Comparing ultrastable lasers at 7 × 10-17 fractional frequency instability through a 2220 km optical fibre network.

Ultrastable lasers are essential tools in optical frequency metrology enabling unprecedented measurement precision that impacts on fields such as atomic timekeeping, tests of fundamental physics, and geodesy. To characterise an ultrastable laser it needs to be compared with a laser of similar performance, but a suitable system may not be available locally. Here, we report a comparison of two geographically separated lasers, over the longest ever reported metrological optical fibre link network, measuring 2220 km in length, at a state-of-the-art fractional-frequency instability of 7 × 10-17 for averaging times between 30 s and 200 s. The measurements also allow the short-term instability of the complete optical fibre link network to be directly observed without using a loop-back fibre. Based on the characterisation of the noise in the lasers and optical fibre link network over different timescales, we investigate the potential for disseminating ultrastable light to improve the performance of remote optical clocks.

Simple and compact diode laser system stabilized to Doppler-broadened iodine lines at 633 nm.

We present a compact iodine-stabilized laser system at 633 nm, based on a distributed-feedback laser diode. Within a footprint of 27×15cm2, the system provides 5 mW of frequency-stabilized light from a single-mode fiber. Its performance was evaluated in comparison to Cs clocks representing primary frequency standards, realizing the SI unit Hz via an optical frequency comb. With the best suited absorption line, the laser reaches a fractional frequency instability below 10-10 for averaging times above 10 s. The performance was investigated at several iodine lines, and a model was developed to describe the observed stability on the different lines.

Ultrastable Silicon Cavity in a Continuously Operating Closed-Cycle Cryostat at 4 K.

We report on a laser locked to a silicon cavity operating continuously at 4 K with 1×10^{-16} instability and a median linewidth of 17 mHz at 1542 nm. This is a tenfold improvement in short-term instability, and a 10^{4} improvement in linewidth, over previous sub-10-K systems. Operating at low temperatures reduces the thermal noise floor and, thus, is advantageous toward reaching an instability of 10^{-18}, a long-sought goal of the optical clock community. The performance of this system demonstrates the technical readiness for the development of the next generation of ultrastable lasers that operate with an ultranarrow linewidth and long-term stability without user intervention.

1.5 µm Lasers with Sub-10 mHz Linewidth.

We report on two ultrastable lasers each stabilized to independent silicon Fabry-Pérot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of 4×10^{-17} for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.

Test of Special Relativity Using a Fiber Network of Optical Clocks.

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10^{-8}, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future.

Transportable Optical Lattice Clock with 7×10

We present a transportable optical clock (TOC) with ^{87}Sr. Its complete characterization against a stationary lattice clock resulted in a systematic uncertainty of 7.4×10^{-17}, which is currently limited by the statistics of the determination of the residual lattice light shift, and an instability of 1.3×10^{-15}/sqrt[τ] with an averaging time τ in seconds. Measurements confirm that the systematic uncertainty can be reduced to below the design goal of 1×10^{-17}. To our knowledge, these are the best uncertainties and instabilities reported for any transportable clock to date. For autonomous operation, the TOC has been installed in an air-conditioned car trailer. It is suitable for chronometric leveling with submeter resolution as well as for intercontinental cross-linking of optical clocks, which is essential for a redefinition of the International System of Units (SI) second. In addition, the TOC will be used for high precision experiments for fundamental science that are commonly tied to precise frequency measurements and its development is an important step to space-borne optical clocks.

A clock network for geodesy and fundamental science.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10(-17) via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10(-17) is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

Reduction of residual amplitude modulation to 1 × 10⁻6 for frequency modulation and laser stabilization.

Active control and cancellation of residual amplitude modulation (RAM) in phase modulation of an optical carrier is one of the key technologies for achieving the ultimate stability of a laser locked to an ultrastable optical cavity. Furthermore, such techniques are versatile tools in various frequency modulation-based spectroscopy applications. In this Letter we report a simple and robust approach to actively stabilize RAM in an optical phase modulation process. We employ a waveguide-based electro-optic modulator (EOM) to provide phase modulation and implement an active servo with both DC electric field and temperature feedback onto the EOM to cancel both the in-phase and quadrature components of the RAM. This technique allows RAM control on the parts-per-million level where RAM-induced frequency instability is comparable to or lower than the fundamental thermal noise limit of the best available optical cavities.

A compact and efficient strontium oven for laser-cooling experiments.

