Optical Frequency Comparison Research Articles

High-Precision Fiber Noise Detection and Comparison over a 260 km Field Fiber Link.

In this paper, we present a high-precision optical frequency noise detection and comparison technique using a two-way transfer method over a 260 km field fiber link. This method allows for the comparison of optical frequencies between remote optical references without the need for data transfer through communication. We extend a previously established two-way comparison technique to obtain all data at the local site. Two optical carrier signals are injected into the bidirectional fiber from both ends, and one carrier is reflected back from the remote end. This enables the phase comparison of the two carrier signals at a single site without the need to transmit experimental data. The common-mode frequency noise induced by the bidirectional fiber link is detected and effectively suppressed without the need for sophisticated active fiber noise control. Our demonstration system, which uses a 260 km field fiber link and a common laser source, achieves a fractional instability of 2.5×10-17 at 1 s averaging time and scales down to 3.5×10-21 at 8000 s. This scheme offers the distinct advantage of completing the comparison at a single site, eliminating the need for remote data transfer via communication. This method is expected to enhance reliability for high-precision frequency comparisons between remote optical clocks and advanced atomic clocks.

Optically synchronized unidirectional optical amplifier-based coherent optical fiber links.

We report on the realization of a unidirectional transmission-based bidirectional erbium-doped fiber amplifier (UTB-EDFA) for the coherent optical fiber links. By applying an optical phase-locked loop (OPLL) between the two unidirectional EDFA (Ui-EDFA) paths, the annoying uncorrelated phase noise between the two paths can be largely suppressed. Promisingly, we can independently optimize the gains of the UTB-EDFAs for bidirectional transmissions, resulting in higher net gain acquired compared with the conventional single-path bidirectional EDFA (SPBA)-based ones. We demonstrate that the fractional frequency instability of the UTB-EDFA-based scheme can be decreased by 26.3% over the most asymmetrical 100 km two-way optical frequency comparison (TWC) system compared with the SPBA-based ones and, more importantly, can acquire higher net gain for unevenly distributed sub-links over ultra-long fiber links, such as 1000 km, by independently optimizing the gains. This technique paves the way for the applications of large-scale fiber networks.

Stability improvement of 40Ca+ optical clock by using a transportable ultra-stable cavity.

The instability of the clock laser is one of the primary factors limiting the instability of the optical clocks. We present an ultra-stable clock laser based on a 30-cm-long transportable cavity with an instability of ∼3 × 10-16 at 1 s-100 s. The cavity is fixed by invar poles in three orthogonal directions to restrict the displacement, meeting the requirements of transportability and low vibration sensitivity. By applying the ultra-stable laser to a transportable 40Ca+ optical clock with a systematic uncertainty of 4.8 × 10-18 and using the real-time feedback algorithm to compensate the linear shift of the clock laser, the short-term stability of the transportable 40Ca+ optical clock has been greatly improved from 4.0×10-15/τ/s to 1.16×10-15/τ/s, measured at ∼100 s-1000 s of averaging time, enriching its applications in metrology, optical frequency comparison, and time keeping.

Nearly-continuous kilometer-scale free-space optical frequency comparison in the presence of Doppler shift

Nearly-continuous kilometer-scale free-space optical frequency comparison in the presence of Doppler shift

Proposal for a hybrid clock system consisting of passive and active optical clocks and a fully stabilized microcomb.

Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of σy(τ) = 9.3 × 10-14τ-1/2 with the averaging time τ, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches σy(τ) = 6.2 × 10-15τ-1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of σy(τ) = 1.9 × 10-11τ-1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.

Proposal for an active whispering-gallery microclock

Optical atomic clocks with compact size, reduced weight and low power consumption have broad out-of-the-lab applications such as satellite-based geo-positioning and communication engineering. Here, we propose an active optical microclock based on the lattice-trapped atoms evanescently interacting with a whispering-gallery-mode microcavity. Unlike the conventional passive clock scheme, the active operation directly produces the optical frequency standard without the need of extra laser stabilization, substantially simplifying the clock configuration. The numerical simulation illustrates that the microclock’s frequency stability reaches at 1 s of averaging, over one order of magnitude better than the recently demonstrated chip-scale optical clock that is built upon rubidium vapor cell and also more stable than current cesium fountain clocks and hydrogen masers. Our work extends the chip-scale clocks to the active fashion, paving the way towards the on-chip quantum micro-metrology, for example, the optical frequency comparison and synchronization between multiple microclocks through frequency microcombs.

