Experimental realization of an optical second with strontium lattice clocks.

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 × 10(-16), have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 × 10(-16). Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 × 10(-16).

Improved tests of local position invariance using 87Rb and 133Cs fountains.

We report tests of local position invariance based on measurements of the ratio of the ground state hyperfine frequencies of 133Cs and 87Rb in laser-cooled atomic fountain clocks. Measurements extending over 14 years set a stringent limit to a possible variation with time of this ratio: d ln(ν(Rb)/ν(Cs))/dt=(-1.39±0.91)×10(-16) yr(-1). This improves by a factor of 7.7 over our previous report [H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)]. Our measurements also set the first limit to a fractional variation of the Rb/Cs frequency ratio with gravitational potential at the level of c(2)d ln(ν(Rb)/ν(Cs))/dU=(0.11±1.04)×10(-6), providing a new stringent differential redshift test. The above limits equivalently apply to the fractional variation of the quantity α(-0.49)(g(Rb)/g(Cs)), which involves the fine-structure constant α and the ratio of the nuclear g-factors of the two alkalis. The link with variations of the light quark mass is also presented together with a global analysis combining other available highly accurate clock comparisons.

Doppler-free spectroscopy of the 1S0-3P0 optical clock transition in laser-cooled fermionic isotopes of neutral mercury.

We report direct laser spectroscopy of the 1S0-3P0 transition at 265.6 nm in fermionic isotopes of neutral mercury in a magneto-optical trap. Measurements of the frequency against the LNE-SYRTE primary reference using an optical frequency comb yield 1 128 575 290 808.4+/-5.6 kHz in 199Hg and 1 128 569 561 139.6+/-5.3 kHz in 201Hg. The uncertainty, allowed by the observation of the Doppler-free recoil doublet, is 4 orders of magnitude lower than previous indirect determinations. Mercury is a promising candidate for future optical lattice clocks due to its low sensitivity to blackbody radiation.

Six-axis inertial sensor using cold-atom interferometry.

We have developed an atom interferometer providing a full inertial base. This device uses two counterpropagating cold-atom clouds that are launched in strongly curved parabolic trajectories. Three single Raman beam pairs, pulsed in time, are successively applied in three orthogonal directions leading to the measurement of the three axis of rotation and acceleration. In this purpose, we introduce a new atom gyroscope using a butterfly geometry. We discuss the present sensitivity and the possible improvements.

High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system.

We report the observation of Raman-Ramsey fringes using a double lambda scheme creating coherent population trapping in an atomic ensemble combined with pulsed optical radiations. The observation was made in a Cs vapor mixed with N2 buffer gas in a closed cell. The double lambda scheme is created with lin perpendicular lin polarized laser beams leading to higher contrast than the usual simple lambda scheme. The pulsed trapping technique leads to narrow fringe widths scaling as 1/(2T) with high contrasts which are no longer limited by the saturation effect. This technique operates in a different way from the classical Ramsey sequence: the signal is done by applying a long trapping pulse to prepare the atomic state superposition, and fringe detection is accomplished by optical transmission during a short second trapping pulse without any perturbation of the dark state.

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

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is 10(-17) for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a CO2/OsO4 frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of 3 x 10(-14) at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as 1 x 10(-14) at 1 s.

New limits on the drift of fundamental constants from laboratory measurements.

We have remeasured the absolute 1S-2S transition frequency nu(H) in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of (-29+/-57) Hz for the drift of nu(H) with respect to the ground state hyperfine splitting nu(Cs) in 133Cs. Combining this result with the recently published optical transition frequency in 199Hg+ against nu(Cs) and a microwave 87Rb and 133Cs clock comparison, we deduce separate limits on alpha/alpha=(-0.9+/-2.9) x 10(-15) yr(-1) and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments mu(Rb)/mu(Cs) equal to (-0.5+/-1.7) x 10(-15) yr(-1). The latter provides information on the temporal behavior of the constant of strong interaction.

Search for variations of fundamental constants using atomic fountain clocks.

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 approximately 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)x 10(-16) yr(-1) (1sigma 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.

Efficient cooling and trapping of strontium atoms.

We report the capture of cold strontium atoms in a magneto-optical trap (MOT) at a rate of 4 x 10(10) atoms/s. The MOT is loaded from an atomic beam decelerated by a Zeeman slower operating with a focused laser beam. The 461-nm laser, used for both cooling and trapping, was generated by sum-frequency mixing in a KTP crystal with diode lasers at 813 nm and a Nd:YAG laser at 1064 nm. As much as 115 mW of blue light was obtained.

Controlling the cold collision shift in high precision atomic interferometry.

