Frequency Standards and Metrology

The following sections are included:

• PREFACE

• Symposium History

• Symposium Photos

• Contents

Theories unifying gravity with other interactions suggest the possibility of temporal and spatial variation of the fundamental "constants" in an expanding Universe. In this review we discuss the effects of variation of the fine-structure constant and fundamental masses on measurements covering the lifespan of the Universe from a few minutes after Big Bang to the present time. Measurements give controversial results, including some hints for variation in Big Bang nucleosynthesis and quasar absorption spectra data. Furthermore there are very promising methods to search for the variation of fundamental constants by comparison of different atomic clocks. Huge enhancements of the relative variation effects happen in transitions between accidentally degenerate nuclear, atomic, and molecular energy levels.

Repeated measurements of the frequency ratio of ¹⁹⁹Hg⁺ and ²⁷Al⁺ single-atom optical clocks over the course of a year yield a constraint on the possible present-era temporal variation of the fine-structure constant α. The time variation of the measured ratio corresponds to a time variation in the fine structure constant of , consistent with no change. The frequency ratio of these clocks was measured with a fractional uncertainty of 5.2 × 10^-17. Stability simulations for optical clocks whose probe period is limited by 1/f-noise in the laser local oscillator provide an estimate of the optimal probe period, as well as a modified expression for the theoretical clock stability.

Radio-frequency electric-dipole transitions between nearly degenerate, opposite parity levels of atomic dysprosium (Dy) were monitored over an eight-month period to search for a variation in the fine-structure constant, α. The data provide a rate of fractional temporal variation of α of (-2.4±2.3) × 10^-15 yr^-1 or a value of (-7.8 ± 5.9) × 10^-6 for k_α, the variation coefficient for α in a changing gravitational potential. All results indicate the absence of significant variation at the present level of sensitivity. We also present initial results on laser cooling of an atomic beam of dysprosium.

We describe the new project FORCA-G, which aims at studying the short range interactions between a surface and atoms trapped in its vicinity. Using cold atoms confined in the wells of an optical standing wave, the atom-surface potential will be measured with high sensitivity using atom interferometry techniques. The experiment will allow a test of gravity at short distances, which will put stringent bounds on a possible deviation from the known laws of physics. FORCA-G will also allow a measurement of the Casimir Polder interaction (QED vacuum fluctuations) with unprecedented accuracy.

The following sections are included:

• Introduction

• Atom Interferometry with 24-Photon-Momentum-Transfer Bragg Beam Splitters

• Noise-Immune, Recoil-Sensitive, Large-Area Atom Interferometers

• Very large area atom interferometers by differential optical acceleration

• Towards fundamental physics measurements by atom interferometry
  • Detection of gravitational waves

• References

We are witnessing the beginning of a new era for space-qualified atomic clocks. These new instruments, characterized by low-mass, low-power consumption, and frequency stabilities comparable to those of ground-based clocks, will allow interplanetary spacecraft radio science experiments at unprecedented Doppler sensitivities.

By adding a digital receiver to the onboard instrumentation, it is possible to take advantage of the frequency stability of a space-qualified atomic clock by linearly combining digitally the multi-link Doppler measurements performed on the ground and onboard. This allows one to optimally suppress the frequency fluctuations of the Earth atmosphere, ionosphere and mechanical vibrations of the ground antenna (the dominant Doppler tracking noises) in the resulting Doppler data set.

After providing the general expression of the optimal combination of the ground and onboard Doppler data, we apply it, as an example, to interplanetary Doppler tracking searches for gravitational radiation. The resulting estimated sensitivity to milliHertz gravitational waves is about one order of magnitude better than that achievable by traditional two-way coherent Doppler experiments.

The Doppler tracking technique discussed in this article can be performed (at minimal additional cost) with future planned interplanetary missions, and extended to other experiments such as spacecraft Doppler tests of relativistic gravity, gravity field measurements, and radio occultations of planetary atmospheres and rings.

Quantum state engineering of ultracold matter and precise control of optical fields have together allowed accurate measurement of light-matter interactions for applications in precision tests of fundamental physics. State-of-the-art lasers maintain optical phase coherence over one second. Optical frequency combs distribute this optical phase coherence across the entire visible and infrared parts of the electromagnetic spectrum, leading to the direct visualization and measurement of light ripples. At the same time, ultracold atoms confined in an optical lattice with zero differential ac Stark shift between two clock states allow us to minimize quantum decoherence while strengthening the clock signal. For ⁸⁷Sr, we achieve a resonance quality factor > 2.4 × 10¹⁴ on the ¹S₀ - ³P₀ doubly forbidden clock transition at 698 nm [1]. The uncertainty of this new clock has reached 1 × 10^-16 and its instability approaches 1 × 10^-15 at 1 s [2]. These developments represent a remarkable convergence of ultracold atoms, laser stabilization, and ultrafast science. Further improvements are still tantalizing, with quantum measurement and precision metrology combining forces to explore the next frontier.