Enhanced Phase Noise Reduction in Localized Two-Way Optical Frequency Comparison

High-stability optical frequency comparison over fiber link enables the establishment of ultrastable optical clock networks, having the potential to promote a series of applications, including metrology, geodesy, and astronomy. In this article, we theoretically analyze and experimentally demonstrate a timedelayed local two-way (TD-LTW) optical frequency comparison scheme with improved comparison stability, showing that the fractional instability of optical frequency comparison over a 50- km transfer link can be reduced from $1.30\times10^{-15}$ to $5.25\times10^{-16}$ at the 1 s integration time with an improvement factor of 2.48. Additionally, we also for the first time model and experimentally verify the effect of the inhomogeneous phase noise along the fiber link on the system performance. We believe that the theory and technique proposed here will be helpful in developing the high-stability optical clock networks over large-area fiber links.

Radium Ion Optical Clock.

We report the first operation of a Ra^{+} optical clock, a promising high-performance clock candidate. The clock uses a single trapped ^{226}Ra^{+} ion and operates on the 7s ^{2}S_{1/2}→6d ^{2}D_{5/2} electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1×10^{-13}/sqrt[τ], where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν=9×10^{-16}. Using the clock, we realize the first measurement of the ratio of the D_{5/2} state to the S_{1/2} state Landé g-factors: g_{D}/g_{S}=0.598 805 3(11). A Ra^{+} optical clock could improve limits on the time variation of the fine structure constant, α[over ˙]/α, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

Branching Optical Frequency Transfer With Enhanced Post Automatic Phase Noise Cancellation

We present a technique for coherence transfer of laser light through a branching fiber link, where the optical phase noise induced by environmental perturbations via the fiber link is passively compensated by remote users without the requirements of any active servo components. At each remote site, an acousto-optic modulator (AOM) is simultaneously taken as a frequency distinguisher for distinguishing its unique frequency from other sites' and as an optical actuator for compensating the phase noise coming from the optical fiber. With this configuration, we incorporate a long outside loop path consisting of a fiber-pigtailed AOM into the loop, enabling the significant reduction of the outside loop phase noise in the passive way. To further address the residual out-of-loop phase noise coming from the interferometer and the two-way optical frequency comparison setup, we design a low-noise active temperature stabilization system. Measurements with a back-to-back system show that the stability in our stabilization system is $2\times10^{-16}$ at 1 s, reaching $2\times10^{-20}$ after 10,000 s. Adopting these techniques, we demonstrate transfer of a laser light through a branching fiber network with 50 km and 145 km two fiber links. After being compensated for the 145 km fiber link, the relative frequency instability is $3.4\times10^{-15}$ at the 1 s averaging time and scales down to $3.7\times10^{-19}$ at the 10,000 s averaging time. This proposed technique is suitable for the simultaneous transfer of an optical signal to a number of independent users within a local area.

Unidirectional two-way optical frequency comparison and its fundamental limitations.

High-quality frequency transfer based on existing telecommunication fiber links allows state-of-the-art microwave and optical clocks to be compared on a continental and potentially even intercontinental scale. We present a half-a-year-long data set of unidirectional optical frequency transfer over a 2×43km urban fiber link. We observe a relative frequency instability of 8.0×10-16 at 1 s and at best 6.0×10-18 at 106s integration time. Our results show that the unidirectional two-way method gives the possibility to perform comparisons of international primary standards over fiber links faster than over satellite links. Moreover, we investigate the major limiting factors of such a unidirectional setup.

