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Abstract
We demonstrate a multi-branch frequency comb for spectral purity transfer incorporating hardware enabled noise cancellation based on a cw noise transfer laser. We verify coherent frequency transfer at stabilities ≈ 2×10−18 in 1 second and < 5×10−21 in 10,000 seconds without any reference cavity.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The extension of optical clocks to wavelengths outside the near infrared spectral range [1,2] will require effective means for coherent frequency transfer across many octaves [3]. For such wide spectral ranges octave spanning supercontinuum generation based on a single amplifier branch [4–7] will not be sufficient for the facilitation of clock comparison. Multi-branch operation allows independent optimization of the signal-to-noise ratio of comb-‘clock laser’ optical beat notes at the expense of phase drift and differential phase noise between the different branches [8,9]. As optical cavities [10] and optical clocks [11] now exhibit stability level in the low parts in 1017 it is essential that optical frequency combs do not hinder measurement of optical frequency ratios [12]. Here we introduce a new method for high precision coherence transfer across essentially any number of amplifier branches with the implementation of simple cw noise transfer lasers that are selected for spectral overlap with the nonlinearly broadened amplifier outputs [13,14]. We demonstrate coherence transfer from 1064 nm to 1560 nm across two amplifier branches with stability ≈ 2×10−18 in 1 second and < 5×10−21 in 10,000 seconds. The method can be easily extended to cover additional spectral ranges, potentially covering even the VUV and mid IR.
Erbium fiber frequency combs are well established for precision clock comparison across different spectral ranges. In fact their relative simplicity and ultra-low noise performance [15] have established erbium frequency combs as the gold standard for precision metrology. However, typical optical clocks require the simultaneous presence of well-defined optical frequencies for their operation, a constraint that is proportionally more difficult to satisfy when clock comparison among a multitude of optical clocks is concerned. To provide the many required wavelengths with high signal/noise ratio from a single branch erbium comb spectrally broadened via supercontinuum generation is therefore beyond the capability of current technology, though some leverage can be obtained via the adaptation of spectral shaping techniques [16].
To overcome these issues Kashiwagi et al. [13] have suggested the use of multi-branch frequency combs with inter-branch noise cancellation which goes beyond the limitations of single-branch combs. Kashiwagi et al. [13] demonstrated a reduction of noise between the non-common amplifier branches using the beats of the generated supercontinua with a common external cw laser reference for branch length stabilization, based on actual physical fiber length stabilization of the various amplifier branches. Giunta et al. [14] improved on these results by implementing a software solution to the noise cancellation problem, relying on the Doppler property of the phase noise φ(ωm) imparted by a fiber of length L, namely its direct scaling with optical frequency. Just as in Kashiwagi et al., for proper frequency comparison across a multi-branch system a common external reference laser is required, which provides a measurement of the inter-branch noise φ(ωm) at frequency ωm. For a selected amplifier branch, the corrected phase noise φ(ωx) at a frequency ωx can then be obtained from φ(ωx) = (ωx/ωm) x φ(ωm), where ωx/ωm is the frequency ratio between the test laser at frequency ωx and the noise transfer laser at ωm. Since the correction can be done in software, no bandwidth restrictions apply, as is unavoidable with an actual physical implementation. In the demonstration by Giunta an ultra-high stability reference laser was used for noise cancellation, whereas noise cancellation was demonstrated by comparison of the relative stability of two frequency combs in different spectral regions.
Here we demonstrate that hardware-based and real-time noise cancellation can be as effective as a software based technique. Since we implement a hardware-based method, the relative frequencies can be obtained without any post processing. Moreover, no precision cavity stabilized laser is required for adequate evaluation of inter-branch phase (frequency) noise. Also we show that noise cancellation can be performed by comparison of single comb lines, which is the scenario as encountered for actual optical clock comparison. As a demonstration we compensate the inter-branch noise of a dual branch Er comb supercontinuum source in a standard laboratory environment. We use a 1550 nm reference laser to monitor the relative inter-branch noise of the dual branch comb and optimize the measurement of the relative frequency stability of the two comb branches at 1064 nm via subtraction of the inter-branch noise at 1550 nm. We demonstrate a relative frequency stability of ≈ 2×10−18 in 1 second and < 5×10−21 in 10,000 seconds at 1064 nm, significantly better than achieved with single branch combs [5–7] and via implementation of noise cancellation software [14]. Evaluation of the modified Allan deviation yields even better results. The monitoring and transmission laser does not necessarily need to be at 1550 nm and 1064 nm. It can be the other way around or any other wavelengths can be chosen. In principle our method can be extended to supply relative frequency stability between spectral lines from the VUV to the mid IR, provided different amplifier branches have some spectral overlap. The spectral overlap can also be provided via additional frequency converting nonlinear crystals.
