Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the 10^-18 level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from 7.7×10^-18 to 6.1×10^-17. Among the results, the ^171Yb^+(E3) clocks at NPL and PTB demonstrated agreement within an uncertainty of 7.7×10^-18, marking the first international verification of two independently developed optical clocks below one part in 10^17. The operation of the ^199Hg clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with ^171Yb^+(E3), ^171Yb, and ^87Sr optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.

Optical clocks provide ultra-precise frequency references that are vital for international metrology as well as for tests of fundamental physics. To investigate the level of agreement between different clocks, we simultaneously measured the frequency ratios between ten optical clocks in six different countries, using fiber and satellite links. This is the largest coordinated comparison to date, from which we present a subset of 38 optical frequency ratios and an evaluation of the correlations between them. Four ratios were measured directly for the first time, while others had significantly lower uncertainties than previously achieved, supporting the advance towards a redefinition of the second and the use of optical standards for international time scales.

In this paper we present our work demonstrating the transfer of quantum cryptographic information over a 78 km optical fiber, as a base for future long distance public quantum links, using a commercial quantum key distribution (QKD) system based on the BBM92 protocol. The system communicates with pairs of polarization-entangled photons generated by the nonlinear optical process of spontaneous parametric down-conversion. The system was put to the test in the laboratory using optical fiber of different lengths up to 112 km and with different link losses up to 29 dB. The QKD system was implemented on single mode standard optical fiber link of 78 km length deployed between the two cities of Braunschweig and Hannover. Characterizations and optimizations of the QKD system and the fiber link have been carried out in order to improve the synchronization, to reduce the quantum bit error rate, and to successfully establish the intercity quantum communication.

The details of fiber Brillouin amplifier modules developed for optical frequency dissemination and installed on the fiber link between Braunschweig and Strasbourg for performing optical clock comparisons are described and documented. The performance of these fiber Brillouin amplification modules is characterized in terms of gain, one-way phase shift, and signal-to-noise ratio across a wide parameter space of signal and pump powers. Finally, upper estimates are derived for the frequency transfer uncertainty contributions resulting from the non-reciprocity induced by the fiber Brillouin amplifier modules based on the characterized one-way phase shift.

Quantum key distribution (QKD) is a prominent technology for exchanging secure keys between two authenticated remote parties. The security in a QKD system is unconditionally ensured by the laws of quantum mechanics which guarantee that any eavesdropping attempts will be identified. In this paper, we report the concept and structure of the Niedersachsen Quantum Link as a QKD testbed. The testbed consists of a 78 km long pair of dark fibers between the cities of Hannover and Braunschweig and is operated by Physikalisch-Technische Bundesanstalt and Leibniz Universität Hannover. One of the dark fibers is reserved for “quantum” applications, while the second fiber is dedicated to the dissemination of time and frequency reference signals as well as classical communication between two sites. This combination of dark “quantum” fiber and integrated time-frequency infrastructure is a unique feature of the Niedersachsen Quantum Link testbed.

Optical clock networks connected by phase-coherent links offer significant potential for advancing fundamental research and diverse scientific applications. Free-space optical frequency transfer extends fiber-based connectivity to remote areas and holds the potential for global coverage via satellite links. Here we present a compact and robust portable, rack-integrated two-way free-space link characterization system. Equipped with plug-and-play capabilities, the system enables straightforward interfacing with various optical systems and facilitates quick deployment for field experiments. In this work, we achieve a fractional frequency instability of 2.0 × 10-19 for an averaging time of 10 s over a 3.4 km horizontal fully folded intra-city free-space link. Moreover, the system maintains an uptime of 94% over 15 hours, illustrating its reliability and effectiveness for high-precision optical frequency comparisons over free-space.

