Long-distance frequency dissemination with a resolution of 10(-17)

Stable optical and radio frequency joint transfer based on a passive phase compensation

We propose a novel scheme that uses only a single passive phase compensation device to achieve stable optical and radio frequency joint transfer. The phase noises of optical and radio frequency can be simultaneously compensated by passively embedding their phase information on the two optical carrier sidebands generated by an electro-optical modulator without using the phase discrimination and active servo controller. As a result, this scheme has many advantages, such as high spectral purity, short settling time and infinite compensation accuracy. We experimentally demonstrate the joint transfer of optical and 1 GHz RF over 120 km fiber spools. The optical frequency stability achieves 6.9 × 10^-17 at 1 s and 7.03 × 10^-19 at 10000 s, while the 1 GHz RF is 6.47 × 10^-13 at 1 s and 3.96 × 10^-16 at 10000 s.

Sensitive seismic sensors based on microwave frequency fiber interferometry in commercially deployed cables

The use of fiber infrastructures for environmental sensing is attracting global interest, as optical fibers emerge as low cost and easily accessible platforms exhibiting a large terrestrial deployment. Moreover, optical fiber networks offer the unique advantage of providing observations of submarine areas, where the sparse existence of permanent seismic instrumentation due to cost and difficulties in deployment limits the availability of high-resolution subsea information on natural hazards in both time and space. The use of optical techniques that leverage pre-existing fiber infrastructure can efficiently provide higher resolution coverage and pave the way for the identification of the detailed structure of the Earth especially on seismogenic submarine faults. The prevailing optical technique for use in earthquake detection and structural analysis is distributed acoustic sensing (DAS) which offers high spatial resolution and sensitivity, however is limited in range (< 100 km). In this work, we present a novel technique which relies on the dissemination of a stable microwave frequency along optical fibers in a closed loop configuration, thereby forming an interferometer that is sensitive to deformation. We call the proposed technique Microwave Frequency Fiber Interferometer (MFFI) and demonstrate its sensitivity to deformation induced by moderate-to-large earthquakes from either local or regional epicenters. MFFI signals are compared to signals recorded by accelerometers of the National Observatory of Athens, Institute of Geodynamics National Seismic Network and by a commercially available DAS interrogator operating in parallel at the same location. Remarkable agreement in dynamical behavior and strain rate estimation is achieved and demonstrated. Thus, MFFI emerges as a novel technique in the field of fiber seismometers offering critical advantages with respect to implementation cost, maximum range and simplicity.

Microwave Frequency Dissemination over a 212 km Cascaded Urban Fiber Link with Stability at the 10−18 Level

To synchronize standard frequency signals between long-distance laboratories, we carried out a frequency dissemination experiment over a 212 km cascaded urban fiber link. This cascaded link was composed of two 106 km fiber links, in which the fiber noise was compensated by two microwave frequency dissemination systems. The two adjacent frequency dissemination systems used different frequency transmitted signals, preventing the influence of signal crosstalk between the received signal of the previous stage and the transmitted signal of the second stage caused by microwave signal leakage. The frequency dissemination over the cascaded link showed a dissemination fractional frequency instability of 6.2 × 10−15 at 1 s and 6.4 × 10−18 at 40,000 s, which is better than the transfer stability over the same 212 km single-stage link.

Temperature-Dependent Group Delay of Photonic-Bandgap Hollow-Core Fiber Tuned by Surface-Mode Coupling

