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Abstract
Challenging experiments for tests in fundamental physics require highly coherent optical frequency references with suppressed phase noise from hundreds of kHz down to μHz of Fourier frequencies. It can be achieved by remote synchronization of many frequency references interconnected by stabilized optical fibre links. Here we describe the path to realize a delocalized optical frequency reference for spectroscopy of the isomeric state of the nucleus of Thorium-229 atom. This is a prerequisite for the realization of the next generation of an optical clock – the nuclear clock. We present the established 235 km long phase-coherent stabilized cross-border fibre link connecting two delocalized metrology laboratories in Brno and Vienna operating highly-coherent lasers disciplined by active Hydrogen masers through optical frequency combs. A significant part (up to tens of km) of the optical fibre is passing urban combined collectors with a non-negligible level of acoustic interference and temperature changes, which results in a power spectral density of phase noise over 105 rad2· Hz-1. Therefore, we deploy a digital signal processing technique to suppress the fibre phase noise over a wide dynamic range of phase fluctuations. To demonstrate the functionality of the link, we measured the phase noise power spectral density of a remote beat note between two independent lasers, locked to high-finesse stable resonators. Using optical frequency combs at both ends of the link, a long-term fractional frequency stability in the order of 10−15 between local active Hydrogen masers was measured as well. Thanks to this technique, we have achieved reliable operation of the phase-coherent fibre link with fractional stability of 7 × 10−18 in 103 s.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Advances in the research of the most accurate optical atomic clocks [1] place high demands on the verification of the achieved stability of the generated time and frequency signals. Therefore, optical fibres equipped with Doppler-induced phase noise suppression techniques [2–6] are used to disseminate these signals for frequency comparison metrology campaigns. Thanks to this fibre noise cancelling technique, it was possible to compare the stability of optical atomic clocks on the order of $10^{-18}$ [7–12], while phase-stabilized optical fibres affected the measurement on the order of $<10^{-19}$ only, for integration times $>10^{4}$ s [13–16].
Phase-coherent links are currently used in many applications, eg. time synchronization of telescopes [17,18], chronological altitude measurement [19], seismic wave detection [20], synchronization of sensory networks in the industry [21]. The development of phase-coherent networks in Europe has led to the formation of the CLONETS consortium, which aims to build and operate a pan-European fibre-based research infrastructure for precise time and frequency dissemination [22,23]. Many phase-coherent optical links have been installed at a national level around the world [24–30], but cross-border international links are still only a few [31]. They are exclusively used for long-term comparisons of the stability of a variety of atomic clocks [32].
One of the important areas of application of coherent fibre links is fundamental research in the field of nuclear physics. The excitation of the Thorium-229 nucleus is a subject of interest nowadays, owing to the possibility of its use for a next-generation frequency reference with ultimate stability, namely a nuclear optical clock [33]. The nuclear transitions of Th-229 (from the isomer state to the ground state) is expected to have a lifetime of the order of $10^{4}$ s [34,35]. Therefore, a very long integration time is required to perform high-resolution spectroscopy, during which the interrogation laser frequency must not be affected by a long-term drift. The most suitable way to achieve this condition is to combine many types of frequency references into composite atomic clocks, which suppress the phase noise of the desired interrogation laser over a wide range of Fourier frequencies, ideally from $10^{-5}$ Hz up to $10^{5}$ Hz. Because the individual frequency references can be separated geographically by hundreds of kilometers, it is necessary to interconnect them with the optical frequency signals using coherent fibre links.