2. Experiment
The experimental set-up is shown in Fig. 1. We use a commercial erbium frequency comb operating at 200 MHz [17], which provides an output which is split into two branches. The 1st branch is amplified to 200 mW and spectrally broadened to an octave spanning supercontinuum in a 50 cm long highly nonlinear fiber with −1.6 ps/nm/km dispersion. A bulk PPLN doubling crystal follows the fiber output and is used for doubling the 2.2 µm section of the supercontinuumand generating the carrier envelope offset (CEO) frequency signal, which is in turn locked to a Rb disciplined microwave reference. The supercontinuum output covers both the 1064 and 1550 nm spectral regions, where the former is used to lock the comb repetition rate to a commercial cw laser operating at 1064 nm (NKT Koheras BASIK Y10). The 1550 nm output is used to phase lock the cw noise transfer laser (RIO) to the frequency comb. To improve the locking bandwidth of the 1550 nm laser, its output is frequency-shifted through an acousto-optic modulator, providing a frequency modulation of the voltage-controlled oscillator driving the AOM with a bandwidth of about 200 kHz. The output of both cw lasers is split in two and directed to interfere with both the outputs of the 1st and 2nd branch. The second branch is identical to the first branch, but for the PPLN doubling crystal. The beat of the 2nd branch output with the 1550 nm laser is used for interbranch noise measurement and the beat of the 2nd branch output with the 1064 nm is used to measure the effectiveness of interbranch noise cancellation. To minimize interbranch noise, all interferometers are constructed in free space. The 1064 nm beat and 1550 nm beat in each branch are detected from the same broadband polarization beam splitter (PBS)’s rejection and transmission port. The CEO frequency is detected with the same detector as the 1064 nm beat. All the signals have a SN ratio >35 dB at 100 kHz resolution, which is measured with single low noise detectors. We elect to not use dual balanced detectors for detection of the beat signals, which prevents us from getting higher SN ratios, but as a result, we are able to reduce any non-common air-spaces to a length < 30 cm, which is critical for the highest stability. The detrimental effect of external air flows is minimized with a 25 mm thickness acrylic enclosure covering the whole system.
Fig. 1. Experimental set up for fiber noise cancellation. The comb is locked to the 1064 nm cw laser via fb1064. The 1550 nm cw laser is locked to the comb with fb1550 via the acousto-optic modulator (AOM) and is used for measuring the inter-branch noise via fb1550n. The noise cancelled beat at 1064 nm is obtained at the output of the mixer with appropriate scaling factors r1, r2, applied to fb1064n and fb1550n.
To enable noise cancellation in hardware the beat signals at 1064 and 1550 nm (fb1064n and fb1550n) are recorded in the second branch and used as local inputs for two independent microwave frequency synthesizers (Valon). The frequency synthesizers are configured to multiply fb1550n and fb1064n by ratios of r1 = 1/1.064 and r2 = 1/1.550 respectively, to scale the phase noise with optical frequency. The noise cancelled beat fb1064c at 1064 nm is then obtained via mixing the output of the two frequency synthesizers with a dual balanced mixer, which produces an output
Note that though we use two independent frequency synthesizers to generate the noise cancelled beat signal fb1064c we could have equally multiplied fb1550n with a frequency ratio of R = r1/r2 via a direct digital synthesizer to produce a noise cancelled output via mixing with the two beat signals fb1064n and R×fb550n. In clock comparison applications the implementation of the frequency mixer produces a frequency offset, which can however be easily accounted for when calculating the difference frequencies of actual clock signals.
To enable frequency stability measurements at the 10−21 level, the beat signal fb1064c was recorded with a low noise phase meter (Microsemi 3120A). The measurement bandwidth is 0.5 Hz. All the RF cables are cut short and the RF amplifiers are sharing the same cold plate for common temperature. 50,000 seconds acquisition time is needed to collect sufficient data for calculating the Allan deviation at 10,000 seconds. We also varied the ratio of r1/r2 slightly and were not able to improve on the results reported here.
