The short-term stability of passive atomic frequency standards, especially in pulsed operation, is often limited by local oscillator noise via intermodulation effects. We present an experimental demonstration of the intermodulation effect on the frequency stability of a continuous atomic fountain clock where, under normal operating conditions, it is usually too small to observe. To achieve this, we deliberately degrade the phase stability of the microwave field interrogating the clock transition. We measure the frequency stability of the locked, commercial-grade local oscillator, for two modulation schemes of the microwave field: square-wave phase modulation and square-wave frequency modulation. We observe a degradation of the stability whose dependence with the modulation frequency reproduces the theoretical predictions for the intermodulation effect. In particular no observable degradation occurs when this frequency equals the Ramsey linewidth. Additionally we show that, without added phase noise, the frequency instability presently equal to 2x10-13 at 1s, is limited by atomic shot-noise and therefore could be reduced were the atomic flux increased.
We report the evaluation of the second order Zeeman shift in the continuous atomic fountain clock FoCS-2. Because of the continuous operation and of its geometrical constraints, the methods used in pulsed fountains are not applicable. We use here time-resolved Zeeman spectroscopy to probe the magnetic field profile in the clock. The pulses of ac magnetic excitation allow us to spatially resolve the Zeeman frequency and to evaluate the Zeeman shift with a relative uncertainty smaller than 10E-16.
An ensemble of rubidium atomic fountain clocks has been put into operation at the U.S. Naval Observatory (USNO). These fountains are used as continuous clocks in the manner of commercial cesium beams and hydrogen masers for the purpose of improved timing applications. Four fountains have been in operation for more than two years and are included in the ensemble used to generate the USNO master clock. Individual fountain performance is characterized by a white-frequency noise level below $2\times 10^{-13}$ and fractional-frequency stability routinely reaching the low $10^{-16}$s. The highest pe…
In precision metrology the determination of the Newtonian gravity constant $G$ represents a real problem, since its history is plagued by huge unknown discrepancies between a large number of independent experiments. In this paper we propose a novel experimental setup for measuring $G$ with a relative accuracy of $10^{-5}$ using a standard cold atomic fountain and matter wave interferometry. We discuss in details the major sources of systematic errors, providing also the expected statistical uncertainty. Feasibility of determining $G$ at a level of $10^{-6}$ level is also discussed.
Ramsey fringes observed in an atomic fountain are formed by the superposition of the individual atomic signals. Due to the atomic beam residual temperature, the atoms have slightly different trajectories and thus are exposed to a different average magnetic field, and a velocity dependent Ramsey interaction time. As a consequence, both the velocity distribution and magnetic field profile are imprinted in the Ramsey fringes observed on Zeeman sensitive microwave transitions. In this work, we perform a Fourier analysis of the measured Ramsey signals to retrieve both the time averaged magnetic fie…
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 thr…
We used a Cs atomic fountain frequency standard to measure the Stark shift on the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the electric field generated by the blackbody radiation. The measures relative shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation -1.49(07)e-14. This value differs from the currently accepted one -1.69(04)e-14. The difference has a significant implication on the accuracy of frequency standards, in clocks comparison, and in a variety of high precision physics tests such as the time stability of fundamental constants.
In this article, we report on the work done with the LNE-SYRTE atomic clock ensemble during the last 10 years. We cover progress made in atomic fountains and in their application to timekeeping. We also cover the development of optical lattice clocks based on strontium and on mercury. We report on tests of fundamental physical laws made with these highly accurate atomic clocks. We also report on work relevant to a future possible redefinition of the SI second.
We report the operation of a dual Rb/Cs atomic fountain clock. 133Cs and 87Rb atoms are cooled, launched, and detected simultaneously in LNE-SYRTE's FO2 double fountain. The dual clock operation occurs with no degradation of either the stability or the accuracy. We describe the key features for achieving such a simultaneous operation. We also report on the results of the first Rb/Cs frequency measurement campaign performed with FO2 in this dual atom clock configuration, including a new determination of the absolute 87Rb hyperfine frequency.
We demonstrate agreement between measurements and ab initio calculations of the frequency shifts caused by distributed cavity phase variations in the microwave cavity of a primary atomic fountain clock. Experimental verification of the finite element models of the cavities gives the first quantitative evaluation of this leading uncertainty and allows it to be reduced to delta nu / nu = 8.4\times10^-17. Applying these experimental techniques to clocks with improved microwave cavities will yield negligible distributed cavity phase uncertainties, less than \pm1\times10^-17.