We present a new method based on a transfer of population by adiabatic passage that allows one to prepare cold atomic samples with a well-defined ratio of atomic density and atom number. This method is used to perform a measurement of the cold collision frequency shift in a laser cooled cesium clock at the percent level, which makes the evaluation of the cesium fountain accuracy at the 10(-16) level realistic. With improvements, the adiabatic passage would allow measurements of density-dependent phase shifts at the 10(-3) level in high precision experiments.

Diode-laser noise conversion in an optically dense atomic sample.

We report on oscillating complex noise spectra obtained when a diode-laser beam passes through a resonant dense Doppler-broadened cesium-vapor cell. Atomic coherence converts the laser phase noise into amplitude noise in the transmitted beam. We have found that the level of amplitude noise is orders of magnitude above the intrinsic laser noise. As a function of laser detuning, this noise extends over several inhomogeneous widths, depending on the spectral frequency. Numerical calculations based on a simple theory remarkably mimic the details of the experimental noise spectra.

Cold collision frequency shifts in a 87Rb atomic fountain.

We present measurements of cavity frequency pulling and collisional frequency shifts in a 87Rb fountain with a frequency resolution of 3x10(-16). Agreement with theory is found for the cavity pulling and the measured collisional shifts. The clock shift is found at least 50 times smaller than in 133Cs.

Measurement of the hydrogen 1S- 2S transition frequency by phase coherent comparison with a microwave cesium fountain clock

We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10(14). Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.

New Accurate Fit of an Extended Set of Saturation Data for the nu(3) Band of SF(6): Comparison of Hamiltonians in the Spherical and Cubic Tensor Formalisms.

An extended set of 321 frequencies of vibration-rotation lines of the nu(3) band of SF(6) has been measured by saturation spectroscopy using various isotopic species of CO(2). A least-squares fit of these data has been performed using an effective Hamiltonian written either with a spherical tensor or with a cubic tensor formalism. We have derived correspondence formulas between the parameters in the two approaches and checked that both formalisms give the same results up to the seventh order. Corrected parameters are given for the fit with a fifth-order Hamiltonian. An accurate representation of the band is obtained at the tenth order (standard deviation approximately 12 kHz) with a remarkable predictive power (better than 40 kHz) for J values

(87)Rb versus (133)Cs in cold atom fountains: a comparison.

We describe the operation of a laser cooled (87)Rb frequency standard and present a new measurement of the (87)Rb ground state hyperfine frequency with a relative accuracy of 2.4x10(-15), by comparison with a Cs fountain primary standard. The measured frequency is 6 834 682 610.904 333(17) Hz. An evaluation of the frequency shift induced by cold collisions gives Deltanu/nu(Rb)=(-7.2+/-20)x10(-24) n , where n is the average atomic density in cm(-3). With our present 1 sigma uncertainty of 10(-15), this measurement is still compatible with 0 and about 300 times smaller than for (133)Cs. We also report a test of a possible variation of the fine structure constant at the level of 2.7x10(-14) yr(-1), comparing Rb and Cs cold atom fountains.

Interrogation oscillator noise rejection in the comparison of atomic fountains.

The frequency stability of an atomic fountain clock can be limited by the phase noise of the interrogation oscillator via the "Dick effect." In this paper we demonstrate the rejection of the phase fluctuations of the interrogation oscillator by the synchronization of atomic fountains. A reduction by a factor of 16 in the Allan standard deviation of the relative frequency difference between two fountains has been obtained.

Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator.

Atomic frequency standards using trapped ions or cold atoms work intrinsically in a pulsed mode. Theoretically and experimentally, this mode of operation has been shown to lead to a degradation of the frequency stability due to the frequency noise of the interrogation oscillator. In this paper a physical analysis of this effect has been made by evaluating the response of a two-level atom to the interrogation oscillator phase noise in Ramsey and multi-Rabi interrogation schemes using a standard quantum mechanical approach. This response is then used to calculate the degradation of the frequency stability of a pulsed atomic frequency standard such as an atomic fountain or an ion trap standard. Comparison is made to an experimental evaluation of this effect in the LPTF Cs fountain frequency standard, showing excellent agreement.

Properties of an oscillator slaved to a periodically interrogated atomic resonator.

In advanced atomic resonators, such as those using a fountain of cold cesium atoms or an ensemble of stored ions, the atomic medium is interrogated periodically, and the control signal of the slaved oscillator is updated at equally spaced time intervals. We analyze the properties of the output frequency of these frequency standards. We establish the equations that describe the time behavior of this frequency. We give the stability condition and the transient response of the frequency feedback loop, the response to systematic frequency changes of the free running oscillator, the frequency stability for given free-running oscillator noise and given optical detection noise, and the limitation of the frequency stability by down-conversion of the intrinsic oscillator frequency noise (Dick effect). We point out that a second integration in the feedback loop may not improve significantly the rejection of slow perturbations, unless a condition relative to the timing of the atom-field interaction is verified.