Our joint research team of TU Wien, BEV–Federal Office of Metrology and Surveing (BEV), and Institute of Scientific Instruments (ISI) has dealt with this task since 2018 within the CC4C project [36]. TU Wien (Austria) performs advanced spectroscopic experiments with the isomeric state of the nucleus of Th-229 ions. It has assembled its own unique optical frequency comb operating in the vacuum-ultravilet (VUV) wavelength range, the synchronization of which is possible using a signal from an external optical reference operating at a telecommunication wavelength of 1542.14 nm. BEV is the Austrian National Metrology Institute and operates a highly-coherent optical reference at 1542.14 nm. The reference output frequency is traceable by an optical frequency comb locked to an active Hydrogen maser (H-maser). Cs atomic clocks, which supply legal time in Austria UTC(BEV), are used for H-maser traceability. ISI (Czech Republic) is a research institution implementing an experimental optical atomic clock with trapped 40Ca+ ions (in cooperation with Palacky University in Olomouc) [37]. The frequency scale includes a variety of optical references, optical frequency combs, and an active H-maser as well.
In this work, we present an important progress in the implementation of delocalized optical frequency reference towards tests of fundamental physics. It includes putting a new cross-border phase-coherent fibre link (235 km long) between ISI (Czech Republic) and BEV (Austria) into operation. This optical link uses the dark channel within the cross-border fibre line Brno-Wien jointly operated by CESNET (Czech National Research and Education Network provider) and ACOnet (Austrian National Research and Education Network provider) with geographical placements shown in Fig. 1. This is the first segment of the planned delocalized composite clock network, in which a stable optical reference signal from ISI is distributed. The coherent fibre link between BEV and TU Wien (24 km additional), thus the second segment, is currently under construction. Highly-coherent lasers at 1542.14 nm at all locations will be synchronized using both coherent fiber link segments and connected to the appropriate local clocks: 40Ca+ optical atomic clock at ISI, Cs clock at BEV, and Thorium nuclear clock experiment at TU Wien.
Fig. 1. The first segment of delocalized optical clock network: the optical fibre link between ISI and BEV (geographic overview).
2. Cross-border optical fibre link ISI - BEV
The exact deployment of the long-haul optical fiber link between ISI Brno and BEV Wien at the network level is shown in Fig. 2. As can be seen the existing communication fibre network infrastructure was modified to allow simultaneous transfer of conventional data, precise time and stable optical frequency. The link is 235 km long and has a total insertion loss of 67 dB. A part of the optical spectrum in the C band is reserved on the shared fibre by means of an optical add-drop multiplexer (OADM) in the range of 1546.12–1540.56 nm (ITU-T channels 39–46). This part of the reserved spectrum (channels 39–46) is used for the transmission of ultra-stable signals, in our case the stable wavelength of 1542.14 nm. Deployed OADMs are based on Thin Film technology providing 25 dB of isolation of transmitted band (channels 39–46) but quite weak isolation (only 15 dB) of the rest of the spectrum, which is used for telecommunication data. Similar OADMs are currently deployed on the fibre link between BEV and TU Wien, as discussed above, in order to provide single path bidirectional transmission for wavelengths of 1542.14 nm or alternatively 1540.56 nm. As can be seen in Fig. 2, another set of OADMs is used for providing coarse wavelength division multiplex (CWDM) at 1510 nm and 1610 nm for remote management of fibre amplifiers. The fibre link exhibits two segments with excessive attenuation of 31 and 30 dB. The attenuation of these segments and last miles (solved passively at both terminals) is compensated using bidirectional optical erbium-doped fibre amplifiers (EDFA) manufactured by Czech Light [38]. These amplifiers are deployed in three variants: CLA Booster Preamp and CLA Dual Inline for data and precise time transfers, CLA BiDi for single path bidirectional transmission of wavelengths.
Fig. 2. Network level of the long-haul optical fiber link between ISI Brno and BEV Wien, which allows simultaneous transfer of stable optical frequency, precise 1PPS time signal and conventional data. Legend (in alphabetical order): ADD, DROP - optical add-drop multiplexer for remote management of CLAs, CLA BiDi - bidirectional EDFA for stable wavelength transfer, CLA Booster Preamp/Inline - EDFA for telecommunication data and time transfer, DEMUX - demultiplexer, DCU - dispersion compensation unit, Filter 42.14 - 1542.14 optical band-pass filter for stable optical frequency transmission, Filter 51.72 - 1551.72 optical band-pass filter for time transmission, 2xMC - media converter for SFP, MUX - multiplexer, ODF - optical distribution frame, SFP - small form factor optical transceiver (for remote management of CLAs), T adaptor - a device for precise time signal transmission [42], 8skip0 - OADM in the range of 1540.56-1546.12 nm (ITU channels 39-46) for stable wavelength transmission.