Surface modes (SM) are highly spatially localized modes existing at the core-cladding interface of photonic-bandgap hollow-core fiber (PBG-HCF). When coupling with SM, the air modes (AM) in the core would suffer a higher confinement loss despite being spectrally within the cladding photonic bandgap, and would be highly dispersive around the avoided crossing (anti-crossing) wavelength. In this paper, we numerically explored how such avoided crossings can play an important role in the tuning of the temperature dependence of group delay of AM of PBG-HCF. At higher temperatures, both the thermo-optic effect and thermal expansion contribute to the redshift of avoided crossing wavelength, giving rise to a temperature dependence of the AM dispersion. Numerical simulations show that the redshift of avoided crossing can significantly tune the thermal coefficient of delay (TCD) of PBG-HCF from -400 ps/km/K to 400 ps/km/K, approximately -120 ppm/K to 120 ppm/K. In comparison with the known tuning mechanism by thermal-induced redshift of photonic bandgap [Fokoua et al., Optica 4, 659, 2017], the tuning of TCD by SM coupling presents a much broader tuning range and higher efficiency. Our finding may provide a new route to design PBG-HCF for propagation time sensitive applications.

Cascaded Microwave Frequency Transfer over 300-km Fiber Link with Instability at the 10−18 Level

Comparing and synchronizing atomic clocks between distant laboratories with ultra-stable frequency transfer are essential procedures in many fields of fundamental and applied science. Existing conventional methods for frequency transfer based on satellite links, however, are insufficient for the requirements of many applications. In order to achieve high-precision microwave frequency transfer over a thousand kilometers of fiber and to construct a fiber-based microwave transfer network, we propose a cascaded system for microwave frequency transfer consisting of three 100-km single-span spooled fiber links using an improved electronic phase compensation scheme. The transfer instability measured for the microwave signal reaches 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s, which agrees with the root-sum-square of each span contribution. It is feasible to extend the length of the fiber-based microwave frequency transfer up to 1200 km using 4 stages of our cascaded system, which is still sufficient to transfer modern cold atom microwave frequency standards. Moreover, the transfer instability of 9.0 × 10−15 at 1 s and 9.0 × 10−18 at 105 s for a 100-MHz signal is achieved. The residual phase noise power spectral density of the 300-km cascaded link measured at 100-MHz is also obtained. The rejection frequency bandwidth of the cascaded link is limited by the propagation delay of one single-span link.

Performance of digital servos in an optical frequency transfer network

We demonstrate the use of three kinds of flexible digital servos for the stabilization of the optical fiber link, the interferometer temperature, and the polarization of the transmitted light at the remote site, respectively. The main fiber noise cancellation digital servo provides a large phase detection range (∼2¹⁰π radians), automatic relock function, and low cycle-slip rate over a 62 km field-deployed fiber link achieved by utilizing a feedback optical actuator of an acousto-optic modulator fed by a voltage-controlled oscillator. The temperature control and polarization control digital servos enable that the temperature of the interferometer can be stabilized at a stability of 0.01 K and the data uptime is enhanced from 85.5% to 99.9% by implementing the polarization controller. The results demonstrate that the performance of the three digital servos is sufficient for high-precision optical frequency transfer applications and indicates comparable performance to existing analog optical frequency control systems. The full digital controlled optical frequency transfer method demonstrated here provides guidance for the development of a low-cost, low-complexity, and high-reliability optical frequency transfer system.

Cost-effective demonstration of fiber-optic frequency transfer

In this paper, we demonstrate a cost-effective solution for fiber-optic frequency transfer. By employing the commercially available small form pluggable (SFP) transceivers and other components for telecom, the scheme is compatible with the existing telecom networks. An experiment testbed based on the common round trip frequency transfer is carried out to investigate the corresponding performance in detail. Compared with the conventional analog electro-optic interconversion scheme, the optical modulation and demodulation employing SFP transceiver has an inferior performance in terms of additive phase noise. However, the scheme enables a much larger operation range of receiving optical power for an optimal system performance, which indicates the certain capability of adapting to different fiber transmission links. On the basis of the established testbed, fiber-optic frequency transfer with a frequency of 1 GHz is demonstrated over a 50 km dispersion-compensated fiber link. Furthermore, the additive phase noise of -84dBc/Hz @1 Hz and -130dBc/Hz @10 kHz is achieved. Simultaneously, the Allan deviation (ADEV) of 9.6×10^-14/s and 8.4×10^-17/10⁴s is reached, respectively. The scheme can provide a relatively feasible solution to implement fiber-optic frequency transfer over the existing telecom network infrastructure.