This article describes recent frequency measurements performed with the LNE-SYRTE atomic clock ensemble. First, we report a new determination of the rubidium 87 hyperfine frequency, performed using Rb and Cs atomic fountains. The measurement has a statistical uncertainty below 10^-16 and an overall uncertainty of 1.1 parts in 10¹⁵. Second, we report the first laser spectroscopy of the ¹S₀-³P₀ optical clock transition at 265.6 nm in laser-cooled fermionic isotopes of neutral mercury. The absolute frequency is measured with a fractional uncertainty of ~ 5 parts in 10¹² which improves upon previous indirect determinations by more than 4 orders of magnitude, an important step toward the realization of an optical lattice clock.

We demonstrate an interferometric scattering technique that allows highly precise measurements of s-wave scattering phase shifts. We collide two clouds of cesium atoms in a juggling fountain clock. The atoms in one cloud are prepared in a coherent superposition of the two clock states and the atoms in the other cloud in an F,mF state. After the two clouds collide, we detect the scattered part of the clock atom's wavefunction for which the phase of the clock coherence is shifted by the difference of the s-wave phase shifts. In this way, we unambiguously observe the differences of scattering phase shifts. These phase shifts are independent of the atomic density to lowest order, enabling measurements of scattering phase shifts with clock accuracy. Recently, we have observed the changes in scattering phase shifts as a function of magnetic field over a range where Feshbach resonances may be expected and inelastic scattering channels open and close. Measurements like these will tightly constrain our knowledge of cesium-cesium interactions. With such knowledge, future measurements may place stringent limits on the time variation of fundamental constants, such as the electron-proton mass ratio, by precisely probing phase shifts near a Feshbach resonance.

We report on an absolute frequency measurement with a single ⁴⁰Ca⁺ ion in a linear Paul trap. A frequency comb referenced to the transportable Cs atomic fountain clock of LNE-SYRTE is used to measure the frequency of a laser exciting the ⁴⁰Ca⁺ 4s ²S_1/2 - 3d ²D_5/2 electric-quadrupole transition. A transition frequency of ν_Ca⁺ = 411 042 129 776 393.2(1.0) Hz was obtained, which corresponds to a fractional uncertainty of 2.4 × 10^-15.

No field in nature truly corresponds to the classical monochromatic ideal. Even the "singlemode" laser can be, in certain regards, a poor approximation: the mode has a width that depends on the photon's cavity lifetime, and amplified-spontaneous-emission produces fluctuations in the laser's output. With regard to metrology, the question is twofold: at what level of precision (stability) does a classical field's stochastic nature become relevant in field/matter interactions, and how does the field's stochastic nature manifest itself in measurements. Unfortunately, answers to those questions are only known in a few specific cases, and general intuitive models are lacking. Here, we provide a short overview of the semiclassical stochastic-field/atom interaction, illustrating how the stochastic nature of a classical field can have a significant effect on spectroscopic signals, and how those effects are not always intuitively obvious. In concluding, we argue that simple, general, intuitive models of the stochastic-field/atom interaction are needed, so that researchers can be alerted as to when and how stochastic-field effects may manifest themselves in precision measurements.

As a consequence of a general trend in the physics of oscillators and clocks towards optics, phase and frequency metrology is rapidly moving to optics too. Yet, optics is not replacing the traditional radio-frequency (RF) and microwave domains. Instead, it adds tough challenges.

Precision frequency-stability measurements are chiefly based on the measurement of phase noise, which is the main focus of this article. Major progress has been achieved in two main areas. The first is the extreme low-noise measurements, based on the bridge (interferometric) method^1,2 in real time or with sophisticated correlation and averaging techniques.^3,4 The second is the emerging field of microwave photonics, which combines optics and RF/microwaves. This includes the femtosecond laser, the two-way fiber links,⁵ the noise measurement systems based on the fiber⁶ and the photonic oscillator.^7,8 Besides, the phenomenology of flicker (1/f) noise is better understood, though the ultimate reasons are still elusive.

This paper describes the current status of an experiment designed to make absolute frequency measurements of a series of optical two-photon 2S-nS, nD transitions in atomic hydrogen. The 2S_1/2-8D_5/2 transition has been observed and a preliminary measurement of its frequency has been made using a femtosecond optical frequency comb. Detailed studies of systematic frequency shifts are in progress. When combined with results from several other experiments worldwide, this work will contribute to an improved determination of the Rydberg constant.

Atomic Clock Ensemble in Space (ACES) is a mission designed to perform accurate tests of Einstein's theory of general relativity and develop applications in time and frequency metrology, global positioning and navigation, geodesy, and remote sensing. Mission concept, scientific objectives, and status of ACES will be discussed and the latest test results presented.

We summarize the scientific and technological aspects of the SAGAS (Search for Anomalous Gravitation using Atomic Sensors) project, submitted to ESA in June 2007 in response to the Cosmic Vision 2015-2025 call for proposals. The proposed mission aims at flying highly sensitive atomic sensors (optical clock, cold atom accelerometer, optical link) on a Solar System escape trajectory in the 2020 to 2030 time-frame. SAGAS has numerous science objectives in fundamental physics and Solar System science, for example tests of general relativity and the exploration of the Kuiper belt. The combination of highly sensitive atomic sensors and of the laser link well adapted for large distances will allow measurements with unprecedented accuracy and on scales never reached before. We present the proposed mission with particular emphasis on the measurements and payload technology.