We describe a new method to determine the position of the atomic cloud during its interaction with the microwave field in the cavity of a fountain clock. The positional information is extracted from the spectrum of the F=3,mF=0 to F=4,mF=-1 hyperfine transition, which shows a position dependent asymmetry when the magnetic C-field is tilted by a few degrees with respect to the cavity axis. Analysis of this spectral asymmetry provides the horizontal center-of-mass position for the ensemble of atoms contributing to frequency measurements. With an uncertainty on the order of 0.1 mm, the obtained i…
An improved measurement of the electron electric dipole moment (EDM) appears feasible using ground-state alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable electron dipole moment (EDM), is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a facto mu~100. We expand the complete time evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin F=3, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent…
We demonstrate launching of laser-cooled Yb atoms in a cold atomic fountain. Atoms in a collimated thermal beam are first cooled and captured in a magneto-optic trap (MOT) operating on the strongly-allowed ${^1S}_0 \rightarrow {^1P}_1$ transition at 399~nm (blue line). They are then transferred to a MOT on the weakly-allowed ${^1S}_0 \rightarrow {^3P}_1$ transition at 556~nm (green line). Cold atoms from the green MOT are launched against gravity at a velocity of around 2.5~m/s using a pair of green beams. We trap more than $10^7$ atoms in the blue MOT and transfer up to 70\% into the green MO…
We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows achieving the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple…
We demonstrate the use of a fiber-based femtosecond laser locked onto an ultra-stable optical cavity to generate a low-noise microwave reference signal. Comparison with both a liquid Helium cryogenic sapphire oscillator (CSO) and a Ti:Sapphire-based optical frequency comb system exhibit a stability about $3\times10^{-15}$ between 1 s and 10 s. The microwave signal from the fiber system is used to perform Ramsey spectroscopy in a state-of-the-art Cesium fountain clock. The resulting clock system is compared to the CSO and exhibits a stability of $3.5\times10^{-14}τ^{-1/2}$. Our continuously ope…
A cesium atomic fountain clock is under development at Huazhong University of Science and Technology (HUST) in China. In this paper, we describe the construction of the entire fountain clock system and report the preliminary results. A frequency stability of $2.5\times 10^{-13} τ^{-1/2}$ has been achieved by inter-comparison with a hydrogen maser, and the factors limiting the frequency stability are also discussed.
Over five years we have compared the hyperfine frequencies of 133Cs and 87Rb atoms in their electronic ground state using several laser cooled 133Cs and 87Rb atomic fountains with an accuracy of ~10^{-15}. These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies : (d/dt)ln(nu_Rb/nu_Cs)=(0.2 +/- 7.0)*10^{-16} yr^{-1} (1 sigma uncertainty). The same limit applies to a possible variation of the quantity (mu_Rb/mu_Cs)*alpha^{-0.44}, which involves the ratio of nuclear magnetic moments and the fine structure constant.
We report on the first comparison of distant caesium fountain primary frequency standards (PFSs) via an optical fiber link. The 1415 km long optical link connects two PFSs at LNE-SYRTE (Laboratoire National de métrologie et d'Essais - SYstème de Références Temps-Espace) in Paris (France) with two at PTB (Physikalisch-Technische Bundesanstalt) in Braunschweig (Germany). For a long time, these PFSs have been major contributors to accuracy of the International Atomic Time (TAI), with stated accuracies of around $3\times 10^{-16}$. They have also been the references for a number of absolute measur…
One of the main limitations of cesium atomic fountains has been the cold collision frequency shift. By using a method based on a transfer of population by adiabatic passage allowing to prepare cold atomic samples with a well defined ratio of atomic density as well as atom number the collisional shift is controlled at the 10E-3 of its value. A calibration of Zeeman sub-states contribution to the clock shift as a function of the field has been performed. Feshbach resonances have been observed for the first time at very low magnetic field and with a very good resolution. A Monte Carlo simulation …
Improvements of the systematic uncertainty, frequency instability, and long-term reliability of the two caesium fountain primary frequency standards CSF1 and CSF2 at PTB (Physikalisch-Technische Bundesanstalt) are described. We have further investigated many of the systematic effects and made a number of modifications of the fountains. With an optically stabilized microwave oscillator, the quantum projection noise limited frequency instabilities are improved to $7.2 \times 10^{-14} (τ/1\,\mathrm{s})^{-1/2}$ for CSF1 and $2.5 \times 10^{-14} (τ/1\,\mathrm{s})^{-1/2}$ for CSF2 at high atom densi…
We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3E-16, with a frequency bias of 0.4E-16. The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wavepackets. We report a total PTB-CSF2 systematic uncertainty of 4.1E-16.