As shown e.g. in [39] discrete/lumped bidirectional amplifiers can’t deliver such gain, achievable maximum is about 21–22 dB, even less in the presence of reflections (connectors, splices, passive component). So obviously all losses of the line can not be compensated and operating above-mentioned bidirectional amplifiers close to the maximal gain brings the possibility of unwanted self oscillations-lasing. Safe operation of bidirectional amplifiers with maximum compensated attenuation with simultaneous lasing prevention is under development and also reduction of reflective events at Wien side are long term goals. Safe operation of bidirectional amplifiers is crucial not only for coherent frequency transmission but also for safe data transmission because of relatively weak isolation of OADMs in the telecom band.
The link itself belongs into Czech Infrastructure for Time And Frequency (CITAF) [40]. It serves for comparison of UTC(TP) and UTC(BEV) since 2011 [41]. According to author’s knowledge it is the globally first cross-border link for precise time and frequency transfer which is in operation.
3. Methods
The ISI - BEV link is assembled as a direct connection of two remote metrological laboratories via one optical fibre with active suppression of fibre phase noise and does not contain a loopback line. Therefore, to evaluate the level of phase noise suppression of the link, we assembled a method based on comparing two independent references (two delocalized H-masers ISI and BEV), whose stability is significantly higher than the phase noise of the unstabilized ISI - BEV link. To perform experimental verification of the active suppression of the fibre link phase noise, we converted the relative stability of H-maser at each site to a highly coherent laser source via an optical frequency comb. Then we evaluated phase noise suppression efficiency of the ISI - BEV link by comparing the stability of a remote beat note of two highly coherent laser sources working at 1542.14 nm with a reference measurement of H-masers acquired by their manufacturers. Therefore, we are investigating a remote beat note of two independent highly coherent laser sources working at 1542.14 nm.
In ISI, a 1542.14 nm low-noise laser locked via an optically referenced optical frequency comb to a 1540.57 nm cavity-stabilized laser (ISI custom design) is being transmitted from ISI to BEV over the fibre link with active fibre noise cancellation (FNC). In BEV, the beat note between the link output and a local 1542.14 nm Menlo Systems ORS optical reference system is measured. H-masers operating at ISI and BEV are left free-running and are adjusted if needed. They serve as low-noise flywheels in atomic clock ensembles at both sites.
3.1 Composite optical frequency reference at ISI
The structure of the stable optical frequency reference at ISI is depicted in Fig. 3 at the left side. The core of the reference is a fibre laser (NKT Koheras Basik) operating at a wavelength of 1540.57 nm (L1540). Initial self-heterodyne measurements have shown that the fibre laser exhibits a visible residual phase noise up to the Fourier frequency of 20 kHz. For that reason, we are using phase noise suppression based on locking the lasers optical frequency to an optical resonator with ultra-high finesse of approx. $4.5\times 10^{5}$ using the Pound-Drever-Hall (PDH) technique. The resonator is manufactured from an ultra-low-expansion material (ULETM) by Stable Laser Systems. The high finesse of the resonator yields a narrow spectral response with a full width at half maximum (FWHM) of approx. 5 kHz. Thus, it provides enough sensitivity for detecting laser frequency changes down to sub-Hz level. The resonator is placed in a vacuum chamber and temperature stabilized to a level better than 1 mK. The bandwidth of the control loop steering the L1540 is approx. 200 kHz. The loop filter response of this control loop is tuned to yield a 20 dB phase noise suppression at 20 kHz Fourier frequency and to approx. 100 dB suppression near DC.
