 parts in 10¹⁵ from measurements of the ion temperature. Our progress to date indicates no serious obstacle to realising a combined fractional frequency uncertainty of 4 × 10^-15 or smaller and a projected stability of approximately 5 × 10^-14τ^-1/2 for a 10 s Ramsey time. The performance of the ¹⁷¹Yb⁺ microwave standard can therefore be comparable to that of a cesium fountain.

Cryogenic microwave oscillators offer the highest short term stability of any frequency sources^1,2,3. This stability and accompanying ultra-low close-in phase noise are made possible by the high quality factors (Q's) available with cooled sapphire or superconducting resonators, and by advantageous thermal properties (low expansion coefficients and small time constants) for solid materials at low temperatures. The capability offered by these oscillators is crucial to several advanced technology areas; notable among these being NASA radio science applications and local oscillator (L.O.) requirements for a new generation of laser-cooled frequency standards. However, until recently cryogenic oscillators were restricted to research laboratories due to the requirements of liquid-helium cooling. A new generation of sapphire resonators is changing that by offering a much broader range of operating parameters than before. With the addition of external compensation, the new resonators make possible ultra-high frequency stability at higher (and much more easily reached) temperatures than previously required. Today, cryocooled compensated sapphire oscillators (CSO's) are being installed in NASA's Deep Space Network⁴ (10K CSO) and work is going on many laboratories around the world to develop an even higher temperature version, one that can be cooled by a single stage cryocooler. This would meet L.O. requirements for the new laser-cooled frequency standards in a small and economical package. We describe these developments and analyze some of their technical aspects in the sections that follow.

The current status of the development of liquid and solid-nitrogen-cooled secondary frequency standards in the Frequency Standards and Metrology (FSM) research group is presented. We are pursuing two different avenues to achieve resonator frequency immunity to ambient temperature fluctuations. The first method uses a resonator design with a self-compensated element. In this case, rutile annuli have been clamped tightly to the upper and lower end faces of a high-Q sapphire single-crystal dielectric resonator. Initially, using this method frequency-temperature annulment was achieved around 54 K with an unloaded Q-factor of about 2.5 × 10⁷ in the design mode of resonance at 12 GHz in a 3 cm diameter resonator. We show that using a solid-nitrogen bath and novel thermal design, 100 nK fluctuations at 1 s of averaging time can be expected in the resonator. Results indicate that an oscillator with a fractional frequency Allan Deviation of sub-10^-14 up to a few hundred seconds, due to temperature control, is a modest expectation. The second method uses a sapphire resonator designed without any self-compensation technique, but relies on the intrinsic difference in temperature sensitivity of a pair of whispering gallery modes to actively control the resonator temperature. The crystal was cut to a size such that two operational modes of resonance (near 9.2 GHz) are separated by a frequency of about 80 MHz. This method utilizes a thermal design similar to the above and a very fast temperature control servo, capable of realizing a few nano-kelvin temperature fluctuations in the resonator. It involves about 3 to 4 orders of magnitude reduction in the frequency fluctuations of a free-running microwave loop oscillator, which translates into a limit on oscillator Allan Deviation of order 10^-15 up to a few hundred seconds.

Applying a light-shift cancellation technique, spectroscopy on the ¹S₀ - ³P₁ transition of ⁸⁸Sr atoms is demonstrated in a one-dimensional optical lattice. Photons elastically scattered by atoms confined in the Lamb-Dicke regime provide a narrow Doppler-free spectrum of ~ 20 kHz. To further reduce potential uncertainties originating from collisional frequency shifts as well as tensor light shifts, we propose to employ the ¹S₀(F = 9/2) - ³P₀(F = 9/2) transition of the ⁸⁷Sr isotope confined in a three-dimensional optical lattice. We anticipate these optical lattice spectroscopy, evading the first order Doppler shift, may offer an alternative approach for precision spectroscopy in neutral atomic ensembles.