We performed an absolute frequency measurement of the $^1S_{0}$-$^3P_{0}$ transition in $^{87}$Sr with a fractional uncertainty of $1.2 \times 10^{-15}$, which is less than one third that of our previous measurement. A caesium fountain atomic clock was used as a transfer oscillator to reduce the uncertainty of the link between a strontium optical lattice clock and the SI second. The absolute value of the transition frequency is 429 228 004 229 873.56(49) Hz.
The absolute frequency of the $^{87}{\rm Sr}$ clock transition measured in 2015 was reevaluated using an improved frequency link to the SI second. The scale interval of International Atomic Time (TAI) that we used as the reference was calibrated for an evaluation interval of five days instead of the conventional interval of one month which is regularly employed in Circular T. The calibration on a five-day basis removed the uncertainty in assimilating the TAI scale of the five-day mean to that of the one-month mean. The reevaluation resulted in the total uncertainty of $10^{-16}$ level for the …
To date, no framework combining quantum field theory and general relativity and hence unifying all four fundamental interactions, exists. Violations of the Einstein's equivalence principle (EEP), being the foundation of general relativity, may hold the key to a theory of quantum gravity. The universality of free fall (UFF), which is one of the three pillars of the EEP, has been extensively tested with classical bodies. Quantum tests of the UFF, e.g. by exploiting matter wave interferometry, allow for complementary sets of test masses, orders of magnitude larger test mass coherence lengths and …
A single-particle Green's function (propagator) is introduced to study the detection of laser-cooled Cesium atoms in an atomic fountain due to RF field gradients in the Ramsey TE011 cavity. The detection results in a state-dependent loss of atoms at apertures in the physics package, resulting in a frequency bias. A model accounting only for motion in one dimension transverse to the symmetry axis of the fountain is discussed in detail and then generalized to two transverse dimensions. Results for fractional frequency shifts due to transverse field gradients are computed for NIST F-1 and F-2 Ces…
The environmental perturbation on atoms is the key factor restricting the performance of atomic frequency standards, especially in long term scale. In this letter, we demonstrate a real-time noise distinguish operation of atomic clocks. The operation improves the statistical uncertainty by about an order of magnitude of our fountain clock which is deteriorated previously by extra noises. The frequency offset bring by the extra noise is also corrected. The experiment proves the real-time noise distinguish operation can reduce the contribution of ambient noises and improve the uncertainty limit …
We use an atomic fountain clock to measure quantum scattering phase shifts precisely through a series of narrow, low-field Feshbach resonances at average collision energies below $1\,μ$K. Our low spread in collision energy yields phase variations of order $\pm π/2$ for target atoms in several $F,m_F$ states. We compare them to a theoretical model and establish the accuracy of the measurements and the theoretical uncertainties from the fitted potential. We find overall excellent agreement, with small statistically significant differences that remain unexplained.
Coherent manipulation of atomic states is a key concept in high-precision spectroscopy and used in atomic fountain clocks and a number of optical frequency standards. Operation of these standards can involve a number of cyclic switching processes, which may induce cycle synchronous phase excursions of the interrogation signal and thus lead to shifts in the output of the frequency standard. We have built a FPGA-based phase analyzer to investigate these effects and conducted measurements on two frequency standards. For the caesium fountain PTB-CSF2 we were able to exclude phase variations of the…
This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the $^{133}$Cs and $^{87}$Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of $1.6\times 10^{-14}τ^{-1/2}$ where $τ$ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of $2\times 10^{-16}$ at $50,000s…
We discuss the theoretical treatment of the microwave lensing frequency shift of the NIST-F1 and F2 atomic fountain clocks by Ashby et al. [Phy. Rev. A. 91, 033624 (2015)]. The shifts calculated by NIST are much smaller than the previously evaluated microwave lensing frequency shifts of other clocks contributing to International Atomic Time. We identify several fundamental problems in the NIST treatment and demonstrate that each significantly affects their results. We also show a smooth transition of microwave lensing frequency shifts to the photon recoil shift for large wave packets.