Optical clocks have improved their frequency stability and estimated accuracy by more than two orders of magnitude over the best caesium microwave clocks that realise the SI second. Accordingly, an optical redefinition of the second has been widely discussed, prompting a need for the consistency of optical clocks to be verified worldwide. While satellite frequency links are sufficient to compare microwave clocks, a suitable method for comparing high-performance optical clocks over intercontinental distances is missing. Furthermore, remote comparisons over frequency links face fractional uncertainties of a few $10^{-18}$ due to imprecise knowledge of each clock's relativistic redshift, which stems from uncertainty in the geopotential determined at each distant location. Here, we report a landmark campaign towards the era of optical clocks, where, for the first time, state-of-the-art transportable optical clocks from Japan and Europe are brought together to demonstrate international comparisons that require neither a high-performance frequency link nor information on the geopotential difference between remote sites. Conversely, the reproducibility of the clocks after being transported between countries was sufficient to determine geopotential height offsets at the level of 4 cm. Our campaign paves the way for redefining the SI second and has a significant impact on various applications, including tests of general relativity, geodetic sensing for geosciences, precise navigation, and future timing networks.

Realizing a clock-based geodetic network with a relative uncertainty level of 10?18 has been a significant objective for the scientific community. This network can be utilized for realizing more accurate geodetic reference frames and for testing the fundamental laws of physics, such as the theory of relativity. Typically, optical fibers are connecting optical clocks in such a network. For the last decades, Global Navigation Satellite Systems (GNSSs) have built a trustful and easy-setup method for frequency and time transfer. However, recently optical fiber link networks showed better frequency instability. In this study, we investigate the limits of GNSS-based frequency transfer links with the help of an optical fiber link as ground truth. Therefore, we analyze the GNSS data acquired in a dedicated common-clock experiment over a 52 km baseline. We focus on developing two algorithms to estimate the receiver clock differences, hence the frequency instability. These are the single difference (SD) approach with ambiguity fixing as a common view technique, and precise point positioning as an all in-view technique. We discuss the frequency instability achieved by the optical fiber link as well. We evaluate further the performance by computing the modified Allan deviation for both cases. The results show that the ambiguity-fixed solution of SD-CV improves the relative frequency instability via GNSS to reach the order of 3–5 · 10^?17 at one day averaging time. In the optical fiber link, which is the basis of the common clock setup, the round-trip instability shows better performance for all averaging times.

Exploiting the outstanding performance of optical atomic clocks for improved timekeeping, relativistic geodesy, and fundamental physics beyond the standard model demands comparing distant state-of-the-art optical clocks. Interferometric optical fiber links have been demonstrated as an eminent method for such frequency comparisons over distances up to thousands of kilometers. However, for such distances, the optical fiber attenuation mandates signal amplification. Fiber Brillouin amplification (FBA) has been proven as an efficient amplification technique for coherent frequency transfer. Demonstrated FBA schemes have been designed based on costly narrow-linewidth pump lasers and analog pump-to-signal phase locking schemes. Furthermore, the high pump power requirement of these FBAs hinders the integration of FBA-based frequency dissemination on fiber connections for shared telecommunication signals in the C-band. In this paper, we propose and experimentally demonstrate a novel FBA module (FBAM) employing cost-effective distributed feedback (DFB) pump lasers assisted by a digital phase locking scheme based on a field programmable gated array. The new FBAM is compact, cost-effective, and directly applicable to different bands, which opens up new opportunities to establish a frequency metrology infrastructure within existing telecommunication fiber networks. Additionally, the small-footprint of the DFB-FBAM allows for frequent amplification stages with lower pump power to reach continental scale optical metrology links with an optimized signal-to-noise ratio. We characterized the DFB-FBAM’s frequency transfer uncertainty using a two-way layout over an in-lab 100 km long optical fiber link and reach a fractional frequency instability of 9.3 × 10−22 at a 10 ks integration time. The DFB-FBAM characterizations show uncertainty contributions of (−2.1 ± 3.3) × 10−22 and below for averaging times >100 ks. For the first time, we assess the temporal Brillouin frequency shift variations in an underground fiber link and implement a scheme to track these changes in a remote FBAM.