Due to higher transition frequencies, optical frequency standards promise significantly improved stability over that of their microwave counterparts. Our laser-cooled ⁴⁰Ca optical frequency standard is based on the ¹S₀ (m = 0) → ³P₁ (m = 0) intercombination line at 657 nm, and has demonstrated a fractional frequency instability of 4 × 10^-15 at 1 s. Using a mode-locked femtosecond-laser-based frequency comb referenced to the primary Cs standard, we have made an absolute frequency measurement of this transition with an uncertainty of ±26 Hz (1σ). A discussion of the major systematic effects in our system is included. In an effort to reduce our largest systematic uncertainty, we have investigated second-stage cooling in one dimension on the narrow "clock" transition, through quenching of the excited state. We have transferred 45 % (22 % net efficiency) of the atoms into a narrow distribution with a temperature of 4 µK, representing a reduction in temperature by a factor of 500.

The relative uncertainty of the optical frequency standard based on the intercombination transition ¹S₀ - ³P₁ (λ ≈ 657 nm) in ⁴⁰Ca has been improved to below 3 × 10^-14 by using a combination of independent optical excitation schemes. Measurements of the optical frequency by a conventional harmonic chain and a femtosecond comb agree well. Further reduction of the uncertainty is expected from the application of a novel quench cooling technique with temperatures reduced below 7 µK.

We explore an efficient method for preparing large samples of ultracold calcium atoms. An optimized conventional (Doppler-limited) magneto–optical trap collects atoms from a Zeeman cooled atomic beam using a strong dipole transition within the singlet system. This transition is not completely closed thus yielding an intense flux of atoms into the metastable triplet state ³P₂. We obtain a flux of above 10¹⁰ atoms/s into the ³P₂ state. We find that our MOT life time of 23 ms is mainly limited by this loss channel and thus the ³P₂ production is not hampered by inelasic collisions. A second magneto–optical trap sharing the same magnetic field gradient is superimposed which captures and further cools the metastables using the narrow–band infrared transition ³P₂ → ³D₃. In our present experiment we were able to prepare 3 × 10⁸ atoms at temperatures below 20 microkelvin within 250 ms. Minor technical improvements of our setup promise to yield above 10¹⁰ atoms at sub–microkelvin temperatures within 1 s.

Recent developments in quantum information processing may be applicable to future atomic clocks. In this paper we discuss two potential applications to trapped-ion frequency standards. In the first, quantum-mechanical entanglement can provide a resource for increased measurement precision in spectroscopy. In the second, we indicate how a simultaneously trapped auxiliary ion species can be used to provide cooling and as a quantum measuring device; this could be used to increase the number of ion species than can be used as frequency standards.

We describe experimental investigations on an optical frequency standard based on a single laser cooled ¹⁷¹Yb⁺ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the ²S_1/2(F = 0) ground state to the ²D_3/2(F = 2) state is used as the reference transition. Its wavelength is 435.5 nm and its natural linewidth is 3.1 Hz. The transition is probed using a diode laser system whose short-term frequency stability is derived from an environmentally isolated ULE cavity. The transition is resolved with a Fourier-limited full halfwidth of approximately 30 Hz. The absolute optical transition frequency was determined using a femtosecond frequency comb generator and a Cs fountain clock as the frequency reference. The measured frequency value is 688 358 979 309 312 Hz at an ambient blackbody radiation field of 300 K. The 1σ fractional uncertainty of this frequency measurement is 1 · 10^-14.

Ultrahigh precision spectroscopy requires the control of the motion of the particle(s) under investigation. This is commonly achieved via laser cooling which is routinely used in many experiments and standard laboratories. Ultimately, sideband cooling of harmonically confined particles allows one to reach the ground state of the oscillatory motion in a trap and thus to achieve the ideal spectroscopic sample: Particles at rest in free space. In this paper, sideband cooling of a single Ca⁺ ions is described using techniques based on coupled transitions as well as on electromagnetically induced transparency (EIT).