Compensation of the Fluctuations of Differential Delay for Frequency Transfer in DWDM Networks

This paper investigates the possibility of improving the stability of radio-frequency transfer in telecommunication dense wavelength division multiplexing fiber-optic networks. As it has been identified, the dispersion compensation fibers (DCFs), frequently used in these networks, cause substantial differential delay, whose temperature-induced fluctuations have the most significant impact on the deterioration of the stability of the frequency transfer. The authors present a method that allows achieving significant improvement in the long-term stability of the frequency transfer. The developed method is based on modeling the impact of DCFs with the help of remotely accessible temperature sensors factory installed by the manufactures in DCF modules. The effectiveness of the proposed solution has been tested on three different long-haul routes (up to 1550 km), set up in the operational Polish National Research and Education Network.

Long Haul Time and Frequency Distribution in Different DWDM Systems

In this paper, we have presented the possibility of time and frequency (T&F) distribution in two generations of dense wavelength-division-multiplexing (DWDM) networks: the older one, equipped with dispersion compensation fiber (DCF) modules, and the newest, without in-line chromatic dispersion compensation (dedicated for coherent signals). The experiments were performed in a 1500-km loop arranged in the PIONIER production network, with T&F signals regarded as so-called "alien wavelength" network service. In the newest DWDM version, we observed very good stability of delivered signals: modified Allan deviation approach 10^-16 for averaging longer than 10⁴ s (for 10-MHz frequency signal), and time deviation below 15 ps for averaging up to 10⁵ s for 1 PPS time signal. These results show that the DWDM alien wavelength service can be used for high-demanding applications like cesium fountains comparisons. Results achieved for the former version of DWDM were about one magnitude worse for a long-term comparison, but it can still be useful for less demanding applications. We found that the main reason for relatively poor results observed in the older generation of DWDM is the impact of the DCFs used in this DWDM approach.

Atomic clocks for geodesy

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10^-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10^-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.

ELSTAB-Fiber-Optic Time and Frequency Distribution Technology: A General Characterization and Fundamental Limits

In this paper, we present an overview of the electronically stabilized (thus named ELSTAB) fiber-optic time and frequency (T&F) distribution system based on our idea of using variable electronic delay lines as compensating elements. Various extensions of the basic system, allowing building a long-haul, multiuser network are described. The fundamental limitations of the method arising from fiber chromatic dispersion and system dynamics are discussed. We briefly characterize the main hardware challenge of the system, which is the design of a pair of low-noise, precisely matched delay lines. Finally, we present experimental results with T&F distribution over up to 615 km of fiber, where we demonstrate frequency stability in the range of 1-7 ×10(-17) for 10(5) s averaging and time calibration with accuracy well below 50 ps. Also, practical implementation of the ELSTAB in the Polish T&F distribution network is shown.

Noise reduction in solid-state lasers using a SHG-based buffer reservoir

The cancellation of resonant intensity noise, from a few kHz up to several GHz, is reported using a second-harmonic generation (SHG) buffer reservoir in a Nd:YAG solid-state laser. This approach is shown to be well suited and easily optimizable for reducing the excess noise lying at the laser relaxation oscillations as well as that originating from the beating between the lasing mode and nonlasing adjacent longitudinal modes. A thorough analysis of noise spectra of both laser and SHG signals confirms definitely that noise reduction is a consequence of a deep laser dynamics modification rather than noise evacuation mechanism.

Enhanced phase stability in passive analog photonic links with coherent Rayleigh noise reduction

Minimizing phase fluctuation along passive analog fiber link is proposed and experimentally demonstrated. By utilizing three different optical wavelengths, we could significantly reduce the effect of coherent Rayleigh noise (CRN). In addition, a phase-locked loop is employed for dynamic phase fluctuation compensation. The RMS phase jitter within two-hour period is reduced to ~1.7131 ps over 40-km fiber link.