We investigate the validation of fiber-based optical frequency transfer for frequency comparison applications. We specifically consider the frequency transfer validation for remote optical clock comparisons and want to ensure interferometric fiber link uncertainty contributions below the combined uncertainty of the clocks under test. The validation is based on signals obtained via looping back from the remote end to the sender site and comparing the input with the output of the loop. These loop-back data need to be averaged over intervals for reaching the validation goal, as the short-term instability of long-distance interferometric fiber links is typically higher than that of optical clocks. We introduce a two-step validation approach and address the finding of a compromise between opposing aspects of averaging: reaching low uncertainties versus achieving a high data coverage of the validated data set via a high temporal resolution of the fault identification. We discuss the impact of different averaging types and of the tolerance of filtering criteria on the achievable estimated uncertainty and on the coverage of the validated data set. Data from four multiple-week-long measurement campaigns on the fiber link between Physikalisch-Technische Bundesansanstalt and University of Strasbourg are used for this assessment.

Here we share the relevant data of the manuscript “Comparing ultrastable lasers at 7×10-17 fractional frequency instability through a 2,220 km optical fibre network”. Raw data was acquired using multiple synchronised, dead-time free frequency counters in Lambda-mode [1]. The integration time for each data point was 1 s. The data provided here have been processed to reflect the fractional frequency difference between the ultrastable lasers at NPL and PTB, scaled to 1542 nm. Specifically, \(y=(\nu_{\text{NPL(ULE)}}\frac{777327}{1126090}-\frac{767233}{767235}\nu_{\text{PTB(Si)}})/194.4 \ \text{THz}\) where \(y\) is the value recorded in the data files, \(\nu_{\text{NPL(ULE)}}\) and \(\nu_{\text{PTB(Si)}}\) are the optical frequencies of the ultrastable lasers at NPL (referenced to a ULE cavity) and PTB (referenced to Si cavity), respectively. The numerators and the denominators of the scaling factors correspond to mode numbers of the optical frequency comb at NPL and PTB, respectively. The expression for \(y\) corresponds to the fractional transfer beat [2] between the NPL and PTB ultrastable lasers. The file “833000_s_874000_s_data_for_fig_2.txt” contains the timeseries data used to compute the modified Allan deviation reported in Fig. 2a. The “0” values correspond to invalid data due to glitches in the operation of the optical fibre link. A linear drift of 40 mHz s-1 has been removed in these data. The file “432000_s_912077_s_data_for_fig_3.txt” contains the timeseries data used in Fig. 3. The “0” values correspond to invalid data due to glitches in the operation of the optical fibre link. These data have additionally been high pass filtered with a cut off frequency of 1 mHz to decouple the short-term instability of the optical fibre link from the drift of the ultrastable lasers (with a characteristic time >1000 s), as described in the manuscript. The files “222000_s_232000_s_data_for_supp_fig_1.txt”, “270000_s_288000_s_data_for_supp_fig_1.txt”, “754000_s_765000_s_data_for_supp_fig_1.txt”, “832000_s_890000_s_data_for_supp_fig_1.txt”, contain the timeseries data used to compute the modified Allan deviation reported in Supplementary Fig. 1. The “0” values correspond to invalid data due to glitches in the operation of the optical fibre link. A linear drift of 40 mHz s-1 has been removed in these data. The temporal starting point is displayed in seconds in the title of the files relative to 00:00 UTC of 2019/07/06. References [1] Dawkins, S. T., McFerran, J. J. & Luiten, A. N. Considerations on the Measurement of the Stability of Oscillators with Frequency Counters. IEEE Transactions on ultrasonics, ferroelectrics, and frequency control 54, 918-925 (2007). [2] Telle, H.R., Lipphardt, B. & Stenger, J. Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements. Appl. Phys. B 74, 1-6 (2002).

We investigate optical frequency dissemination over a 1400 km long fiber link in looped configuration over a pair of underground fibers between Braunschweig and Strasbourg. This fiber link is the first to combine fiber Brillouin amplifiers with a repeater laser station. Phase-coherent operation over more than five days is demonstrated. We analyze the repeatability of the performance over four campaigns and present results of 65 d in total. The weighted mean of the fractional frequency offset of the transferred optical frequency over the complete data set is (-1.1 +/- 0.4) x 10(-20). By analyzing the stabilization signals of the two individual fibers, the correlation of the phase noise on the two fibers is shown to be > 98%.