This is a report on behalf of the World Team of Stable Laser and Optical Frequency Measurement Enthusiasts, even if most detailed illustrations draw mainly from our work at JILA. Specifically we trace some of the key ideas that have led from the first stabilized lasers, to frequency measurement up to 88 THz using frequency chains, revision of the Definition of the Metre, extension of coherent frequency chain technology into the visible, development of a vast array of stabilized lasers, and finally the recent explosive growth of direct frequency measurement capability in the visible using fs comb techniques. We present our recent work showing a Molecular Iodine-based Optical Clock which delivers, over a range of time scales, rf output at a stability level basically equivalent to the RF stability prototype, the Hydrogen Maser. We note the bifurcation between single-ion-based clocks – likely to be the stability/reproducibility ultimate winners in the next generation – and simpler systems based on gas cells, which can have impressive stabilities but may suffer from a variety of reproducibility-limiting processes. Active Phase-Lock synchronization of independent fs lasers allows sub-fs timing control. Copies of related works in our labs may be found/obtained at our website http://jilawww.Colorado.edu/yehalllabs.

We describe three different tests of Relativity, a test of the isotropy of the speed of light, a test of the independence of the speed of light on the velocity of the laboratory, and a test of the gravitational clock shift for an electronic clock. The three tests, using cryogenic optical resonators (COREs) have yielded improvements of the best previous tests by up to a factor of three. The potential for future improvements is discussed.

We report on the short-term frequency stability of a Nd:YAG laser at 946 nm. The frequency-stable laser will be used for ultra-high resolution spectroscopy of the 5s^{2 1}S₀ - 5s5p ³P₀ clock transition in In⁺ and will ultimately serve as a local oscillator of an optical frequency standard based on a single trapped indium ion [1,2]. To resolve the extremely narrow ¹S₀ - ³P₀ resonance (γ = 0.82 Hz) at 237 nm the frequency-quadrupled Nd:YAG laser needs to be frequency-stable on a sub-Hertz scale for measurement times up to several 10 s. We obtain the frequency stability of the laser by locking it onto an external high-finesse reference cavity placed on an actively vibration-isolated platform.

In this article we summarize our progress in developing and testing a femtosecond-laser- based optical clockwork that provides a single-step phase-coherent connection between emerging optical frequency standards and the cesium microwave standard on which the SI second is based. This clockwork enabled absolute optical frequency measurements with statistical uncertainty ~ 2 × 10^-15, and it was used in the demonstration of an optical clock with instability ≤ 7 × 10^-15 in 1 s. Recent experiments demonstrate the intrinsic fractional instability and inaccuracy of the clockwork are less than 6.3 × 10^-16 in 1 s and 4 × 10^-17, respectively.

We measure the frequencies of stabilized lasers at NMIJ/AIST with respect to the SI second, using a frequency comb generated from an ultrafast mode-locked laser and broadened over one octave with a photonic-crystal fiber. Each frequency of a mode of the comb was stabilized to microwave frequency standards by a self-referencing technique. The frequencies of an iodine-stabilized Nd:YAG laser at 532 nm and an iodine-stabilized He-Ne laser at 633 nm are determined with an uncertainty of 0.34 kHz and 1.1 kHz, respectively. The frequency of a rubidium-two-photon-stabilized extended-cavity laser diode at 778 nm is also measured.

The accuracy of an optical frequency standard based on a trapped and laser cooled single ⁸⁸Sr⁺ ion at 445-THz has been extended to measurements at 1.5 µm and 633 nm. An absolute frequency link is described for the measurement of radiation in the 1.5 µm telecommunication band. This has been applied to the measurement of a frequency doubled diode laser stabilized on the Rb S-D two-photon transition at 778 nm developed at Université Laval. Also described are recent results concerning a broadly tunable 1.5 µm reference based on saturated absorption resonances in acetylene. Ion referenced, absolute frequency measurements at 633 nm are described which have improved the knowledge of the widely used I₂/HeNe standard frequency at 474-THz. A key element in these measurements is the use of a 28.8-THz OsO₄ stabilized, CO₂ laser system to span the frequency interval between the single ion standard and the I₂/HeNe system. Progress in the improved reproducibility of this system is described.

We have made a frequency standard at the 1.5 mm region using the saturated absorption of the ν₁ + ν₃ band of ¹³C₂H₂ molecule. We have also measured the optical frequency of the acetylene-stabilized standard referring to the Rb two-photon transition at 778 nm.