We have recently completed a breadboard ion-clock physics package based on Hg ions shuttled between a quadrupole and a 16-pole rf trap. With this architecture we have demonstrated short-term stability ~1-2 × 10^-13 at 1 second, averaging to 10^-15 at 1 day. This development shows that H-maser quality stabilities can be produced in a small clock package, comparable in size to an ultra-stable quartz oscillator required for holding 1-2 × 10^-13 at 1 second. This performance was obtained in a sealed vacuum configuration where only a getter pump was used to maintain vacuum. Because the tube is sealed, the Hg source and Neon buffer gas are held indefinitely, for the life of the tube. There is no consumption of Hg in this system unlike in a Cs beam tube where lifetime is often limited by Cs depletion. The vacuum tube containing the traps has now been under sealed vacuum conditions for over three years with no measurable degradation of ion trapping lifetimes or clock short-term performance. A 3-liter prototype physics package now in development will be described.

Precision Doppler spectroscopy in astrophysics is limited by the stability of calibration sources, as well as the number, width and distribution of available calibration lines. Broadband frequency combs generated from mode-locked femtosecond lasers have revolutionized precision laboratory spectroscopy. We present a laser comb with up to 40 GHz line-spacing, generated from a 1 GHz repetition-rate "source comb" and a Fabry-Perot filtering cavity. The line spacing can be optimized for use with any high-resolution astronomical spectrograph. Our prototype, which we have recently tested with the Tillinghast Reflector Echelle Spectrograph on Mt. Hopkins, provides a 100-nm band of calibration light centered on 850 nm, in the center of the a region difficult to calibrate with atomic sources. The astro-comb should allow more than an order-of-magnitude improvement in sensitivity to changes in Doppler-shifts and cosmological redshifts, with significant impact on many fields, including stellar seismology, cosmology, and the search for extrasolar earths.

VLBI is a powerful astronomical technique that allows data from widely separated radio telescopes to be combined into interferometric arrays that can image the sky with exceptional angular resolution. At the heart of a VLBI station is a highly stable frequency reference that locks heterodyne receivers and enables the phase of radiation from a cosmic source to be preserved. Subsequent correlation of data streams from two VLBI stations provides fourier components of sky brightness, and with many antennas, an accurate image of the radio sky can be reconstructed with an angular resolution equal to the ratio of observing wavelength to antenna separation. At the highest frequencies and longest baselines, angular resolutions approach 30 micro arcseconds, over a thousand times finer than the Hubble Space Telescope. With such resolution, a number of astrophysical phenomena can be studied in detail, including the Super Massive Black Hole candidate, SgrA* (Sagittarius A "star"), at the center of the Milky Way Galaxy. To maintain phase coherence for observing wavelengths shortward of 1.3mm requires frequency standards to be stable over 1-10 second intervals, which is a coherence time set by atmospheric turbulence. Historically, Hydrogen masers have been used as VLBI references, but for short wavelength observations new frequency sources are available that outperform masers over the integration times of interest. I will discuss the stability requirements for VLBI and describe how future VLBI experiments can image the accretion disk and Event Horizon of the black hole at the Galactic Center.

Thales Electron Devices is leading a French-Swiss industries and research institutes consortium aiming at developing an Optically-pumped Space Cesium Clock for Galileo. The technical objective of this development is to demonstrate a frequency stability of 1 × 10^-12 τ^-1/2 compatible with an operational lifetime of twelve years. The present clock demonstrator combines the simplest and best technologies available, among those the single optical wavelength scheme and the dark fringe Ramsey cavity. Presently a clock operational signal-to-noise ratio of 21'300 Hz^1/2 has been recorded for a Cs oven heated at 100°C. The clock frequency stability has been measured to be 2.3 × 10^-12 τ^-1/2. The current limitations and future improvements are discussed.

We discuss configurations of optical lattice clocks from the viewpoint of lattice geometries and quantum statistics of interrogated atoms. This leads to two promising schemes: a one-dimensional lattice loaded with spin-polarized fermions and a three-dimensional lattice loaded with bosons. These two optical lattice clocks based on fermionic ⁸⁷Sr and bosonic ⁸⁸Sr were demonstrated by measuring the frequency stability as well as their isotope shift. In addition, we address the ongoing experimental challenges for optical lattice clocks.

We describe the development and latest results of an optical lattice clock based on neutral Yb atoms, including investigations based on both even and odd isotopes. We report a fractional frequency uncertainty below 10^-15 for ¹⁷¹Yb.

We review the recent progress at LNE-SYRTE on an optical lattice clock using Sr atoms. We discuss the required lattice depth to cancel motional effects in such a clock and show that a relatively small lattice depth is sufficient provided the lattice is oriented vertically. We also demonstrate an accurate frequency measurement of the Sr clock transition with accuracy in the low 10^-15 range. Finally, we describe a new non-destructive method to detect the atoms in the clock and discuss the expected associated improvement in the frequency stability of the clock.