Fig. 3. Overall setup of the experimental 235 km long fibre link between ISI and BEV. Legend (in alphabetical order): AOM - acousto-optic modulator, CLA BiDi - Czech Light EDFA for single path bidirectional stable wavelength transmission, CTR - frequency counter, DRIFT COMP. - optical resonator drift compensation controller, FNC control - fiber noise cancellation controller (see section 3.3 and Fig. 4), FIBRE LINK - long-haul fibre link (see section 2. and Fig. 2), FM - Farraday mirror, ISOL. - optical isolator, L1540 - Koheras Basik @ 1540.57 nm, L1542 - Koheras Basik @ 1542.14 nm, $\Delta \nu$ - frequency difference between a pair of COMB1 and COMB2 teeth, PD - photodetector, ORS 1542 - MenloSystems ORS @ 1542.14 nm, PLL - phase-locked-loop controller, RFSA - RF spetrum analyzer, RF SYNTH. - RF synthesizer; blue lines - optical signals; black lines - electrical signals.
Because the length of the resonator drifts due to the aging effect of the ULE material, the laser locked to the resonator follows slow changes in resonant frequency with a long-term linear trend of approx. 70 mHz$\cdot$s-1. To eliminate optical frequency drifts, the following disciplining scheme is used. The laser output is coupled to an optical frequency comb (COMB1) setup via an acousto-optic modulator AOM1. The COMB1 is Menlo Systems M-Comb with 250 MHz repetition rate. For fast locking of its repetition frequency (400 kHz bandwidth) to external optical reference, the COMB1 is equipped with intracavity electro-optic modulator (EOM). Using this EOM in a control loop COMB1 is optically referenced to the optical frequency of L1540, which means its repetition frequency $f_{rep1}$ is steered by a servo loop so a frequency offset between the L1540 and the nearest comb tooth remains constant. The offset frequency $f_{ceo1}$ of the COMB1 is locked to the local active hydrogen maser H-MASER1 (T4 Science iMaser 3000) with servo loop bandwidth of approx. 7 kHz (pump diodes current modulation). Any change in the reference laser frequency of the L1540 will result in a deviation of the $f_{rep1}$. Therefore, the $f_{rep1}$ is being monitored using a sensitive digital phase detector referenced by the H-MASER1. The phase deviation from zero is then minimized by the controller steering the AOM1 in the servo loop. The result of this complex set-up is a 1540.57 nm laser wave with a narrow spectral peak thanks to the optical resonator lock reducing the residual phase noise of the L1540 up to Fourier frequencies of approx. 20 kHz and long-term fractional frequency stability as good as $10^{-15}$ in $10^{4}$ s transferred from the H-MASER1 (see section 4.2 for H-MASER1 fractional frequency stability), as well as a frequency highly stable and coherent optical frequency comb spectrum generated by the COMB1.
To match the working wavelength of the stabilized fibre link and of the laser at BEV, another fibre laser (NKT Koheras Basik) working at 1542.14 nm (L1542) is phase locked to an appropriate comb tooth of the COMB1. The radiation of the L1542 is then disseminated over the long-haul link to BEV. The operating wavelength of L1542 is in accordance with the optical frequency band centre of the ITU channel 44. The locking principle of the L1542 utilizes an offset beat scheme where a beat note signal as a product of the L1542 and the tooth of the COMB1 optical mixing is compared by a phase detector with the reference signal from the H-MASER1. The output error of the phase detector is minimized by a fast analogue phase-locked-loop controller (PLL) with bandwidth of approx. 150 kHz controlling the wavelength of L1542 and thus narrowing its spectral peak. The $f_{ceo1}$ signal subtraction from the L1542 and COMB1 beat note is not necessary since the residual phase noise power spectral density (PSD) of the $f_{ceo1}$ signal affecting the selected tooth at 1542.14 nm, which is still relatively close to the tooth used for locking the COMB1 to the L1540 reference, is approx. $10^{-8}$ rad2$\cdot$Hz-1 in the worst case. This value is still several orders of magnitude below the fibre-link phase noise PSD levels as will be shown in section 4.1.