The accumulated results of absolute frequency measurements (AFM) carried out in 1997–2000 with transportable double-mode He-Ne/CH₄ optical frequency standards (λ = 3 .39μm) in a collaboration of several laboratories are presented. The performance of this secondary optical frequency standard is estimated on the level of 10^-13 (in repeatability), and 1 × 10^-14/s (in stability). The next steps towards He-Ne/CH₄ standards with one order of magnitude better performance, including devices based on monolithic zerodur resonators, are discussed. Important applications of transportable He-Ne/CH₄ optical frequency standards have appeared now due to dramatic progress in the field of optical frequency measurements. Used to stabilize the repetition rate of a Ti:Sa fs laser, these compact secondary standards can transfer their performance into the whole optical range covered by a fs comb. Thus they can play the role of a narrow spectrum interrogative oscillator for super-accurate optical or microwave frequency standards substituting in some tasks a H-maser or oscillators based on cryogenic sapphire resonators.

The following sections are included:

• Introduction

• Apparatus

• References

In this paper we present an experiment that allows a reduction of the average atomic density of an atomic fountain operation by nearly an order of magnitude without serious reduction of the number of atoms used to generate the atomic reference signal, thus preserving the short term stability performance of the clock.

The Time and Frequency Division of the National Institute of Standards and Technology (NIST) is developing a miniature laser-cooled Cs-fountain frequency standard. We anticipate that this device will be useful as a transportable reference for comparison of standards at other laboratories. Additionally, it could be useful for measuring the gravitational clock shift at various locations. We discuss the objectives of this device, the features of the physics package and preliminary results.

We briefly report on the progression of the Horace project and on the possibilities of improvement of the frequency performances of Horace. The expected stability for our atomic clock is evaluated to be below the 10^-12τ^-1/2 floor.

We report the effort of LHA in the field of miniature thermal cesium beam clocks using optical pumping and detection. Two ways are considered: high frequency performance clocks for navigation applications and low-cost medium frequency performance clocks for telecommunication applications.

We started evaluation of the Cs atomic fountain designed as a primary frequency standard. The magnetic field distribution in the interaction zone was measured precisely using a field sensitive transitions |F = 3, m = ± 1 > → |F = 4, m = ± 1 > to estimate the second order Zeeman shift with an uncertainty below 10^-16.

The following sections are included:

• Introduction

• Results

• Conclusions

• References

In this work we present the status of the Brazilian program on scientific time and frequency metrology established at Center of Optical and Photonical Science, in São Carlos four years ago [1]. We report major shifts evaluated, in order to characterize our standard. We have applied the method proposed by Makdissi et.al. [2,3] to our clock in order to determine the Rabi frequency, the second-order Doppler shift and the end-to-end cavity phase shift. By this method, we could also obtain information about the behavior of the shifts as a function of the modulation amplitude. The improvements here reported were responsible for a gain of two orders of magnitude in the frequency standard's stability. We present the evaluation of our frequency standard and a progress report of our atomic fountain.

The ⁸⁸Sr⁺ frequency standard is one of several promising optical quantum oscillators that have the potential to surpass the accuracy and stability of the best atomic clocks. In this article we review the present state of our ⁸⁸Sr⁺ frequency standard, and the changes planned to improve on it.

Among the earth-alkaline ions proposed for an optical frequency standard, Ca⁺ occupies a special position due to its easy-access wavelengths. We describe our work for the preparation of a single ion at rest in a modified miniature Paul trap.

A frequency standard, based on the 674 nm ²S_1/2 - ²D_5/2 optical "clock" transition in a laser cooled trapped strontium ion has been measured and evaluated at the UK National Physical Laboratory. The frequency measurement, using a fs laser comb, is described elsewhere in these proceedings. Experimental and theoretical investigations have been made of the frequency reproducibility. The observed reproducibility is ≈1 part in 10¹³ of the optical frequency with prospects of improvement to below a few parts in 10¹⁵ level, if the RF micro-motion can be minimised simultaneously in all three directions.