We report on the first absolute transition frequency measurement at the 10^{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the S1/2-D5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency f_Ca+ = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of three of the Cs standard. Future improvements are expected to lead to …
We describe a measurement of the frequency of the 2S1/2(F = 0) - 2D3/2(F' = 2) transition of 171Yb+ at the wavelength 436 nm (frequency 688 THz), using a single Yb+ ion confined in a Paul trap and two caesium fountains as references. In one of the fountains, the frequency of the microwave oscillator that interrogates the caesium atoms is stabilized by the laser that excites the Yb+ reference transition with a linewidth in the hertz range. The stability is transferred to the microwave oscillator with the use of a fiber laser based optical frequency comb generator that also provides the frequenc…
We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between an $^{171}$Yb optical lattice clock and a $^{133}$Cs fountain microwave clock that span 298 days with an uptime of 15.4 $\%$. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from $10^{-22}$ eV/$c^{2}$ to $10^{-20}$ eV/$c^{2}$ are set, assuming that each of these couplings is the dominant source of the modulation in the frequ…
Atomic fountain clocks launch laser-cooled balls of atoms upwards to some height $h$ in the local gravitational field where they experience both second-order Doppler shifts and gravitational frequency shifts. It is shown in this paper that the net shift, relative to a reference at the launch point, is $ g h/3 c^2$. We derive the next most significant correction to this expression, and show that the value of $g$ should be corrected for Coriolis and centripetal effects.
We have measured the 1S - 2S transition frequency in atomic hydrogen via two photon spectroscopy on a 5.8 K atomic beam. We obtain $f_{1S-2S} = 2 466 061 413 187 035 (10)$ Hz for the hyperfine centroid. This is a fractional frequency uncertainty of $4.2\times 10^{-15}$ improving the previous measure- ment by our own group [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)] by a factor of 3.3. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.
Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant $α$ and the proton-to-electron mass ratio $μ$. We measure the frequency of the $^2S_{1/2}\rightarrow {^2F_{7/2}}$ electric octupole (E3) transition in $^{171}$Yb$^+$ against two caesium fountain clocks as $f(E3) = 642\,121\,496\,772\,645.36(25)$~Hz with an improved fractional uncertainty of $3.9\times 10^{-16}$. This transition frequency shows a strong sensitivity to changes of $α$. Togethe…
In this paper, we demonstrate a simple scheme of 6.835 GHz microwave frequency synthesizer based on the sub-sampling phase lock loop (PLL) technique. The application of the sub-sampling PLL is the key to simplify the architecture of the synthesizer in this scheme. A 100 MHz oven controlled crystal oscillator (OCXO) with ultra-low phase noise is used as the initial signal source. Then a dielectric resonant oscillator (DRO) of 6.8 GHz is directly phase locked to the 100 MHz OCXO utilizing the sub-sampling PLL. Benefiting from the sub-sampling PLL, the processes of microwave frequency multiplicat…
We use six years of accurate hyperfine frequency comparison data of the dual rubidium and caesium cold atom fountain FO2 at LNE-SYRTE to search for a massive scalar dark matter candidate. Such a scalar field can induce harmonic variations of the fine structure constant, of the mass of fermions and of the quantum chromodynamic mass scale, which will directly impact the rubidium/caesium hyperfine transition frequency ratio. We find no signal consistent with a scalar dark matter candidate but provide improved constraints on the coupling of the putative scalar field to standard matter. Our limits …
We report the direct excitation of the highly forbidden (6s^2) 1S0 - (6s6p) 3P0 optical transition in two odd isotopes of ytterbium. As the excitation laser frequency is scanned, absorption is detected by monitoring the depletion from an atomic cloud at ~70 uK in a magneto-optical trap. The measured frequency in 171Yb (F=1/2) is 518,295,836,593.2 +/- 4.4 kHz. The measured frequency in 173Yb (F=5/2) is 518,294,576,850.0 +/- 4.4 kHz. Measurements are made with a femtosecond-laser frequency comb calibrated by the NIST cesium fountain clock and represent nearly a million-fold reduction in uncertai…