3.2 Optical frequency reference at BEV
The structure of the stable optical frequency reference at BEV is shown in Fig. 3 at right side. BEV operates an ultra-low noise optical frequency comb (Menlo Systems FC1500-250-ULN) with both the offset $f_{ceo2}$ and repetition $f_{rep2}$ frequency locked to a local active hydrogen maser H-MASER2 (Symmetricom MHM 2010). The optical frequency comb at BEV (COMB2) is equipped with EOMs for fast locking of its repetition and offset frequencies with approx. 400 kHz loop bandwidth. While locked to a radio frequency reference the residual root mean square (RMS) phase noise of $f_{rep2}$ signal is $9.13\times 10^{-4}$ rad (integrated over 1 Hz–10 kHz) and the residual RMS phase noise of $f_{ceo2}$ beat signal is $6.73\times 10^{-2}$ rad (integrated over 100 Hz–2 MHz).
The COMB2 adopting its fractional frequency stability from H-MASER2 is used for measuring the optical frequency of the highly coherent Menlo Systems ORS optical reference system working at 1542.14 nm deployed at BEV (ORS 1542). The ORS 1542 is a RIO Planex diode laser that is locked to an external ULE resonator with the PDH technique. The optics compartment of ORS 1542 includes a vacuum system, which shields the resonator from acoustic and thermal fluctuations. The laser’s wavelength is 1542.14 nm (ITU channel 44) and its high short time stability reaches 10-14 to 10-15 for 102 s integration time. The ORS 1542 frequency drifts because of the aging of the ULE resonator material at a rate of roughly 20 mHz$\cdot$s-1. The simultaneous measurement of the optical frequency of the ORS 1542 with the help of the COMB2 allows for off-line compensation of the ORS 1542 drift.
3.3 Fibre link noise cancellation setup
From the optical point of view, our fibre noise cancellation setup uses a general scheme based on a Michelson interferometer with a fibre noise cancellation AOM2 with a nominal frequency $f_{AOM2}$=80 MHz and an end-shifter AOM3 with a nominal frequency $f_{AOM3}$=40 MHz [43–45].
The FNC controller electronics processes a 240 MHz in-loop beat, detected by a fast photodetector (PD2). The electronics is a custom design developed by ISI. The signal chain is based on an analog I/Q demodulator processing the primary RF signal, a loop filter realized by a 32-bit digital signal processor (DSP) and a dedicated direct digital synthesizer chip (DDS) driving the fibre noise cancellation AOM2, see Fig. 4. The high-performance DSP ($f_{CPU}$=480 MHz, 2024 CoreMark/1027 DMIPS) used in the setup is STMircoelectronics STM32H753 [46], which allows real-time signal processing with sampling rates up to several MS$\cdot$s-1. The advantage of using mixed analog/digital design is that the analog I/Q demodulation does not consume any computing power of the DSP. This allows achieving higher phase detection bandwidth than in the case of I/Q demodulation realized by software processing on the same hardware platform. The in-loop beat note signal is filtered by a band-pass filter BP with the central frequency of 240 MHz followed by a RF amplifier A and converted to a 100 MHz intermediate frequency signal by a double-balanced RF mixer MIX. The intermediate frequency is defined as a difference between the nominal signal frequency of 240 MHz and the local oscillator LO reference frequency of 140 MHz generated by the four-channel DDS chip (Analog Devices AD9959), the channel DDS CH3. After consecutive filtering by an intermediate frequency band-pass filter BP with the center frequency of 100 MHz, the signal is amplified by the next RF amplifier A and led to inputs of two parallel double-balanced mixers 2 x MIX that form an I/Q demodulator producing the pair of baseband in-phase and quadrature (I and Q) signals. The 100 MHz reference signals I reference and Q reference for the I/Q demodulator are generated by the DDS channels DDS CH1 and DDS CH2 respectively and mutually phase shifted by $\frac {1}{2}\pi$ rad. Finally the I and Q signals are processed by a pair of anti-aliasing low pass filters LP with corner frequency of 700 kHz to match the sampling criterion of the ADC. The instantaneous phase of the intermediate frequency signal relative to the I/Q demodulator reference is computed by the DSP from the pair of I and Q signals. These signals are being digitized by a two–channel 16-bit analog-to-digital (ADC) converter with sampling rate $f_s$ = 2 MS$\cdot$s-1. Working