At the National Physical Laboratory we are developing a neutral atom optical clock based on strontium atoms held in an optical lattice during the clock frequency measurement. The innovation of lattice-type clocks has greatly reduced velocity-related systematic frequency shifts compared to ballistic expansion neutral atom clocks. However, with predicted fractional uncertainties as low as 10^-18, many previously unexplored systematic effects become relevant, especially in dealing with shifts due to blackbody radiation. We are designing a compact, diode-laser-based system, with a view to future transportable systems, and which includes a novel permanent-magnet-based Zeeman slower and a blackbody measurement chamber.

We report the observation and interpretation of collision-induced perturbations in a ⁸⁸Sr lattice clock. Losses are observed in the collision channels ¹S₀+³P₀ and ³P₀+³P₀. Furthermore, we observe broadening and shift of the clock transition by collisions.

In this paper we present the current status in the realization of a new generation of high accuracy frequency standards at INRIM, whose relative frequency uncertainty is expected to achieve and possibly pass the 10^-16 range. Currently we are developing a nitrogen cooled cryogenic Cs fountain and a dipole trap neutral Yb optical clock. This development will allow us to make an absolute measurement of the Yb clock frequency against a primary frequency reference in the low 10^-16 range.

Singly ionized ytterbium offers a number of possibilities to realize frequency standards in the optical frequency range. Two narrow-linewidth reference transitions, one at a wavelength 436 nm and the other at 467 nm, are of particular interest for practical implementations of single-ion optical clocks. The frequency ratio of these transitions is expected to be a very sensitive probe for the constancy of the fine structure constant. We outline our related experimental work and in particular the status of the 436 nm (688 THz) single-ion optical frequency standard developed at PTB.

The 5s ²S_1/2-4d ²D_5/2 electric quadrupole transition in a single trapped and laser-cooled ⁸⁸Sr⁺ ion provides the reference for a highly stable and accurate optical clock. This paper describes recent progress on the ⁸⁸Sr⁺ optical clocks under development at NPL. An ultrastable laser at 674 nm is used to excite the clock transition and a fractional frequency resolution of 2 × 10^-14 has been achieved, corresponding to a linewidth of 9 Hz. A relative frequency instability of 2 × 10^-15 at 5000 s has been observed in the comparison between two similar systems and the fractional uncertainty in the absolute frequency of the clock transition is 3.8 × 10^-15. Improvements to the experimental arrangement are in progress and are expected to lead to a ⁸⁸Sr⁺ optical clock with stability and reproducibility exceeding that of the primary caesium standard.

The single cold ¹⁷¹Yb⁺ ion has two optical clock transitions available. One of these is the ²S_1/2 - ²D_3/2 quadrupole (E2) transition at 436 nm. The other is the ²S_1/2 - ²F_7/2 octupole (E3) transition at 467 nm, which has an extremely narrow theoretical linewidth on account of the 6-year lifetime of its F_7/2 upper level. This paper reports progress on both these clock transitions at NPL. In particular, the absolute frequency of the observed octupole transition has recently been measured with an uncertainty of 12 Hz (1σ) for an octupole linewidth of < 40 Hz. Contributions from major shifts such as the AC Stark shift and second order Zeeman shift have been measured, and quadrupole and blackbody shifts estimated. The frequency ratio between the ¹⁷¹Yb⁺ quadrupole and octupole transitions demonstrates one of the largest sensitivities for monitoring possible time variation of the fine structure constant. Ultra-stable probe laser light at 436 nm has recently been generated to interrogate the quadrupole clock transition, in preparation for measuring both clock transitions simultaneously.

We describe progress towards ultra-accurate and stable standards of frequency and time at the National Research Council of Canada (NRC). Emphasis is placed on the research associated with creating a reliable and workable optical frequency standard and secondary realization of the second based on a single trapped and laser cooled ion of strontium at 445 THz. Work is described on recent results of probe resolution, stability, and the ability to connect this reference frequency with existing and developed RF standards at NRC. An overview is also presented of the group's progress in the development of a Cs fountain based standard for the realization of the second and upcoming determinations of the reference single ion frequency.

Optical spectroscopy has matured to the most precise measurement tool in physics thanks to advances in single ion trapping and the possibility to directly measure the frequency of laser light. However, almost 50 years after the invention of the laser the spectral region that can be investigated in this way is still restricted to wavelengths below the near ultraviolet. The much larger spectral band of the extreme ultraviolet (XUV), where many fundamental transitions of say hydrogen like ions reside, is thus far unexplored by high precision laser spectroscopy. One possible route to narrow band radiation in this region could be the use of high order harmonics generated with short laser pulses of high repetition rate focused in a gas jet. Meanwhile µW power levels in the XUV at multi-MHz repetition rates have been demonstrated which are the main prerequisites for this method. The 1S-2S two photon transition at 60 nm in singly ionized helium is a rewarding candidate because it allows sensitive tests of quantum electrodynamics.