The following sections are included:

• Introduction

• Ground state cooling

• Experimental System

• Progress

A simplified and modified multiconfigrational Hartree-Fock (MCHF) method is applied to calculate the isotope shifts (IS) in alkali-like atoms. We have calculated the IS of lower transitions in a series of alkali-like system such as B₂⁺,Ca⁺, Ba⁺, which are in agreement with other works. And the IS of 5S_1/2—4D_3/2,5/2 transitions in ^87,88Sr⁺, which are useful to study the Sr⁺ optical frequency standard, are evaluated.

The following sections are included:

• Introduction

• The 'recoil' splitting without recoil

• References

Absolute frequency measurements of a transportable optical frequency standard based on a He-Ne/CH₄ laser at λ = 3.39 µm stabilized on the central 7-6 component of the hyperfine structure of the F₂⁽²⁾ methane absorption line were made. For the first time, two different phase-coherent frequency chains based on the femtosecond comb technology and a transportable cesium fountain clock were used in the experiment.

We present the latest results on using continuous-wave optical parametric oscillators (cw-OPOs) for high-resolution Doppler-free saturation spectroscopy of methane and point out the resulting potential for future optical frequency standards. We also propose a new scheme for combining cw-OPOs with the recently developed femtosecond frequency combs to provide a versatile bridge between optical frequency standards in the visible, near-infrared and mid-infrared spectral ranges.

The optical Ramsey resonances (ORR) need additional inventions for possibility of registration, because the simplest one (in two separated in space fields) is vanishing due to averaging over transverse velocity distribution. There is a lot of realizations of ORR. In all of them there is quite necessary to take correctly into account the transverse velocity distribution and real (Gaussian) shape of laser fields. In this work we suggest a way of describing the Ramsey resonance for arbitrary saturation and arbitrary transverse laser field shape, which takes into account the first order term correction to resonance approximation (zero pulse width) of the order of a/L (a is the width of the laser beam, L is a distance between laser beams). Additional rather interesting phenomenon consists in non-trivial performance of the recoil effect in case of ORR, different for each variant. In this respect the most interesting of them are the ORR in 3 standing waves and so called linear ORR (in two standing waves separated by λ/2 grating), where we have a few (more than 2) recoil components: in first case with different shapes, in second one of the same shape but with different intensities.

We present results of a frequency comparison of iodine stabilized frequency-doubled Nd:YAG lasers at 532 nm as well as absolute frequency measurements of different molecular iodine absorption lines [1,2], performed at the Max-Planck-Institut für Quantenoptik, Garching.

Recent measurements of hyperfine splittings of I₂ have been performed both by stimulated Raman spectroscopy [1-3] and by saturation spectroscopy [4], from which, the rotation dependence of the hyperfine coupling constants has been investigated in detail in the lower state. With these new data, it is possible to analyze independently the ground and excited states of this molecule and to obtain an improved predictive fit of iodine lines used as optical frequency standards.

New direct observation data on the 2S-2P atomic states coherent mixing upon hydrogen atoms passage through a metal-wall slit are presented. The suggested experimental scheme uses the long-range interaction as a component of an atomic interferometer. Qualitative and quantitative estimates of the atom-surface interaction are obtained for various experimental designs.

A gyroscope based on de Broglie wave interferences of cold Caesium atoms is under construction. It uses stimulated Raman transitions to manipulate the atomic wave packets ¹. We address two possible sources of noise in the case of our setup: phase fluctuations due to propagation of the Raman lasers in optical fibres and geometrical wavefront aberrations on the same lasers.

The principle of the experiment is to measure the recoil of the atom when it absorbs or emits photons. This leads to the measurement of the ratio h/M_x between Planck constant (h) and the atomic mass M_x. The aim of the experiment is to give a measurement of the fine structure constant with an uncertainty better than 10^-7 that is better than the total dispersion of the actual determinations of α (2.4 10^-7).

The principle of operation, the realization, and some preliminary results of a simple pendulum experiment aimed at the determination of G are briefly described.