Feed-forward digital phase compensation for long-distance precise frequency dissemination via fiber network

We demonstrate precise microwave frequency dissemination of a hydrogen maser synchronized frequency comb over a 120 km commercial fiber link. The phase noise was compensated by a feed-forward digital compensation scheme, where the value of locally detected phase noise was first transmitted to the remote user end via a wavelength division multiplexing channel in the same fiber link and then compensated directly at the user end. The fractional frequency instability was measured to be at 5.28×10(-16)/s.

Phase stabilized downlink transmission for wideband radio frequency signal via optical fiber link

In this paper, we propose and demonstrate a phase stabilized wideband downlink transmission scheme, which directly transmits the received radio frequency (RF) signals from remote antennas to central station. A reference RF tone is round-trip transferred between the central station and remote end to obtain the delay variation caused by the fiber link. The delay variation is then used to alter a tunable laser. Since optical carriers with different wavelengths propagate at different velocities in fiber, a tunable optical delay line is realized to cancel the delay variation of the fiber link. The tunable delay range is in proportion to the length of the fiber link, which means a very long delivery distance can be expected. Experimentally, a RF signal at frequency of 2.50 GHz has been downlink transferred through a 45 km fiber link, with stability of 3.3 x 10⁻¹³ at 1 s and 7.5 x 10⁻¹⁷ at 10⁴s.

Buffer reservoir approach for cancellation of laser resonant noises

The introduction of a buffer reservoir mechanism with optimized time-constants and cross sections in a laser system enables breaking any resonant exchange between the population inversion and photon population over an extremely wide bandwidth. The associated noise cancellation, including the excess noise at relaxation oscillations and spontaneous-signal beating, is experimentally evidenced up to 16 GHz in an Er,Yb laser comprising a GaAs two-photon absorber. Such approach is shown to preserve the laser linewidth quality and is advantageously implemented for optical distribution of frequency references.

Phase fluctuation cancellation of anonymous microwave signal transmission in passive systems

A phase fluctuation cancellation approach for anonymous microwave signal transmission over fiber link is proposed and demonstrated. Unlike most previous schemes that used for active systems, our proposal is suitable for passive systems by utilizing the optical signal feedback and electrical signal phase-locking. Experimental results show that phase drifts of 7.7-ps, 54-ps and 96-ps (RMS value) for 2.45-GHz signals could be reduced to 3.1-ps, 3.8-ps and 8.5-ps after 1-km, 10-km and 25-km SMF transmission over an eight-hour period, respectively. Overall system performance is limited by the coherent Rayleigh noise and could be further optimized.

Distribution of high-stability 10 GHz local oscillator over 100 km optical fiber with accurate phase-correction system

We have developed a radio-frequency local oscillator remote distribution system, which transfers a phase-stabilized 10.03 GHz signal over 100 km optical fiber. The phase noise of the remote signal caused by temperature and mechanical stress variations on the fiber is compensated by a high-precision phase-correction system, which is achieved using a single sideband modulator to transfer the phase correction from intermediate frequency to radio frequency, thus enabling accurate phase control of the 10 GHz signal. The residual phase noise of the remote 10.03 GHz signal is measured to be -70  dBc/Hz at 1 Hz offset, and long-term stability of less than 1×10⁻¹⁶ at 10,000 s averaging time is achieved. Phase error is less than ±0.03π.