An optical frequency comb, based on a stretched-pulse, mode-locked erbium fibre laser, has been developed to measure the clock transition frequency at 445 THz of a Sr⁺ single-ion optical frequency standard. The comb employs separate amplifier branches for the control of the carrier-envelope offset frequency and for the measurement of the clock frequency of the optical standard. Continous locking periods for the comb of over three days have been observed.

We report on the realization of a new technique for a phase-coherent link between the visible and infrared spectral ranges provided by a continuous-wave OPO in combination with a Ti:Sapphire femtosecond laser comb. We have developed a CH₄-based infrared molecular clock by phase locking the repetition rate frequency of a Ti:Sapphire femtosecond laser comb to the optical frequency of a He–Ne/CH₄ standard. We also performed a direct absolute frequency comparisons between an iodine stabilized laser at 532 nm and a methane stabilized laser at 3.39 µm.

This paper reports a number of improvements to a Ti:sapphire-based frequency comb. Changes to the spectral broadening set up, f.2f self-referencing arrangement and servo system are described, including a novel scheme for group-delay dispersion compensation using Wollaston prisms. In combination, these changes improved the signal-to-noise ratio of the carrier-envelope offset beat by 15 dB and increased its frequency stability by more than four orders of magnitude, as well as enabling it to be locked continuously for many hours without optical adjustment.

The National Institute of Standards and Technology operates a cesium fountain primary frequency standard, NIST-F1, which has been contributing to International Atomic Time (TAI) since 1999. At the time of the last Symposium on Frequency Standards and Metrology in 2001, the uncertainty of the standard was δf/f₀ ≃ 1 × 10^-15, which was at that time the state-of-the art. During the intervening 7 years we have improved NIST-F1 so that the uncertainty is currently δf/f₀ ≃ 3× 10^-16, dominated by uncertainty in the Blackbody radiation induced frequency shift. In order to circumvent the uncertainty associated with the blackbody shift we have built a new fountain, NIST-F2, in which the microwave interrogation region is cryogenic (80K) reducing the blackbody shift to negligible levels. We briefly describe here the series of improvements to NIST-F1 which have allowed its uncertainty to reach the low 10^-16 level and present the first results from NIST-F2.

The U.S. Naval Observatory (USNO) has a program to field operational atomic fountain clocks for augmentation of the USNO timescale and master clock. We present the design and characterization of our engineering prototype and the initial results for the first two operational fountain clocks. In addition, we briefly discuss the new Master Clock Facility that houses the operational devices.

The second laser cooling - Cesium fountain clock NIM5 at the National Institute of Metrology (NIM) China adopts the (1,1,1) direct OM (Optical Molasses) configuration. NIM5 has been running with a stability of 3 × 10^-15/d and an operation ratio of 99% since 2007. Preliminary evaluations of NIM5 in 2008 showed a typical combined uncertainty of 3 × 10^-15. The NIM5 clock is operating in parallel with NIM's first fountain clock NIM4. NIM4 and NIM5 are used to steer the frequency of the calculated NIM atomic time TA-c(NIM) and the first set of results are promising. We are now at the stage of comparing the frequency of NIM5 with UTC to support the independent frequency shift evaluations of NIM5 and contribute to the international atomic time in the near future.

We have developed a compensated multi-pole Linear Ion Trap Standard (LITS) that eliminates nearly all frequency sensitivity to residual ion number variations. When operated with ¹⁹⁹Hg⁺, this trapped ion clock has recently demonstrated extremely good stability over a 9-month period. The short-term stability has been measured at 5 × 10^-14/τ^1/2 and an upper limit on long-term fractional frequency deviations of < 2.7 × 10^-17/day was measured in comparison to the laser-cooled primary standards and to the post-processed ultra-stable version of TAI known as TTBIPM using GPS carrier phase time transfer. We have also made a first measurement of the Hg⁺/Hg collision shift and place a limit of +3.8(7.2) × 10^-8/Pa on the shift constant.

In this paper we proposed a frequency standard based on pulsed coherent storage (PCS), the basic idea of the PCS scheme is combining the information storage technique with the optical pumping method. It shows that the Ramsey pattern is printed on the coherence of the atom states, then is detected in the form of the retrieval light. The proposed PCS frequency standards are free of light shifts, low Q requirement, high signal contrast and low noise background. The estimated frequency stability is 2 × 10^-14 in 1 second. Meanwhile we report the progress in laser cooling of atoms in an integrating sphere, some experimental results are given. This cooling method provides a robust source which is suitable to construct a compact PCS clock.

We present a first uncertainty estimate for CSF2, the second Cs fountain clock at PTB. Initial measurements of the collisional shift and the quadratic Zeeman effect have recently been completed. Simultaneous measurements with CSF1 show a short term relative instability of the frequency difference of 2.6 × 10^-13 (τ/s)^-1/2 for averaging time τ and a relative stability of better than 10^-15 after 7 × 10⁴ s.