The ¹S₀-¹D₂ transition in Calcium presents a great interest for metrological application. In particular is very attractive the perspective of realizing an optical reference based on 915 nm two-photon transition. An experiment is in progress in this direction. As a first step, we have build a Ti:Sa laser operating at 915 nm and an absorption cell in which we can observe and measure the corresponding electrical quadrupole absorption transition at 457.5 nm.

We report our progress towards the development of optical frequency standards based on cold and trapped calcium atoms. We set up a Calcium MOT working on the ¹S₀-¹P₁ resonant transition at 423nm. This MOT can load around 4 × 10⁶ atoms with a density of 8 × 10⁹ atoms/cm³ in 7 ms.

We outline progress towards the realisation of optical frequency standards based on narrow two-photon transitions in atomic silver. Subjects described include the detection of metastable atoms and the indirect determination of the 661.2 nm clock transition frequency.

We developed a deep-ultraviolet(UV) single-mode coherent light source through two-stage highly efficient frequency conversions using external cavities. In the first stage, the second-harmonic power of 500 mW was obtained by frequency doubling of a 746 nm Ti:sapphire laser with a conversion efficiency of 40%. In the second stage, 50 mW power at around 252 nm was obtained by doubly resonant sum-frequency mixing of 373 nm light from the first-stage conversion and 780 nm light from a diode laser. The output performances of this deep-UV light source are sufficient for realizing the laser cooling of neutral silicon atoms.

The first Frequency Standards and Metrology Seminar was held in Quebec in 1971. At that time the measurement of the frequencies of lasers had become a reality for precise measurement, and the laser, by then a decade old, was being turned into a useful instrument for science. Today, 30 years later, we find the same field of research opening new horizons – moving beyond pragmatic measurement standards towards testing the basic theories of physics itself.

Actively mode-locked Erbium-doped fiber lasers (EDFL) have been studied for generating stable ultra-fast pulses (< 2 ps) at high repetition rates (> 5 GHz) [1,2]. These devices can be compact and environmentally stable, quite suitable for fiber-based high-data-rate communications and optical ultra-fast analog-to-digital conversions (ADC) [3]. The pulse-to-pulse jitter of an EDFL-based pulse generator will be ultimately limited by the phase noise of the mode-locking microwave source (typically electronic frequency synthesizers). On the other hand, opto-electronic oscillators (OEO) using fibers have been demonstrated to generate ultra-low phase noise microwaves at 10 GHz and higher [4]. The overall phase noise of an OEO can be much lower than commercially available synthesizers at the offset-frequency range above 100 Hz. Clearly, ultra-low jitter pulses can be generated by taking advantage of the low phase noise of OEOs. In this paper, we report the progress in developing a new low-jitter pulse generator by combing the two technologies. In our approach, the optical oscillator (mode-locked EDFL) and the microwave oscillator (OEO) are coupled through a common Mach-Zehnder (MZ) modulator, thus named coupled opto-electronic oscillator (COEO) [5]. Based on the results of previous OEO study, we can expect a 10 GHz pulse train with jitters less than 10 fs.

We give a short description of a new optical frequency measurement system based on a femtosecond laser. First results in measuring an I₂ stabilized Nd:YAG frequency standard are reported.

The possibility of the stabilization of double-frequency operation in a solid-state laser with an anisotropic cavity and intracavity harmonic generation (ISHG) is proposed and investigated. The double-frequency operation stability conditions have been obtained for ISHG in the type II phase-matched crystal KTP.

We report on our progress towards the realization of coherent light sources delivering sub-Hz linewidths and frequency drifts below 0.01 Hz/s, as enabling technologies for the ultra-high-precision spectroscopy of trapped ions. To date, we have concentrated on the servo-locking, via the Pound-Drever-Hall (PDH) technique, of two makes of commercial infrared (1064nm) Nd:YAG lasers (viz NPRO's) to the fringes of various lab-designed ultra-high-finesse etalons, incorporating either ULE or mono-crystalline sapphire spacers. The two main thrusts of our recent work have been (i) the enhancement of the locking accuracy through the optimisation of optical/electro-optical components and peripheral servo-electronics, and (ii) the design, construction and commissioning of two "creep-free" etalons, whose spacers and mirrors exclusively comprise c-axis-aligned, high-purity sapphire, held at liquid-helium temperatures.