Here we describe a compact and efficient strontium oven well suited for laser-cooling experiments. Novel design solutions allowed us to produce a collimated strontium atomic beam with a flux of 1.0 × 10(13) s(-1) cm(-2) at the oven temperature of 450 °C, reached with an electrical power consumption of 36 W. The oven is based on a stainless-steel reservoir, filled with 6 g of metallic strontium, electrically heated in a vacuum environment by a tantalum wire threaded through an alumina multi-bore tube. The oven can be hosted in a standard DN40CF cube and has an estimated continuous operation lifetime of 10 years. This oven can be used for other alkali and alkaline earth metals with essentially no modifications.

Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons.

We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition (1)S(0)-(3)P(0) at 698 nm with bosonic (88)Sr. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with (88)Sr shows no degradation due to collisions on the fractional uncertainty level of 10(-16).

Optical frequency transfer via 146 km fiber link with 10 -19 relative accuracy.

We demonstrate the long-distance transmission of an ultrastable optical frequency derived directly from a state-of-the-art optical frequency standard. Using an active stabilization system we deliver the frequency via a 146-km-long underground fiber link with a fractional instability of 3 x 10(-15) at 1 s, which is close to the theoretical limit for our transfer experiment. After 30,000 s, the relative uncertainty for the transfer is at the level of 1 x 10(-19). Tests with a very short fiber show that noise in our stabilization system contributes fluctuations that are 2 orders of magnitude lower, namely, 3 x 10(-17) at 1 s, reaching 10(-20) after 4,000 s.

Diode laser with 1 Hz linewidth.

We report an ultranarrow-linewidth laser spectrometer at 657 nm, consisting of a diode laser locked in a single stage to a stable high-finesse reference cavity. The system is characterized by comparison with a second independent system. From beat frequency measurements a linewidth below 1.5 Hz (FWHM) and a fractional instability of less than 2 x 10(-15) for 1 s of averaging time are observed.

Optical clock with ultracold neutral atoms.

We demonstrate how to realize an optical clock with neutral atoms that is competitive to the currently best single ion optical clocks in accuracy and superior in stability. Using ultracold atoms in a Ca optical frequency standard, we show how to reduce the relative uncertainty to below 10(-15). We observed atom interferences for stabilization of the laser to the clock transition with a visibility of 0.36, which is 70% of the ultimate limit achievable with atoms at rest. A novel scheme was applied to detect these atom interferences with the prospect to reach the quantum projection noise limit at an exceptional low instability of 4 x 10(-17) in 1 s.

Doppler cooling and trapping on forbidden transitions.

Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of (40)Ca atoms has been cooled and trapped to a temperature as low as 6 microK by operating a magnetooptical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method, more than 10% of precooled atoms from a standard magnetooptical trap have been transferred to the ultracold trap. Monte Carlo simulations of the cooling process are in good agreement with the experiments.

Short-pulse properties of optical frequency comb generators.

An optical frequency comb generator, based on a simple electro-optic modulator in an optical resonator, can produce high-repetition-rate picosecond pulses. Unlike conventional picosecond lasers, the properties of these pulses are greatly affected by detuning the optical cavity and by dispersion caused by the electro-optic crystal. Picosecond pulses were studied in a physical device by numerical simulation and intensity autocorrelation measurements. The pulse width and pulse-to-pulse spacing were greatly affected by detuning the input laser frequency and the resonance of the optical resonator, and the numerical simulations showed that dispersion causes temporal ripples that are antisymmetric between pulse pairs.

Lifetime of the metastable 6s' [(1/2)](0) clock state in xenon.

To investigate the potential of a proposed optical frequency standard, we have measured the lifetime of the metastable 6s' [(1/2)](0) state in xenon. Magneto-optically trapped xenon atoms were prepared in the 6s' [(1/2)](0) state, and the time dependence of the vacuum-ultraviolet decay signature was analyzed. The total decay rate of 75(3) s(-1) is the sum of a 7.8(38)-s(-1) spontaneous emission rate (1-sigma uncertainties) and a much larger deexcitation rate that is due to a transition driven by room-temperature blackbody radiation.

Determination of the xenon 6s[3/2](2)-6s'[1/2](0) clock frequency by interferometric wavelength measurements.

We have determined the wave number of the optical two-photon clock transition 6s[3/2](2)-6s'[1/2](0) in xenon by interferometrically comparing the wavelengths of the 6s[3/2](2)-6p'[1/2](1) (lambda = 450 nm) and 6s'[(1/2)] (0)-6p'([1/2]) (lambda = 764 nm) transitions with an iodine-stabilized 633-nm He-Ne laser. These measurements determine the frequency of the two-photon transition [4564.610902(13) cm(-1) for (132)Xe] to better than 1 MHz and provide precise values for the isotope shifts and the hyperfine structures of these transitions.