The AC Stark shift induced by blackbody radiation is a major source of systematic uncertainty in present-day cesium microwave frequency standards. The shift is parametrized in terms of a third-order electric polarizability $α_0^{(3)}$ that can be inferred from the static electric field displacement of the clock transition resonance. In this paper, we report on an all-optical CPT pump-probe experiment measuring the differential polarizability $Δα_0^{(3)} = α_0^{(3)}(F{=}4) - α_0^{(3)}(F{=}3)$ on a thermal Cs atomic beam, from which we infer $ α_0^{(3)}(F{=}4) = 2.023(6)_{stat}(9)_{syst}~Hz/(kV/…
In this paper we report the evaluation of an optical lattice clock based on neutral mercury down to a relative uncertainty of $1.7\times 10^{-16}$. Comparing this characterized frequency standard to a Cs atomic fountain we determine the absolute frequency of the $^1S_0 \rightarrow \phantom{}^3P_0$ transition of $^{199}$Hg as $ν_{\mathrm{Hg}} = 1 128\,575\,290\,808\,154.62\,$Hz $\pm\,0.19\,$Hz (statistical) $\pm\,0.38\,$Hz (systematic), limited solely by the realization of the SI second. Furthermore, by comparing the mercury optical lattice clock to a Rb atomic fountain, we determine for the fi…
SI-traceable measurements of optical frequencies using International Atomic Time (TAI) do not require a local primary frequency reference, but suffer from an uncertainty in tracing to the SI second. For the measurement of the $^{87}$Sr lattice clock transition, we have reduced this uncertainty to low $10^{-16}$ level by averaging three sets of ten-day intermittent measurements, in which we operated the lattice clock for $10^4$ s on each day. Moreover, a combined oscillator of two hydrogen masers was employed as a local flywheel oscillator (LFO) in order to mitigate the impact of sporadic excur…
We compare two optical clocks based on the $^2$S$_{1/2}(F=0)\to {}^2$D$_{3/2}(F=2)$ electric quadrupole (E2) and the $^2$S$_{1/2}(F=0)\to {}^2$F$_{7/2}(F=3)$ electric octupole (E3) transition of $^{171}$Yb$^{+}$ and measure the frequency ratio $ν_{\mathrm{E3}}/ν_{\mathrm{E2}}=0.932\,829\,404\,530\,965\,376(32)$. We determine the transition frequency $ν_{E3}=642\,121\,496\,772\,645.10(8)$ Hz using two caesium fountain clocks. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the…
We perform Ramsey-Bordé spectroscopy on laser-cooled magnesium atoms in free fall to measure the 1S0 \rightarrow 3P1 intercombination transition frequency. The measured value of 655 659 923 839 730 (48) Hz is consistent with our former atomic beam measurement (Friebe et al 2008 Phys. Rev. A 78 033830). We improve upon the fractional accuracy of the previous measurement by more than an order of magnitude to 7e-14. The magnesium frequency standard was referenced to a fountain clock of the Physikalisch-Technische Bundesanstalt (PTB) via a phase-stabilized telecom fiber link and its stability was …
We have demonstrated the possibility for a compact frequency standard based on a sample of cold cesium atoms. In a cylindrical microwave cavity, the atoms are cooled and interrogated during a free expansion and then detected. The operation of this experiment is different from conventional atomic fountains, since all the steps are sequentially performed in the same position of space. In this paper we report the analysis of a Ramsey pattern observed to present a 47 Hz linewidth and a stability of 5x10^-13 for an integration time longer than 100s. Some of the main limitations of the standard are …
We present a new method for accurate mid-infrared frequency measurements and stabilization to a near-infrared ultra-stable frequency reference, transmitted with a long-distance fibre link and continuously monitored against state-of-the-art atomic fountain clocks. As a first application, we measure the frequency of an OsO4 rovibrational molecular line around 10 $μ$m with a state-of-the-art uncertainty of 8x10-13. We also demonstrate the frequency stabilization of a mid-infrared laser with fractional stability better than 4x10-14 at 1 s averaging time and a line-width below 17 Hz. This new stabi…
We report the first contribution to the international atomic time (TAI) based on a secondary representation of the SI second. This work is done with the LNE-SYRTE FO2-Rb fountain frequency standard using the $^{87}$Rb ground state hyperfine transition. We describe FO2-Rb and how it is connected to local and international time scales. We report on local measurements of this frequency standard in the SI system, i.e. against primary frequency standards, down to a fractional uncertainty of $4.4\times 10^{-16}$, and on the establishment of the recommended value for the $^{87}$Rb hyperfine transitio…