with the quadrature pair of baseband signals allows to separate the information about the beat note phase from the amplitude fluctuations. Since this solution does not require any digital frequency dividers for the input signal, it provides a higher immunity to drops in beat note signal-to-noise ratio than legacy analogue methods based on double-balanced phase detectors working in $\pm \frac {1}{2}\pi$ rad range or phase-frequency detectors [47,48]. The unwrapped instantaneous phase of the signal is represented by a 32-bit value where the 16 least significant bits represent the fraction of the $2\pi$ rad cycle and the 16 most significant bits represent the number of whole $2\pi$ rad cycles. The theoretical resolution of the computed phase value is thus $2\pi \cdot 2^{-16}$ rad. The real-time unwrapping extends the phase-tracking interval to $<-2^{16}\pi ;~+2^{16}\pi )$. The described phase detector is able to track the phase of the input signal, provided a sudden excursion of its frequency greater than $\frac {1}{2}f_s$ does not occur during a single sampling period. Afterwards, the unwrapped phase is processed by a cascade of configurable digital filters forming the loop filter: a P-I-D controller and a 1st-order low-pass. Finally a 32-bit tuning word is being output to the channel DDS CH4 (AOM signal) over the SPI bus with 500 kS$\cdot$s-1 sampling rate. Sampling rates of the ADC and DDS are all synchronized to an external clock reference, which is H-MASER1.
Fig. 4. Block schematics of the fibre noise cancellation electronics developed by ISI. Legend (in alphabetical order): A - RF amplifier, ADC - analog to digital converter, AOM - acousto-optic modulator, BP - band-pass filter, DAC - digital to analog converter, DDS - direct digital synthesizer, DSP - digital signal processor, LP - low-pass filter, LO -local oscillator signal, I - in-phase signal, MIX - double-balanced RF mixer, PID - proportional-intergral-derivative controller, Q - quadrature signal, SPI - serial peripheral interface
Due to the round-trip delay of 2.35 ms accumulated on the 235 km long link, the maximum achievable bandwidth of the control loop is approx. 120 Hz [3]. However, for links with a shorter length, the described hardware is capable of control loop bandwidths of up to 50 kHz. The digital signal processor also has implemented a remote configuration of the computational algorithm of the P-I-D controller for the fiber noise cancelation technique. Thanks to this capability, it is possible to tune the control parameters to optimal operation via remote access from a computer.
4. Results and discussion
During the years 2018 - 2020, the ISI-BEV long-haul phase-coherent fibre link was built. The complex optical setups and electronics were developed, optimized, and finally installed in both ISI and BEV laboratories. In 2021, pilot measurements took place, which led to the fine-tuning of particular control loops, minimization of drifts of ISI L1542 and ORS 1542 references, and the effective fibre noise cancelation of the ISI-BEV link. The measuring campaign was carried out during September and October of 2021 followed by processing and verification of all measured signals.
4.1 Phase noise measurement
Figure 5 shows phase noise PSD of the beat note between the ISI L1542 laser transmitted over the 235 km long link and the BEV ORS 1542. The chart shows a comparison between phase noise PSD measured with the stabilized and with the free-running link. The control loop bandwidth is approx. 120 Hz. Under given conditions, fibre noise cancellation is most effective for Fourier frequencies below 10 Hz. The integrated RMS phase noise of the beat note in the 1–10 Hz Fourier frequency interval is 318.3 rad for a free-running link and 1.3 rad for the stabilized link. This is approximately the same amount of noise as produced by a laser with a line width of 5 Hz, which is also shown for comparison in the chart.
Fig. 5. Phase noise power spectral density of the observed beat note between the link end at BEV and the local ORS laser for stabilized operation of the link (solid red) and free-running operation of the link (solid blue). The in-loop beat phase noise power spectral density measured at the trasmitting side in locked operation (dashed cyan) and a theoretical phase noise power spectral density of a 5-Hz linewidth laser (dashed black) are shown for comparison.