Stable radio-frequency transfer over optical fiber by phase-conjugate frequency mixing

We demonstrate long-distance (≥100-km) synchronization of the phase of a radio-frequency reference over an optical-fiber network without needing to actively stabilize the optical path length. Frequency mixing is used to achieve passive phase-conjugate cancellation of fiber-length fluctuations, ensuring that the phase difference between the reference and synchronized oscillators is independent of the link length. The fractional radio-frequency-transfer stability through a 100-km "real-world" urban optical-fiber network is 6 × 10(-17) with an averaging time of 10(4) s. Our compensation technique is robust, providing long-term stability superior to that of a hydrogen maser. By combining our technique with the short-term stability provided by a remote, high-quality quartz oscillator, this system is potentially applicable to transcontinental optical-fiber time and frequency dissemination where the optical round-trip propagation time is significant.

Stable radio-frequency delivery by λ dispersion-induced optical tunable delay

We propose and demonstrate a novel stable radio frequency (RF) delivery system based on a radio-over-fiber link. The proposed scheme acts as a long phase-locking loop where an optical tunable delay line is involved to compensate dynamically for the time-delay variation that arises from fiber-link fluctuation. An optical carrier with variable wavelength under fiber-link dispersion results in the desired tunable delay. The tunable range is in proportion to the length of the fiber link, so a large phase-error correction capacity under long-distance delivery can be realized. The large as well as fine optical-delay tunability is experimentally demonstrated, and the RF reference of 2.42 GHz is transferred for 54 km where a time jitter compression factor of 588 is achieved.

Progress in atomic fountains at LNE-SYRTE

We give an overview of the work done with the Laboratoire National de Métrologie et d'Essais-Systèmes de Référence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the (87)Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

Enhancing long-term stability of the optoelectronic oscillator with a probe-injected fiber delay monitoring mechanism

Optoelectronic oscillators (OEOs), based on optical fiber loops to act as a high-Q cavity, are capable of generating stable radio-frequencies (RF). The long-term frequency stability of the OEO is then limited by the cavity variation that is mainly induced by temperature sensitivity of the optical fiber. In order to actively stabilize the OEO cavity, we employ the technique of RF transfer over optical fibers. We propose and experimentally demonstrate a dual-loop-OEO scheme to enhance the long-term stability with an injected probe signal to monitor the phase variation in the fiber loops. The experimental results show that the resulting spread-spectrum signal is useful in monitoring the fiber delay without observable interference. The relationships between the measured frequency and the monitored delay are theoretically and numerically discussed. We also estimate the long-term stability of the proposed OEO scheme with the cavity phase correction. The corrected result shows the long-term frequency stability of the proposed OEO is within 8.4×10(-8) at one day.

Long-term stable frequency transfer over an urban fiber link using microwave phase stabilization

We report a novel technique for highly stable transfer of a frequency comb over long optical fiber link. The technique implements an electronic compensation loop to cancel out the phase fluctuations that is introduced by the fiber. We utilized this technique to transfer a stable microwave frequency through a 20 km urban fiber link and an 80 km open air fiber link respectively. For the 20 km urban fiber link, the active compensation system reduced the phase fluctuation from 75 mrad (118 ps) to 4 mrad (6.3 ps) in 48 hours, and the frequency stability was improved by three orders of magnitude. For the 80 km open air fiber link, the active compensation system reduced the rms phase fluctuation from 580 mrad (914 ps) to 10 mrad (16 ps) in 24 hours, and the frequency stability was improved by two orders of magnitude.

Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy

Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.

Cascaded multiplexed optical link on a telecommunication network for frequency dissemination

We demonstrate a cascaded optical link for ultrastable frequency dissemination comprised of two compensated links of 150 km and a repeater station. Each link includes 114 km of Internet fiber simultaneously carrying data traffic through a dense wavelength division multiplexing technology, and passes through two routing centers of the telecommunication network. The optical reference signal is inserted in and extracted from the communication network using bidirectional optical add-drop multiplexers. The repeater station operates autonomously ensuring noise compensation on the two links and the ultra-stable signal optical regeneration. The compensated link shows a fractional frequency instability of 3 x 10(-15) at one second measurement time and 5 x 10(-20) at 20 hours. This work paves the way to a wide dissemination of ultra-stable optical clock signals between distant laboratories via the Internet network.

