Accurate laser frequency locking to optical frequency combs under low-signal-to-noise-ratio conditions.

We demonstrate a method for accurately locking the frequency of a continuous-wave laser to an optical frequency comb under conditions where the signal-to-noise ratio is low, too low to accommodate other methods. Our method is typically orders of magnitude more accurate than conventional wavemeters and can considerably extend the usable wavelength range of a given optical frequency comb. We illustrate our method by applying it to the frequency control of a dipole lattice trap for an optical lattice clock, a representative case where our method provides significantly better accuracy than other methods.

Lorentz-symmetry test at Planck-scale suppression with a spin-polarized 133 Cs cold atom clock.

We present the results of a Local Lorentz Invariance (LLI) test performed with the 133Cs cold atom clock FO2 [1], hosted at SYRTE. Such test, relating the frequency shift between 133Cs hyperfine Zeeman substates to the Lorentz violating coefficients of the Standard Model Extension (SME), has already been realized in [2] and led to state-of-the-art constraints on several SME proton coefficients. In this second analysis we used an improved model, based on a second order Lorentz transformation and a SCRMF nuclear model, which enables us to extend the scope of the analysis from purely proton to both proton and neutron coefficients. We have also become sensitive to the isotropic coefficient ~cTT, another SME coefficient that was not constrained in [2]. The resulting limits on SME coefficients improve by up to 13 orders of magnitude the present maximal sensitivities for laboratory tests and reach the generally expected suppression scales at which signatures of Lorentz violation could appear [3].

Lorentz-Symmetry Test at Planck-Scale Suppression With a Spin-Polarized 133Cs Cold Atom Clock.

We present the results of a local Lorentz invariance (LLI) test performed with the 133Cs cold atom clock FO2, hosted at SYRTE. Such a test, relating the frequency shift between 133Cs hyperfine Zeeman substates with the Lorentz violating coefficients of the standard model extension (SME), has already been realized by Wolf et al. and led to state-of-the-art constraints on several SME proton coefficients. In this second analysis, we used an improved model, based on a second-order Lorentz transformation and a self-consistent relativistic mean field nuclear model, which enables us to extend the scope of the analysis from purely proton to both proton and neutron coefficients. We have also become sensitive to the isotropic coefficient , another SME coefficient that was not constrained by Wolf et al. The resulting limits on SME coefficients improve by up to 13 orders of magnitude the present maximal sensitivities for laboratory tests and reach the generally expected suppression scales at which signatures of Lorentz violation could appear.

Searching for an Oscillating Massive Scalar Field as a Dark Matter Candidate Using Atomic Hyperfine Frequency Comparisons.

We use 6 yrs 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 are complementary to previous results that were only sensitive to the fine structure constant and improve them by more than an order of magnitude when only a coupling to electromagnetism is assumed.

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).

Prototype of an ultra-stable optical cavity for space applications.

We report the main features and performances of a prototype of an ultra-stable cavity designed and realized by industry for space applications with the aim of space missions. The cavity is a 100 mm long cylinder rigidly held at its midplane by a engineered mechanical interface providing an efficient decoupling from thermal and vibration perturbations. Intensive finite element modeling was performed in order to optimize thermal and vibration sensitivities while getting a high fundamental resonance frequency. The system was designed to be transportable, acceleration tolerant (up to several g) and temperature range compliant [-33°C ; 73°C]. Thermal isolation is ensured by gold coated Aluminum shields inside a stainless steel enclosure for vacuum. The axial vibration sensitivity was evaluated at (4 ± 0.5) × 10(-11)/(m.s(-2)), while the transverse one is < 1 × 10(-11)/(m.s(-2)). The fractional frequency instability is

Laser locking to the 199Hg 1S0-3P0 clock transition with 5.4 × 10(-15)/✓τ fractional frequency instability.

With 199Hg atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is ~15 Hz. Here we lock an ultrastable laser to this ultranarrow 1S0-3P0 clock transition and achieve a fractional frequency instability of 5.4×10(-15)/✓τ for τ ≤ 400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0×10(-17) s(-1) (-16.9 mHz s(-1) at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4×10(-16) per cavity.

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.

Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = 5.7×10(-15).

We present an assessment of the (6s2) (1)S0 ↔ (6s6p)(3)P0 clock transition frequency in 199Hg with an uncertainty reduction of nearly 3 orders of magnitude and demonstrate an atomic quality factor Q of ∼10(14). The 199Hg atoms are confined in a vertical lattice trap with light at the newly determined magic wavelength of 362.5697±0.0011 nm and at a lattice depth of 20E(R). The atoms are loaded from a single-stage magneto-optical trap with cooling light at 253.7 nm. The high Q factor is obtained with an 80 ms Rabi pulse at 265.6 nm. We find the frequency of the clock transition to be 1,128,575,290,808,162.0±6.4(syst)±0.3(stat) Hz (i.e., with fractional uncertainty=5.7×10(-15)). Neither an atom number nor second order Zeeman dependence has yet been detected. Only three laser wavelengths are used for the cooling, lattice trapping, probing, and detection.

Optical lattice trapping of 199Hg and determination of the magic wavelength for the ultraviolet 1S(0)↔3P(0) clock transition.

We report on the Lamb-Dicke spectroscopy of the doubly forbidden (6s(2))(1)S(0)↔(6s6p)(3)P(0) transition in (199)Hg atoms confined to a vertical 1D optical lattice. With lattice trapping of ≲10(3) atoms and a 265.6 nm probe laser linked to the LNE-SYRTE primary frequency reference we have determined the center frequency of the transition for a range of lattice wavelengths and at two lattice trap depths. We find the Stark-free (magic) wavelength to be 362.53(0.21) nm-essential knowledge for future use of this line in a clock with anticipated 10(-18) range accuracy. We also present evidence of the laser excitation of a Wannier-Stark ladder of states in a lattice of well depth 10E(R).

Sub-Doppler cooling of fermionic Hg isotopes in a magneto-optical trap.

Laser cooling and trapping of neutral mercury is performed in a single-stage (1)S(0)↔(3)P(1) 3D magneto-optical trap. We give a detailed account of the atom cloud size and temperature for both bosonic ((200)Hg and (202)Hg) and fermionic ((199)Hg and (201)Hg) isotopes. The bosonic isotope temperatures are in close agreement with Doppler cooling theory, while temperatures obtained for the fermionic isotopes are lower, suggesting the presence of sub-Doppler cooling. A minimum temperature of 29±4 µK is achieved for (201)Hg.

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.

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.

Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock.

Over a two-year duration, we have compared the frequency of the 199Hg+ 5d(10)6s (2)S(1/2)(F=0)<-->5d(9)6s(2) (2)D(5/2)(F=2) electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral 133Cs. These measurements show that any fractional time variation of the ratio nu(Cs)/nu(Hg) between the two frequencies is smaller than +/-7 x 10(-15) yr(-1) (1sigma uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of g(Cs)(m(e)/m(p))alpha(6.0) at the same level.

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.

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.

(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.