Systematic Frequency Error in Laser Synchronization Circuits for Fiber-Optic Time Transfer Systems.

The paper addresses the problem of a systematic frequency error occurring in semiconductor-laser frequency-synchronization circuits based on counting the beat note between the two lasers in a reference time interval using a high-frequency prescaler. Such synchronization circuits are suitable for operation in ultra-precise fiber-optic time-transfer links, used e.g. in time/frequency metrology. The error occurs when the power of the light coming from the reference laser, to which the second laser is synchronized, is below about -50 dBm to -40 dBm, depending on the details of particular circuit implementation. The error can reach tens of MHz if left out of consideration and does not depend on the frequency difference between the synchronized lasers. Its sign can be positive or negative, depending on the spectrum of the noise at the prescaler input and the frequency of the measured signal. In the paper we present the background of the systematic frequency error, discuss important parameters allowing for predicting the error value, and describe the simulation and theoretical models being helpful for designing and understanding operation of discussed circuits. The theoretical models presented here show good agreement with the experimental data, which demonstrates the usefulness of proposed methods. Implementing polarization scrambling to mitigate the effect of polarization misalignment of the lights of the lasers used was considered and the resulting penalty was determined.

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.

Optical-frequency transfer over a single-span 1840 km fiber link.

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of 2×10(-15) for a gate time τ of 1 s reaching 4×10(-19) in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about 3×10(-19). The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ(-2) slope in the modified Allan deviation, which is also derived theoretically.

A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place.

Optical clocks show unprecedented accuracy, surpassing that of previously available clock systems by more than one order of magnitude. Precise intercomparisons will enable a variety of experiments, including tests of fundamental quantum physics and cosmology and applications in geodesy and navigation. Well-established, satellite-based techniques for microwave dissemination are not adequate to compare optical clocks. Here, we present phase-stabilized distribution of an optical frequency over 920 kilometers of telecommunication fiber. We used two antiparallel fiber links to determine their fractional frequency instability (modified Allan deviation) to 5 × 10(-15) in a 1-second integration time, reaching 10(-18) in less than 1000 seconds. For long integration times τ, the deviation from the expected frequency value has been constrained to within 4 × 10(-19). The link may serve as part of a Europe-wide optical frequency dissemination network.

Long-distance remote comparison of ultrastable optical frequencies with 10(-15) instability in fractions of a second.

We demonstrate a fully optical, long-distance remote comparison of independent ultrastable optical frequencies reaching a short term stability that is superior to any reported remote comparison of optical frequencies. We use two ultrastable lasers, which are separated by a geographical distance of more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a commercial telecommunication network. The remote characterization spans more than one optical octave and reaches a fractional frequency instability between the independent ultrastable laser systems of 3 x 10 (-15) in 0.1 s. The achieved performance at 100 ms represents an improvement by one order of magnitude to any previously reported remote comparison of optical frequencies and enables future remote dissemination of the stability of 100 mHz linewidth lasers within seconds.

Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber.

We describe the use of fiber Brillouin amplification (FBA) for the coherent transmission of optical frequencies over a 480 km long optical fiber link. FBA uses the transmission fiber itself for efficient, bi-directional coherent amplification of weak signals with pump powers around 30 mW. In a test setup we measured the gain and the achievable signal-to-noise ratio (SNR) of FBA and compared it to that of the widely used uni-directional Erbium doped fiber amplifiers (EDFA) and to our recently built bi-directional EDFA. We measured also the phase noise introduced by the FBA and used a new and simple technique to stabilize the frequency of the FBA pump laser. We then transferred a stabilized laser frequency over a wide area network with a total fiber length of 480 km using only one intermediate FBA station. After compensating the noise induced by the fiber, the frequency is delivered to the user end with an uncertainty below 2 x 10(-18) and an instability sigma y(tau) = 2 x 10(-14) /(tau/s).

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.

Limit on the present temporal variation of the fine structure constant.

The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant alpha in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in 171Yb+ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio f(Yb)/f(Cs) of (-1.2+/-4.4)x10(-15) yr(-1), consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of alpha at the level of 2.0x10(-15) yr(-1) (1sigma), corresponding so far to the most stringent limit from laboratory experiments.