Chiral oxorhenium(V) complexes as candidates for the experimental observation of molecular parity violation: a structural, synthetic and theoretical study

We report the synthesis and resolution of a series of new chiral "3 + 1" oxorhenium(V) complexes, designed for high-resolution laser spectroscopy experiments probing molecular parity-violation (PV) effects in the Re=O stretching mode frequency. These complexes display a particularly simple chemical structure, with the rhenium atom as the stereogenic center, and show large PV energy differences according to our calculations. They were obtained in the racemic and enantioenriched forms, in the latter case by using either semi-preparative chiral HPLC resolution or enantioselective synthesis. The vibrational transition frequency differences between the enantiomeric pairs due to PV have been calculated with two- and four-component relativistic Hamiltonians using Hartree-Fock (HF) and density functional theory (DFT). For three complexes, including one synthesized in enantioenriched form, our HF calculations predict frequency differences above the present resolution limit of 1 Hz. These results confirm the order of magnitude for the calculated HF PV vibrational frequency differences reported earlier for this class of compounds [P. Schwerdtfeger and R. Bast, J. Am. Chem. Soc., 2004, 126, 1652]. However, at the DFT level the PV vibrational frequency differences are in some cases reduced by an order of magnitude, but are still within the sensitivity of 0.01 Hz, which is the anticipated sensitivity in a new proposed experiment. We therefore believe that the present study represents an important step towards the experimental observation of PV in molecular systems, and emphasizes the extreme sensitivity of the PV vibrational frequency difference to the chemical environment around the rhenium center.

Atmospheric transfer of optical and radio frequency clock signals

The phase instability induced during the transfer of radio frequency and optical clock signals through the turbulent atmosphere was measured in a rooftop experiment. Radio frequency intensity modulation of a laser to transmit signals over 100 m results in an Allan deviation of 1.31x10(-10) at 1 s. Optical transfer is more accurate at 1.68x10(-13) at 1 s. As a consequence, fiber links are more suitable for the transfer of optical frequencies over very long distances while free space transmission might find applications in short distances of less than 1 km.

Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network

Optical frequency at 1542 nm was coherently transferred over a 120-km-long installed telecom fiber network between two cities (Tsukuba and Tokyo) in Japan separated by more than 50 km. The phase noise induced by the fiber length fluctuations was actively reduced by using a fiber stretcher and an acousto-optic modulator. The fractional frequency instability of the one-way transmitted light was reduced down to less than 8.0 x 10(-16) at an averaging time of 1s, which is limited by the theoretical limit deduced from the length and the intrinsic noise of the fiber.

Measurement of the fundamental thermal noise limit in a cryogenic sapphire frequency standard using bimodal maser oscillations

We report observations of the Schawlow-Townes noise limit in a cryogenic sapphire secondary frequency standard. The effect causes a fundamental limit to the frequency stability, and was measured through the novel excitation of a bimodal maser oscillation of a Whispering Gallery doublet at 12.04 GHz. The beat frequency of 10 kHz between the oscillations enabled a sensitive probe for this measurement of fractional frequency instability of 10(-14) tau(-1/2) with only 0.5 pW of output power.

Stability of the proton-to-electron mass ratio

We report a limit on the fractional temporal variation of the proton-to-electron mass ratio as 1/(m(P)/m(e)) partial differential/partial differential(t)(m(P)/m(e))=(-3.8+/-5.6) x 10(-14) yr(-1), obtained by comparing the frequency of a rovibrational transition in SF6 with the fundamental hyperfine transition in Cs. The SF6 transition was accessed using a CO2 laser to interrogate spatial 2-photon Ramsey fringes. The atomic transition was accessed using a primary standard controlled with a Cs fountain. This result is direct and model-free.

Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10{-17}

The phase coherence of an ultrastable optical frequency reference is fully maintained over actively stabilized fiber networks of lengths exceeding 30 km. For a 7-km link installed in an urban environment, the transfer instability is 6 x 10{-18} at 1 s. The excess phase noise of 0.15 rad, integrated from 8 mHz to 25 MHz, yields a total timing jitter of 0.085 fs. A 32-km link achieves similar performance. Using frequency combs at each end of the coherent-transfer fiber link, a heterodyne beat between two independent ultrastable lasers, separated by 3.5 km and 163 THz, achieves a 1-Hz linewidth.

Direct determination of the Boltzmann constant by an optical method

We have recorded the Doppler profile of a well-isolated rovibrational line in the nu(2) band of (14)NH(3). Ammonia gas was placed in an absorption cell thermalized by a water-ice bath. By extrapolating to zero pressure, we have deduced the Doppler width which gives a first measurement of the Boltzmann constant k(B) by laser spectroscopy. A relative uncertainty of 2 x 10(-4) has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

Design and metrological features of microwave synthesizers for atomic fountain frequency standard

In this paper we describe the improved redesign of the microwave frequency synthesizers for Laboratoire National d'Essais-Systèmes de Référence Temps-Espace (LNE-SYRTE) atomic fountains. The synthesizers use a cryogenic oscillator to generate both Cs and Rb hyperfine frequencies based on a new distribution frequency of 1 GHz. The main metrological features (phase noise, long-term phase stability, and spectral purity) of the synthesizers have been measured in situ connected to an atomic fountain and are compatible with an accuracy goal of 10(-16) for the atomic fountains. The simultaneous test of two different synthesizers on the FO2 atomic fountain at the 10(-16) level also is reported.

Remote transfer of ultrastable frequency references via fiber networks

Three distinct techniques exist for distributing an ultrastable frequency reference over optical fibers. For the distribution of a microwave frequency reference, an amplitude-modulated continuous wave (cw) laser can be used. Over kilometer-scale lengths this approach provides an instability at 1 s of approximately 3 x 10(-14) without stabilization of the fiber-induced noise and approximately 1 x 10(-14) with active noise cancellation. An optical frequency reference can be transferred by directly transmitting a stabilized cw laser over fiber and then disseminated to other optical and microwave regions using an optical frequency comb. This provides an instability at 1 s of 2 x 10(-14) without active noise cancellation and 3 x 10(-15) with active noise cancellation [Recent results reduce the instability at 1 s to 6 x 10(-18).] Finally, microwave and optical frequency references can be simultaneously transmitted using an optical frequency comb, and we expect the optical transfer to be similar in performance to the cw optical frequency transfer. The instability at 1 s for transfer of a microwave frequency reference with the comb is approximately 3 x 10(-14) without active noise cancellation and <7 x 10(-15) with active stabilization. The comb can also distribute a microwave frequency reference with root-mean-square timing jitter below 16 fs integrated over the Nyquist bandwidth of the pulse train (approximately 50 MHz) when high-bandwidth active noise cancellation is employed, which is important for remote synchronization applications.

Fiber-laser frequency combs with subhertz relative linewidths

We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the heterodyne beat signal between two independent frequency combs that are phase locked to a common cw optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz relative linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter of approximately 1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is approximately 1 fs. This performance approaches that of Ti:sapphire frequency combs.

Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation

We demonstrate a new, simple technique for measuring IR frequencies near 30 THz by using a femtosecond (fs) laser optical comb and sum-frequency generation. The optical frequency is directly compared with the distance between two modes of the fs laser, and the resultant beat note is used to control this distance, which depends only on the repetition rate of the fs laser. The absolute frequency of a CO2 laser stabilized onto a SF6 two-photon line has been measured for the first time to the authors' knowledge. This line is an attractive alternative to the usual saturated absorption OsO4 resonances used for the stabilization of CO2 lasers. First results demonstrate a fractional Allan deviation of 3 x 10(-14) at 1 s.