We present theoretical and experimental studies concerning the realization of a rubidium vapor cell frequency standard based on the pulsed optical pumping (POP) technique. This technique is extremely powerful since it avoids in principle the light shift effect and the noise conversions from the laser to the clock signal. The detection of the clock transition in the microwave domain (the so called POP maser) has been extensively investigated at INRIM and a frequency stability of 1.1 × 10^-12τ^-1/2 has been measured until integration times of 10⁵ s, reaching the level of 5 × 10^-15 (drift removed). The optical detection is still under evaluation but this technique may lead in effect to some advantages with respect to the microwave detection, such as a lower or negligible cavity pulling, a lower operation temperature (which implies a lower spin exchange contribution) and a higher signal-to-noise ratio. All these features may lead to a better frequency stability performance than that previously reached.

In this paper we present some experimental results obtained with a laboratory setup of a pulsed optically pumped rubidium vapor cell with buffer gas frequency standard. A central Ramsey fringe with FWHM of Δν = 140 ± 10Hz is observed in the transmitted optical signal, and a central Ramsey fringe with FWHM of Δν = 60 ± 10Hz is also observed in the free-induced decay signal at the end of the second microwave pulse. The effect of the microwave pulse power upon the Ramsey fringe is studied.

Our alternative approach to primary fountain standards is based on a continuous beam of laser-cooled atoms. Besides circumventing stability limitations inherent to pulsed operation, a continuous beam is also interesting from the metrological point of view since it provides a different accuracy budget where density related frequency shifts are negligible. Two continuous fountains — FOCS–1 and FOCS–2 — have been designed and assembled. This contribution gives the present status of this work.

In this paper we describe a new clock based on ²⁰¹Hg⁺. All previous mercury ion clocks have been based on ¹⁹⁹Hg⁺. We have recently completed construction of the ²⁰¹Hg⁺ clock and will describe modifications to the design of our existing ¹⁹⁹Hg⁺ clocks to accommodate the new isotope. We will also describe initial spectroscopic measurements of the hyperfine manifold, and possible future experiments. One experiment could place a limit on variations in the strong interaction fundamental constant ratio m_q/Λ_QCD.

We report on our development of a compact and high-performance laser-pumped Rubidium atomic frequency standard. The clock design is based on optical-microwave double-resonance using cw optical pumping, and a physical realization as simple as possible. Main development goals are a short-term instability of ≤ 6 × 10^-13 τ^-1/2 and a flicker floor of ≤ 1 × 10^-14 up to one day. Here we discuss our approaches for controlling the clock's main physical parameters in view of optimized frequency stability.

A Raman-Ramsey Cs cell atomic clock based on Coherent Population Trapping is studied. High contrasts and narrow width Ramsey fringes are achieved by combining an original double-lambda scheme and a pulsed interrogation technique. The pulsed method allows a strong reduction of the light shift effect and avoids the power broadening. Removing a drift attributed to the cell, the clock frequency stability has been measured to be 7 × 10^-13 τ^-1/2.

In trying to implement temperature compensation of high-Q metallic microwave cavities with the two-metal technique, crippling problems arise from the exceedingly high uncertainty with which the Coefficients of Thermal Expansion (CTE) of the two metals are known, and from their non linearity with temperature. A novel approach is here proposed, following which both problems can be separately addressed, opening the way for improvement of the resonance frequency temp-co into the 10^-10/K and possibly the 10^-11/K region.

Cryogenic sapphire oscillators, developed at the University of Western Australia, have now been in operation around the world continuously for many years. We describe and summarize their design, construction and performance. Fractional-frequency fluctuations below 6 × 10^-16 at integration times between 10 and 200 s have been repeatably achieved at X-band.

We present the design geometry of an optical horizontal cavity. The Finite Elements Modelling analysis is used to predict and decrease the influence of vibrations on the cavity stabilized laser. Inspired by the results of this simulation, a horizontal cavity is constructed. The vibration sensitivity components measured for this cavity are equal to or better than 1.4 × 10^-11/(m.s^-2) for all spatial directions.

We report here results obtained with the Cryogenic Whispering Gallery Mode Sapphire Maser Resonator-Oscillator. The first characterization against the UWA cryogenic sapphire oscillator exhibited frequency instability of orders 10^-14 at 1 second limited by the readout system we used. We also report, for the first time, on the measurement of the fundamental limit (thermal noise) for a microwave resonator.

We describe an optical phase lock loop (PLL) designed to recover an optical carrier at powers below one picowatt in a Deep Space optical transponder. Previous low power optical phase lock has been reported with powers down to about 1 pW. We report the demonstration and characterization of the optical phase locking at femtowatt levels. We achieved a phase slip rate below one cycle–slip/second at powers down to 60 femtowatts. This phase slip rate corresponds to a frequency stability of 1 × 10^-14 at 1 s, a value better than any frequency standard available today for measuring times equal to a typical two–way delay between Earth and Mars. The PLL shows very robust stability at these power levels. We developed simulation software to optimize parameters of the second order PLL loop in the presence of laser flicker frequency noise and white phase (photon) noise, and verified the software with a white phase noise model by Viterbi. We also demonstrated precise Doppler tracking at femtowatt levels.