Die vorliegende Arbeit dokumentiert die Entwicklung eines Ankunftszeitmonitorsystems mit verbesserter Zeitauflosung fur den Freie-Elektronen-Laser in Hamburg (FLASH) am Deutschen Elektronen-Synchrotron (DESY). Die Notwendigkeit der Entwicklung dieses Systems ergab sich aus der Anforderung auch bei Experimenten mit Elektronenpaketladungen von nur 20 pC, anstelle der bisher verwendeten 500 bis 3000 pC, eine Zeitauflosung von 10 fs zu erzielen. Das gesamte System muss hierzu eine Bandbreite von etwa 40 GHz aufweisen. Zur Realisierung wurde zunachst eine Studie neuer potentieller Pickupelektroden mittels Computersimulationen durchgefuhrt. Unter Berucksichtigung der elektrischen und mechanischen Eigenschaften sowie der Herstellbarkeit wurde ein konusformiger Pickup ausgewahlt. Grenzen fur die Produktionstoleranzen wurden anhand einer ausfuhrlichen Simulationsstudie ermittelt. Die Ergebnisse der Vermessung des elektrischen Verhaltens eines Prototypen zeigten gute Ubereinstimmung mit den Simulationsergebnissen. Das elektrische Signal des Pickups wird auf einen elektro-optischen Modulator (EOM) geleitet. Die erhohte Bandbreite erfordert den Austausch der bestehenden EOMs. Es existieren nur wenige EOMs, welche nominell die geforderte Bandbreite aufweisen. Sie wurden im Labor hinsichtlich ihrer Eigenschaften, wie optische Modulationstiefe und optischer Verluste untersucht und das geeignetste Modell ausgewahlt. Schlieslich werden Aufbaukonzepte prasentiert. Der erweiterte Ladungsbereich erfordert einen Betrieb mit zwei Modi fur niedrige und hohe Ladungen, wobei jeder Modus einen Fein- und einen Grobkanal besitzt. Der Grobkanal dient zur Bestimmung des Arbeitsfensters des Feinkanals. Um die hohe Ankunftszeitgenauigkeit des Gesamtsystems zu garantieren kommt der Wahl der HF-Kabel eine wichtige Bedeutung zu. Diese mussen einerseits die Anforderung an die hohe Bandbreite erfullen und zudem eine geringe Dampfung aufweisen. Ein Prototyp des neuen Ankunftszeitmonitorsystems wurde realisiert und vermessen. Aufgrund von Verfugbarkeitsproblemen musste dabei zunachst auf ein EOM Modell mit geringerer Bandbreite zuruckgegriffen werden, um die Funktionalitat zu demonstrieren. Gemas Computersimulationen wird das neue Ankunftszeitmonitorsystem bei Verwendung des geplanten EOM die geforderte Genauigkeit von 10 fs ab einer Elektronenpaketladung von etwa 55 pC erzielen. Die unerwartet hohe Dampfung der Verkabelung vom Pickup bis zum EOM bei Frequenzen oberhalb von etwa 20 GHz erlaubt es nicht diese Genauigkeit bei 20 pC Ladung zu erreichen. Bei dieser Paketladung kann eine Genauigkeit von etwa 27 fs erwartet werden.

In this paper we report on the present status and performance of the laser-optical synchronization system at FLASH, as well as its upcoming upgrades and new installations. These include the connection of the FLASH II extension, high-resolution electron bunch arrival time monitors for low charges, an improvedmaster laser pulse distribution scheme, sub-10 fs jitter synchronization of the pump-probe laser and arrival time measurements of the UV pulses on the e-gun photocathode. Together with the planned connections of the acceleration modules to the optical master laser and the migration of the low-level hardware to the MTCA.4 platform, an outlook to slow and fast feedback strategies is given.