Following our earlier work on a new approach to synthesising the Cs hyperfme frequency of 9.192 GHz, we describe developments on its further refinements. The salient feature of our design is that it is based mainly on frequency division and requires no narrow band filter stages. Tests indicate an internal fractional frequency stability of 1.5 × 10^-15 at 10 s and 1 × 10^-18 at 1 day. The temperature coefficient is approximately 0.1 ps to 0.5 ps/K. We have added digital control of the oscillators so that no mechanical tuning is needed over a 25-year lifetime. The unit is powered by 24 ± 4 VDC and uses RS 432 for the output frequency and phase control and monitoring functions. We also describe a general design to produce simultaneously outputs of 9.192 GHz for Cs, 6.834 GHz for Rb, 1.42 GHz for H-maser, 40.5 GHz for Hg⁺, 10GHz for femtosecond pulse repetition rate generation, etc. The synthesiser can be phase locked to an external reference of 5, 10 or 100 MHz or a microwave cryogenic oscillator.

A new RF/microwave architecture was developed at LHA for a compact caesium clock. This architecture may be used either in a low-cost medium performance clock or in a high performance clock for navigation applications. It comprises a very small number of components or modules, and it does not require any adjustment or tuning. This architecture naturally reduces the microwave leaks at 9192,6…MHz that may be a problem in a compact high performance clock. It makes it possible to obtain various – including very high-performance levels with a cheap electronics using low cost electronic modules. The expected thermal stability is about a few ps/K and the first measured phase noise performances are consistent with a 1. 10^-12 τ ^-1/2 frequency stability. A similar architecture may be implemented in various frequency standards.

The paper reports on methods for the measurement of phase and amplitude noise, mainly intended for the characterization of two-port devices (DUT) and for the exploration of physical phenomena. Nesting two interferometers results in reduced residual noise in real-time measurements. Under some hypotheses, it is possible to correlate the output of two detectors, and to further reduce the residual noise.

The following sections are included:

• Arithmetic of Beat Frequency Measurements

• Arithmetic of Phase Locking and 1/f Frequency Noise

• Acknowledgments

• References

Just as it is possible to stabilize the frequency of an electromagnetic field to an atomic resonance between energy eigenstates, so it is possible to stabilize the intensity or brightness of a field to an atomic Rabi-resonance. For ease of reference, we term such a device an "atomic candle." Originally, the atomic candle was developed to stabilize microwave power in the gas-cell atomic clock, thereby eliminating the clock's instability due to microwave power variations. However, atomic candle applications may extend well beyond the area of precise timekeeping, since the device basically provides a means for detecting subtle amplitude changes in strong electromagnetic fields. Here, we describe the general operation of the atomic candle and discuss some of its potential applications.

We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). Because of limited space this short communication is only an update of a previous more complete paper [1] (henceforth referred to as P1) pointing out the advances and changes since June 2001. We recommend the reader to consult that paper for a more detailed account of the theory.

The main goal of this paper is to analyze the higher-order Stark effect on hyperfine structure (hfs) components of Cs and Rb atoms as well as the temperature-dependent shift of 6S_1/2 hfs splitting due to blackbody radiation effects on the 6S_1/2(I=3, M_I=0) - 6S_1/2(I=4,M_I=0) clock transition. An estimate is given based on the model potential method for the contribution of an infinite series over bound states, including the integral over the continuum, for second- and higher-order matrix elements.

Transition F4-F'5 in D₂ Cs line was studied using polarization spectroscopy methods for the cases when enhanced absorption signals are observed. Experiment was realized with counter-propagating saturating and probing laser beams, both of which could have independently varied polarization. It was experimentally observed that there are three cases when one may observe enhanced absorption signal (or inverted pick). These cases are: i) saturating and probing beams have one and the same circular polarization; ii) saturating beam has the circular polarization and probing one has the linear polarization: iii) both beams have the crossed linear (not⊥) polarization. It is experimentally shown that one may construct powerful enhanced absorption resonance signal. Theoretical interpretation and some potential applications are given.

