Andre Luiten

Considerations on the measurement of the stability of oscillators with frequency counters

The most common time-domain measure of frequency stability, the Allan variance, is typically estimated using a frequency counter. Close examination of the operation of modern high-resolution frequency counters shows that they do not make measurements in the way commonly assumed. The consequence is that the results typically reported by many laboratories using these counters are not, in fact, the Allan variance, but a distorted representation. We elucidate the action of these counters by consideration of their operation in the Fourier domain, and demonstrate that the difference between the actual Allan variance and that delivered by these counters can be very significant for some types of oscillators. We also discuss ways to avoid, or account for, a distorted estimation of Allan variance

Cold atom clocks and applications

This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the 133Cs and 87Rb 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 × 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 × 10−16 at 50 000 s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10−16, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using 87Rb and 133Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests.

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.

Tests of Lorentz invariance using a microwave resonator.

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to delta-beta + 1/2 = (1.5+/-4.2) x 10(-9) and beta-alpha - 1= (-3.1+/-6.9) x 10(-7) which is of the same order as the best previous result for the former and represents a 30-fold improvement for the latter.

Ultra-low-noise microwave extraction from fiber-based optical frequency comb

In conclusion, we have used two FOFC based optical to microwave division frequency synthesizers referenced to a common optically source to create 11.55 GHz microwave signals with a relative frequency stability of 1.6×10-16 at 1 s. The relative phase noise spectral density at a 1 Hz offset from the 11.55 GHz carrier is measured at 111 dBrad2/Hz, limited by the readout system noise floor. Long term stability and accuracy down to 3×10-19 at 65536 s was also demonstrated from a set of 3 days continuous measurement. These results are obtained with classical double balanced mixers measurement scheme. By using a noise measurement system based on the carrier suppression method and advanced noise reduction techniques we are able to improve the results down to a phase noise spectral density at a 1 Hz of 117 dBrad2/Hz and a FFS is of 1.5×10-19 at 1000s (for a single system).

Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation

In this Letter we report on an all optical-fiber approach to the synthesis of ultralow-noise microwave signals by photodetection of femtosecond laser pulses. We use a cascade of Mach-Zehnder fiber interferometers to realize stable and efficient repetition rate multiplication. This technique increases the signal level of the photodetected microwave signal by close to 18 dB. That in turn allows us to demonstrate a residual phase-noise level of -118 dBc/Hz at 1 Hz and -160 dBc/Hz at 10 MHz from a 12 GHz signal. The residual noise floor of the fiber multiplier and photodetection system alone is around -164 dBc/Hz at the same offset frequency, which is very close to the fundamental shot-noise floor.

BNM-SYRTE fountains: recent results

This paper describes several recent improvements of the BNM-SYRTE fountain ensemble. A new method for controlling the cold collision shift with improved accuracy has been proposed and demonstrated. A thorough investigation of some cold collision properties of 133Cs is presented, including the observation of molecular Feshbach resonances. Finally, a new microwave synthesis scheme based on a fully operational cryogenic oscillator is presented. With this, a fractional frequency instability below 2 times 10-14tau-frac12 is obtained routinely

Design and realization of a flywheel oscillator for advanced time and frequency metrology

In this article, we describe a new frequency synthesis system that includes a low phase noise cryogenic sapphire oscillator (CSO) and an H-maser to provide metrological low-noise signals to time and frequency experiments. Implementing this system as a local oscillator for a Cs cold atom fountain, a record frequency stability of 1.6×10−14τ−1∕2 is obtained.

Cryogenic sapphire oscillator with exceptionally high frequency stability

Extremely high short-term frequency stability has been realised in oscillators based on liquid helium cooled sapphire resonators with a modified mounting structure. These oscillators have exhibited an Allan deviation of about 5.4/spl times/10/sup -16//spl tau//sup -1/2/ for integration times (/spl tau/) of 1 to 4 s and a minimum of 2.4/spl times/10/sup -16/ at 32 s.

Improved test of Lorentz invariance in electrodynamics

We report new results of a test of Lorentz invariance based on the comparison of a cryogenic sapphire microwave resonator and a hydrogen-maser. The experimental results are shown together with an extensive analysis of systematic effects. Previously, this experiment has set the most stringent constraint on Kennedy-Thorndike type violations of Lorentz invariance. In this work we present new data and interpret our results in the general Lorentz violating extension of the standard model of particle physics (SME). Within the photon sector of the SME, our experiment is sensitive to seven SME parameters. We marginally improve present limits on four of these, and by a factor seven to ten on the other three.