4.2 Fractional frequency stability
The chart in Fig. 6 shows the test-report data of the H-masers and catalogue values of the ORS 1542 laser for comparison [49], which contribute to the measured fractional frequency stability between ISI and BEV references as described further. As can be seen in the chart, according to the manufacturer’s test reports, the best fractional frequency stability of H-MASER1 of approx. $1\times 10^{-15}$ can be observed for the integration time in the vicinity of $10^{4}$ s. H-MASER2 achieves fractional frequency stability better than $3\times 10^{-15}$ for integration time above $10^{4}$ s. The cavity-stabilized ORS 1542 laser on the other hand exhibits fractional frequency stability better than both H-masers for integration time under 35 s.
Fig. 6. Fractional frequency stability of ISI (red) and BEV (blue) H-masers from manufacturer test reports. Catalogue values of fractional frequency stability of the ORS 1542 (yellow) [49]. Expressed by the means of overlapping Allan deviation $\sigma _{y}$ vs. integration time $\tau$.
At both sides of the link, long-term drifts of local cavity-stabilized lasers are being monitored by beating with optical frequency combs referenced to local active H-masers. At the ISI side this long-term drift is actively eliminated with a slow servo loop with a bandwidth of $10^{-2}$ Hz, which was described earlier.
Since at the present time the link does not have any independent return path to perform out-of-loop measurement, a long-term measurement of the in-loop beat frequency at the transmitting side was conducted to asses the link stability. We used an Agilent 53230A frequency counter switched to $\Pi$ regime by using "RCON" command [50]. The $\Pi$ regime was chosen to assure the measured frequency data can be used for computing Allan deviations by its original definition [51,52]. From this data set the fractional stability of the optical frequency transfer was computed by the means of the overlapping Allan deviation shown in Fig. 7. For locked operation, the presented in-loop beat measurement gives an idea of the maximum achievable stability of the link omitting additional perturbations introduced for example by uncompensated fibre optic components. It can be seen that for the phase-stabilized link the values converge to less than $7\times 10^{-18}$ for integration times greater than $10^{3}$ s. The fractional stability of the free-running fibre link however resides in 10-14 to 10-13 order of magnitude for integration times below 104 s.
Fig. 7. Fractional frequency stability between ISI and BEV H-masers measured using the fibre link by the means of $\Delta \nu$ difference frequency (thick black), see Fig. 3 and text. Measured fractional optical frequency transfer stability for free-running (yellow) and Doppler-compensated link (violet). For comparison: Theoretical fractional frequency stability between the masers (blue); Fractional stability between the H-masers measured by the GNSS common-view technique (red). Expressed by the means of overlapping Allan deviation $\sigma _{y}$ vs. integration time $\tau$.
At the BEV side, the beat note between the link output and the local laser detected by PD 4 is being band-pass filtered by a tracking oscillator with 10 Hz bandwidth and its frequency measured by a K+K Messtechnik FXE80 frequency counter CTR2 working in the $\Pi$ regime. The frequency difference between the ORS 1542 laser and a tooth of the COMB2 referenced by the local H-MASER2 is detected by PD 3 and measured simultaneously by frequency counter CTR1 (K+K FXE80). After subtracting these measured frequencies as outlined in Fig. 3 we are in-fact measuring remotely the frequency difference between the closest pair of COMB1 and COMB2 teeth, while COMB1 is referenced by H-MASER1 and COMB2 is referenced by H-MASER2. Provided the optical frequency combs are operating with identical repetition frequencies and therefore the index of the utilized comb tooth $N$ closest to the operating optical frequency of the link is the same at both sites, the difference frequency referred as $\Delta \nu$ in Fig. 3 can be expressed as $\Delta \nu =N(f_{HM1}-f_{HM2})+f_{OFFS}$, where $f_{HM1}$ is the reference frequency produced by H-MASER1, $f_{HM2}$ is the reference frequency produced by H-MASER2. The additive term $f_{OFFS}$ is a sum of all offset frequencies present in the link setup (L1542 offset from COMB1 tooth, $f_{ceo1}, f_{ceo2}, f_{AOM2}, f_{AOM3}$). Sub-mHz short-term fluctuations of $f_{OFFS}$ at 1 s integration time are negligible to the operating optical frequency. Thus, the fractional stability of $\Delta \nu$ relative to the operating optical frequency of the link should be interpreted as the remotely measured fractional frequency stability between H-MASER1 and H-MASER2.