The radio frequency repetition rate of an infrared erbium-doped mode locked fibre laser is transferred over 50 km of spooled single mode fibre (SMF). The pulse broadening caused by the chromatic dispersion of the fibre is partially counteracted by incorporating a matched length of dispersion compensating fibre (DCF). The fibre-induced phase noise is cancelled by means of a fibre stretcher at the transmitter end. The transfer frequency stability delivered at the 'user' end is measured to be better than 5 × 10^-15 τ^-1/2 for integration times longer than 1 s.

We describe an ultra-stable laser system used to probe the clock transition of the ⁸⁸Sr⁺ single ion optical frequency standard at NRC. The laser performance is determined primarily by the reference Fabry-Perot cavity which is stabilized at the temperature where the thermal expansion coefficient of the spacer is zero. The frequency stability was studied by comparing the frequency of the laser locked to the reference cavity with that of the ⁸⁸Sr⁺ clock transition. After subtraction of a piecewise linear drift, the laser frequency reaches a stability of 5 × 10^-16 at an averaging time of 3000 s. The laser linewidth was investigated by recording high resolution spectra of one of the Zeeman components of the clock transition. A Fourier-transform limited linewidth of ≈ 4.3 Hz, corresponding to a fractional frequency resolution of 1 × 10^-14, was observed for a 200 ms probe pulse length.

We describe the setup and the characterization of a 698 nm master-slave diode laser system to probe the ¹S₀-³P₀ clock transition of strontium atoms confined in a 1D optical lattice. The frequency noise and the linewidth of the laser system have been measured with respect to an ultrastable 657 nm diode laser with 1 Hz linewidth. The large frequency difference of more than 25 THz was bridged using a femtosecond fiber comb as transfer oscillator. In a second step the virtual beat was used to establish a phase lock between the narrow line 657 nm laser and the strontium clock laser. This technique allowed to transfer the stability from the 657 nm to the 698 nm laser.

We investigated the measurement floor and link stability for the transfer of an ultra-stable optical frequency via an optical fiber link. We achieved a near-delay-limited instability of 3 × 10^-15/(τ·HZ) for 147 km deployed fiber, and 10^-20 (τ = 4000 s) for the noise floor.

We transferred the frequency of an ultra-stable laser achieving a link distance of 172 km by implementing a recirculation loop on a continuous 86 km optical fiber fully installed in the urban environment of Paris. The link is fed with a 1542 nm cavity stabilized fiber laser having a sub-Hz linewidth. The fiber-induced phase noise is measured and cancelled with an all fiber-based interferometer using commercial off-the-shelf pigtailed optical telecommunications components. The compensated link shows an Allan deviation of a few 10^-16 at one second and a few 10^-19 at 10⁴ seconds.

We describe recent work at NIST to develop compact, low-power instruments based on a combination of precision atomic spectroscopy, advanced diode lasers and microelectromechanical systems (MEMS). Designed to be fabricated in parallel in large numbers, these "chip-scale" atomic devices may eventually impact a wide range of applications, from the global positioning system to magnetic resonance imaging and inertial navigation. We focus here on recent work to develop compact, high-performance magnetometers.

The authors have developed a Chip-Scale Atomic Clock (CSAC) of sufficiently low power and small size to enable atomic timing in portable battery-powered devices. The collaboration of diverse research teams in clock technology, micro-electromechanical systems (MEMS), and optoelectronic devices has resulted in size and power reduction of atomic clock technology by more than two orders of magnitude. In 2007, we completed a pre-production build and evaluation of ten identical CSACs, with power <125 mW and short-term stability of σ_y(τ) < 2 × 10^-10 τ^{-1/2 1}. This paper reviews the physics and engineering considerations which underlie CSAC technology, describes in detail our CSAC implementation, and presents the results from the pre-production build.

HORACE is a compact cold cesium atomic clock designed for space applications and onboard systems. The operation of this clock is different from fountains since the laser cooling, the microwave interrogation and the detection are sequentially performed inside the spherical microwave cavity. A short term relative frequency stability of 2.2 · 10^-13 τ^-1/2 is reported. Preliminary results on mid term show that a level of 4 · 10^-15 is reached after 5 · 10³ s integration time. Limitations are investigated.

We have investigated the lin∥lin CPT signal in the ⁸⁷Rb D1 manifold when the atoms are contained in low pressure buffer gas cells. We predict the achievable clock frequency stability, basing our considerations on the signal-to-noise measurements. We show that a short-term stability of about 2 · 10^-11 τ^1/2 may be reached in a compact system using a modulated VCSEL, this value is mainly limited by the detection noise level and can be improved up to a factor 4 by using high frequency phase sensitive detection. Under the same experimental condition a challenging short-term stability of 1-3 · 10^-13 τ^1/2 can be achieved by using the PL ECDLs.