We demonstrate a novel method for the experimental observation of nonlinear magneto-optical effects in cesium vapour using V-type three-level atomic configuration.

We report on the development of a small, low mass and power, and high stability mercury trapped ion frequency standard for spaceflight. The design performance goal is fractional frequency stability reaching into the 10^-6 range with technologies that allow for 10 years of continuous operational life. Key system elements include using a nitrogen buffer gas for long vacuum pump life and a multi-pole ion trap to minimize sensitivity to the second order Doppler shift.

We describe a microwave cavity clock experiment to perform improved tests of Local Position Invariance and Lorentz Invariance on the International Space Station. Significant improvements over present bounds are expected in both cases. The oscillators will also be used to enhance the performance of atomic clocks being developed elsewhere for use in space.

The following sections are included:

• Discussion

• Results

• Bibliography

A novel and compact diode-pumped Er-Yb:glass laser operating at around 1.54 μm wavelength was developed with single-frequency and linearly-polarized output power in excess of 10 mW over a continuous tunability range of more than 10 nm. In a first set of experiments the laser was frequency doubled at 770.1 nm, in a single-pass PPLN crystal waveguide with internal second harmonic conversion efficiency of ~220 W^-1, and the second harmonic beam was used for high-resolution saturation spectroscopy of the ³⁹K 4S_1/2-4P_1/2 line. Frequency locking was performed to a 10.6 MHz crossover line achieving frequency stability below 4 × 10^-12 for integration times between 100 ms and 100 s. In a second set of experiments the laser was frequency locked to the 1 MHz Doppler-free absorption of ¹³C₂H₂ P(16) line at 1.543 μm wavelength. This was accomplished by using a high-finesse Fabry-Perot structure including the low-pressure ¹³C₂H₂ Brewster cell and locking by the FM sideband technique. The achieved frequency stability, as evaluated from the error signal, is in the range of ±20 kHz and the correspondingly calculated Allan deviations give σ_y(τ) = 8 × 10^-12 τ^-1/2 and σ_y < 10^-12 for τ > 70s.

When we succeeded in stabilizing the oscillation frequency of a semiconductor laser, it was done, using the Rb absorption line and its Faraday effect as an external frequency reference. Both AC and DC magnetic fields were applied to the Rb cell to modulate the absorption line and obtain the very sensitive error-signal, without directly modulating the oscillation frequency.

Our semiconductor laser oscillation-frequency-stabilization method combines the use of the etalon and the Rb-D₂ absorption line as frequency references, along with the PEAK method, which we devised specifically for the purpose. Our method is expected to produce the stable frequency reference in a wide frequency range around 1.5 µm wavelength region.

In attempting to increase second harmonic generation (SHG) output-power of semiconductor lasers, we employed a single optical feedback loop. When we doubled the number of feedback loops, SHG light-output stability increased significantly. We also observed that the number of longitudinal modes decreased, indicating that optical output-power was concentrated, in the center oscillation mode, in a multi-longitudinal mode laser.

This paper reports sensitive measurement of the power spectral density of semiconductor laser frequency fluctuations over a wide frequency range (about 9 decades, starting from 1 Hz and ending over 1 GHz). This broad range allows the observation of flicker and white noise contributions, as well as contributions from the current source driving the laser. The high sensitivity of the setup, reaching +13 dB relative to 1 Hz²/Hz, enables the measurement of the impacts of the optical feedback used for linewidth reduction purposes, as well as long-term stabilization schemes. In particular, it shows clearly the frequency noise reduction when optical feedback is applied. The setup has been used to characterize the frequency noise of a DFB laser, whose linewidth is reduced with feedback from a confocal cavity, as well as frequency-stabilized to a two-photon transition of ⁸⁷Rb.

A 778 nm diode laser frequency standard has been developed, based on 5S_1/2-5P_5/2 2-photon transitions in ⁸⁵Rb and ⁸⁷Rb. A preliminary assessment of the system's performance is presented.

The following sections are included:

• List of Participants

• Index of Contributors