The measured fractional stability of the $\Delta \nu$ value relative to the working optical frequency of the 1542.14 nm lasers is shown in Fig. 7 as a thick black curve. For integration time $\tau$ shorter than 100 s, the graph reveals the fractional frequency stability between the ISI and BEV lasers. It is apparent that the short-term part of the curve (for $\tau <3~s$) is limited by the fractional stability of the optical frequency transfer. For $\tau$ above 100 s, the plot is in agreement with the expected fractional frequency stability between the active H-masers referencing the local optical frequency combs at the end points of the link. For comparison with other long-haul fractional frequency stability measurement methods, the data obtained using global navigation satellite system (GNSS) common-view measurement technique [53,54] is also provided in Fig. 7. As is clearly visible, the phase-coherent fibre link has an unprecedently lower phase noise and confirms privileged position in the process of remote comparison of highly-stable frequencies generated by references working with fractional frequency stability $10^{-14}$ and better.
4.3 Long-term operation of the link
In addition to evaluating the mutual stability of ISI and BEV references, we were also interested in the level of phase-noise suppression for a time interval of several days. Figure 8 shows the evolution of the in-loop beat phase noise PSD for a set of selected Fourier frequencies measured at PD 2 by the FNC electronics. The visible drop out was caused intentionally to demonstrate the amount of in-loop beat fibre noise suppression. The set of spectrum monitoring data starts on a Tuesday (October 12th 2021) and ends on Saturday (October 16th 2021). In urban areas like Brno and Wien the road traffic is the most intense during day hours of business days. The least traffic is at night and during weekend days. It can be observed that the amount of the residual phase noise fluctuates on a time-of-day and day-of-week basis in correlation with changes in road traffic intensity.
Fig. 8. Evolution of in-loop beat phase noise power spectral density during a 4-day measurement shown for a set of selected Fourier frequencies.
5. Conclusion and outlook
The presented results prove the long-term functionality of the coherent fibre link established between ISI and BEV. We have shown that it is suitable for disseminating a stable optical frequency reference using ITU channel 44 with high fractional frequency stability over a wide interval of integration times. The deployed fibre noise cancellation electronics with digital signal processing applied on beat note phase calculation and loop filtering is able to cope with time varying signal-to-noise ratio of the in-loop beat and large optical frequency excursions due to Doppler effect occurring in urban fibre networks.
The next step is the completion of the phase-coherent fibre link from BEV to TU Wien (24 km), where a new optical reference at the wavelength of 1542.14 nm is currently being put into operation. A frequency chain for synchronizing the VUV optical frequency comb at TU Wien, which is the basis of the Th-229 nuclear clock experiment, is also under construction. The proven ISI - BEV line will be used for a unique implementation of delocalized atomic clock network in central Europe.
Funding
European Metrology Programme for Innovation and Research (17FUN07, 20FUN01); Grantová Agentura České Republiky (19-14988S); Ministerstvo Školství, Mládeže a Tělovýchovy (CZ.02.1.01/0.0/0.0/164_026/0008460).
Acknowledgments
The work has been performed within the project 17FUN07 CC4C. The final measuring campaign has been supported within the project 20FUN01 TSCAC. Projects 17FUN07 CC4C and 20FUN01 TSCAC both have received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. The research was also supported by projects: 19-14988S (GA CR) and CZ.02.1.01/0.0/0.0/164_026/0008460 (MEYS CR).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
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