We review the stability and accuracy achieved by the reference atomic time scales TAI and TT(BIPM). We show that they presently are at the level of a few 10^-16 in relative value, based on the performance of primary standards, of the ensemble time scale and of the time transfer techniques. We consider how the 1 × 10^-16 value could be reached or superseded and which are the present limitations to attain this goal.

We present a unified treatment of frequency-standard biases that vary significantly during the period of measurement. We introduce three time-dependent weight functions built from the solution of the unperturbed equations of motion for a two-level system. By integrating a weight function together with the time dependence of a perturbation over the excitation period we find the change in the lineshape and can deduce any biases. The same weight function may be used for treating more than one cause of a bias.

Given the scientific potential of established and evolving quantum technologies and the new proposed detector for gravitational wave astronomy MIGO (Matter-wave Gravitational Wave Observatory) it is timely and beneficial to characterize some "actual" prototype and gather important in-depth knowledge in atom interferometry.

Of first and foremost importance is distinguishing the interferometric approach of real space detectors (based on an apparatus layout whose elements are massive optics or diffraction gratings that fix the ends of the interferometer arms) and the inertial sensors based on a superposition of atomic states, where no arm end is assigned by any optics, but rather the superposition starts and ends at given times meanwhile accruing a relative phase between the different momentum states.

The studies presented at the VII Symposium on Frequency Standards and Metrology aim at identifying the potential and sensitivity limits of atom interferometers, based on demonstrated concepts. Their sensitivity is determined by the competition between the signal induced by various disturbances versus that induced by the external fields of interest; the effects depend on the configuration, since different schemes respond differently to the same excitations.

The result is a feasibility exploration that demonstrates the actual capability of operating systems. It identifies both the properties and limitations that are characteristic of atom interferometers. The behaviour of such systems must be fully understood in order to have a basis for the development of the next generation of atom interferometers, as detectors applicable in tests of general relativity and as sensors of gravitational waves.

We present the evaluation of the performances of our cold atom gyroscope. The gyroscope is based on two cold Cesium atom sources, which are manipulated thanks to Raman transitions. We show that the short term sensitivity is limited by the quantum projection noise and the long term sensitivity by wave front distortion of the Raman lasers. A study of the bias and scaling factor completes the characterization of the sensor.

We present a new design for the mobile and robust gravimeter GAIN (Gravimetric Atom Interferometer), which is based on interfering ensembles of laser cooled ⁸⁷Rb atoms in an atomic fountain configuration. With a targeted accuracy of a few parts in 10¹⁰ for the measurement of local gravity, g, this instrument would offer about an order of magnitude improvement in performance over the best currently available absolute gravimeters. Together with the capability to perform measurements directly at sites of geophysical interest, this will open up the possibility for a number of interesting applications. We report on important subsystems of this atom interferometer, including a rack-mounted laser system and a compact vacuum chamber. Furthermore, a high flux 2-dimensional Magneto-optical trap capable of providing up to 10¹² atoms/second and a high-power laser system providing 6.4 W at 780 nm are presented.

A time domain Ramsey atom interferometer was constructed using two geometric beam splitters and a geometric phase shifter, which were formed by laser-controlled pulses with a relative phase.

An active optical clock is a special bad cavity laser with perturbation-free medium lasing transition. Spectrum narrowing due to laser mechanism expressed by modified Schawlow-Townes formula improves its high stability of the center frequency of active optical clock by several orders of magnitude is expected. The ultimate limit factor caused by Johnson thermal noise in conventional ultra-stable cavity can be reduced by cavity-pulling effect. In this paper, we will discuss the main features of different configurations of active optical clock, including thermal atomic beam, laser slowed atomic beam, optical lattice and magneto-optical trap trapped atoms. The applications of active optical clock in sub-natural linewidth laser spectroscopy and ultra-long coherence-time laser are discussed here also. Besides the active optical clock, several new concepts including Ramsey laser — a laser based on Ramsey separated fields method, active atom interferometry, and kilosecond laser are introduced.

The 7.6-eV-isomer of Thorium-229 offers the opportunity to perform high resolution laser spectroscopy of a nuclear transition. We give a brief review of the investigations of this isomer. The nuclear resonance connecting ground state and isomer may be used as the reference of an optical clock of very high accuracy using trapped and laser-cooled thorium ions, or in a compact solid-state optical frequency standard of high stability.

We discuss an approach for generating optical combs using four-wave mixing process in a nonlinear whispering gallery mode resonator. We show that pumping the resonator with strong enough continuous wave coherent light results in appearance of optical sidebands around the optical carrier. The pumping threshold of the oscillation can be in a few microWatt range for resonators with an ultra-high quality factor. Natural cascading of the the nonlinear process leads to mode locking of the sidebands and emergence of an optical frequency comb. Demodulation of the comb by means of a fast photodiode produces a high frequency spectrally pure RF signal, the frequency of which is given by the resonator morphology.

Several theoretical schemes have been proposed to improve clock synchronization making advantage of distributed entanglement and quantum states. We propose here to use the quantum correlations in pairs of energy-time entangled photons for frequency comparison.

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