3. Noise cancellation
To verify the validity of the approach, we measured the noise floor of the two DDS’ and the mixer. Figure 2 shows the in-loop Allan deviation of the frequency stability of the mixer output, applying the in-loop fb1064 and fb1550 signals to both DDS’. We obtain a frequency stability < 4×10−19 at 1 second and < 2×10−21 at 2000 second. The Allan deviation increases after 2000 second, whereas the modified Allan deviation continues to average down. We also measured the in-loop Allan deviation of the locked fceo signal and the beat signal of the 1st branch with the cw laser at 1064 nm, which is also shown in Fig. 2. The frequency stability of the in-loop data is at the level of 10−19 at 1 second and averages down as 1/τ with averaging time τ.
Fig. 2. Allan deviation (red dot) and Modified Allan Deviation (red square) of the beat signal between two DDS signals clocked by fb1064 and fb1550. Blue dot and square = in-loop Allan deviation and Modified Allan Deviation of the locked beat signal of the 1st branch with the cw laser at 1064 nm. Black dot and square = in-loop Allan deviation of the locked fceo signal.
The Allan deviation and modified Allan deviation of the out of loop beat signal of the 1064 nm section from the second branch supercontinuum output with the cw 1064 nm reference laser before and after noise cancellation is shown in Fig. 3. We see that noise cancellation can reduce the interbranch noise by a factor of around 30 −100, depending on averaging times. At 1 second we obtain an Allan deviation before noise cancellation of 5*10−17 in 1 second and after noise cancellation we obtain ≈2×10−18. At 10,000 seconds the Allan deviation reduces to 2.7×10−19 before and 4.4×10−21 after noise cancellation. It is interesting that even with noise cancellation we observe a small frequency noise bump at 10 seconds, which is indicative of some residual non-common mode noise, which we attribute to residual non-common free space paths in our bulk interferometers [5,7]; further vibration isolation and operation in vacuum would be needed for further noise reduction. We were also able to ‘eliminate’ the small frequency noise bump by not implementing a tight phase lock of the noise transfer laser to the first branch, i.e. by removing the AOM. The result is shown in Fig. 4, which shows an Allan deviation of 3.4×10−18 at 1 second, an Allan deviation of 1.05×10−18 at 10 seconds and an Allan deviation of 8.6×10−21 at 10000 seconds. The data without AOM are slightly worse than achieved with AOM. The higher noise without AOM measured at 1 second masks the noise bump at 10 s and the stability appears to average down better.
Fig. 3. Red dot and square: Allan deviation and modified Allan deviation of uncorrected fbeat signal fb1064n at 1064 nm. Black dot and square: Allan deviation and modified Allan deviation of noise cancelled fbeat signal fb1064c at 1064 nm.
Fig. 4. Red dot and square: Allan deviation and modified Allan deviation of noise cancelled fbeat signal fb1064c at 1064 nm measured without tight phase locking of the 1550 nm noise transfer laser to the comb, i.e. with and without use of the AOM shown in Fig. 1. Black dot and square: Allan deviation and modified Allan deviation of noise cancelled fbeat signal fb1064c with AOM, i.e. with tight phase locking.
Overall the frequency stability is better than achieved with single branch combs [5–7] due to the higher SN ratio of the beat signals. The frequency stability is also better than achieved with software based noise-cancellation [14], which we attribute to improved thermal shielding in our set-up and reduced non-common paths. Moreover the data from Fig. 3 indicate that slightly better frequency stability should be possible by further minimizing any non-common optical paths by for example inserting the interferometers in Fig. 1 in vacuum. A higher SN ratio for the fbeat signals can improve the relative stability of the two branches further.
4. Conclusions
We have reduced fiber noise in multi-branch frequency comb systems to record low levels, demonstrating an Allan deviation of ≈ 2×10−18 in 1 second and < 5×10−21 in 10,000 seconds by careful minimization of non-common path lengths and implementation of a hardware based noise cancellation technique. The method can be applied to provide a direct estimate of relative stability of optical clock wavelengths spread around multiple octaves without any software post processing and will be invaluable for the definition of a new time standard based on simultaneous evaluation of different clock systems as well as the adaptation of future nuclear clocks.
Disclosures
All authors: IMRA America, Inc. (F,E).
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.
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