Characterization of the Frequency Stability of a Multibranch Optical Frequency Comb

Presently, ultra-precise optical clocks’ comparisons can be performed easily using the optical frequency combs (OFCs) as a transfer oscillator. In this scheme, different OFC branches are usually used to enable optical clocks’ comparison at different wavelengths. Some branches may involve processes such as optical amplification, second-harmonic generation, self-phase modulation, and propagation through fibers. Such processes can degrade the stability of the comparison if they are uncommon between branches. In this article, a technique is introduced to investigate the applicability of multibranch OFCs to perform ultra-precise optical frequency comparisons. This technique is based on generating a software-transfer beat (STB) between the OFC branches under investigation and the fundamental or the second-harmonic outputs from a frequency-stabilized laser to a hyperfine component from the two-photon transition 5S $_{1/2} \to 5\text {D}_{5/2}$ in rubidium. In addition, a simple compensation scheme is proposed to enhance the relative stability between OFC branches to enable the comparison of the best available optical clocks.

Ultra-broadband dual-branch optical frequency comb with 10−18instability

Coherently bridging across wide spectral regions in the optical domain with ultra-high precision will enable progress in optical spectroscopy and time and frequency metrology. We report optical frequency synthesis at the 10−18 instability level based on a novel technique actively canceling the differential phase noise of a dual-branch Er-fiber based optical frequency comb spanning 500–2200 nm. We validate the method with an out-of-loop measurement demonstrating the stability transfer from 1560 nm to 780 nm with an instability level at 3×10−18 at 1 s averaging time and 1×10−19 at 1000 s (approximately averaging on 1×10−17/τ), limited mainly by uncompensated optical interferometers used to detect optical beatnotes. To confirm this limitation, we propose an experimental setup that eliminates the excess noise induced by uncompensated optical paths and show that the proposed method exhibits an ultimate unprecedented instability level at 6×10−19 at 1 s averaging time when two optical signals can share a common photodetector. The system realized becomes a powerful and universal tool for optical frequency comparison and spectral purity transfer across the visible and infrared domains.

Optical-Frequency Measurements with a Kerr Microcomb and Photonic-Chip Supercontinuum

Dissipative solitons formed in Kerr microresonators may enable chip-scale frequency combs for precision optical metrology. Here we explore the creation of an octave-spanning, 15-GHz repetition-rate microcomb suitable for both f-2f self-referencing and optical-frequency comparisons across the near infrared. This is achieved through a simple and reliable approach to deterministically generate, and subsequently frequency stabilize, soliton pulse trains in a silica-disk resonator. Efficient silicon-nitride waveguides provide a supercontinuum spanning 700 to 2100 nm, enabling both offset-frequency stabilization and optical-frequency measurements with >100 nW per mode. We demonstrate the stabilized comb by performing a microcomb-mediated comparison of two ultrastable optical-reference cavities.

Hybrid fiber links for accurate optical frequency comparison

We present the experimental demonstration of a local two-way optical frequency comparison over a 43-km-long urban fiber network without any requirement for measurement synchronization. We combined the local two-way scheme with a regular active noise compensation scheme that was implemented on another parallel fiber leading to a highly reliable and robust frequency transfer. This hybrid scheme allowed us to investigate the major limiting factors of the local two-way comparison. We analyzed the contributions of the interferometers at both local and remote locations to the phase noise of the local two-way signal. Using the ability of this setup to be injected by either a single laser or two independent lasers, we measured the contributions of the demodulated laser instabilities to the long-term instability. We show that a fractional frequency instability level of 10−20 at 10,000 s can be obtained using this simple setup after propagation over a distance of 43 km in an urban area.

Laser-Frequency Stabilization Based on Steady-State Spectral-Hole Burning inEu3+∶Y2SiO5

We present and analyze a method of laser-frequency stabilization via steady-state patterns of spectral holes in Eu(3+)∶Y(2)SiO(5). Three regions of spectral holes are created, spaced in frequency by the ground-state hyperfine splittings of (151)Eu(3+). The absorption pattern is shown not to degrade after days of laser-frequency stabilization. An optical frequency comparison of a laser locked to such a steady-state spectral-hole pattern with an independent cavity-stabilized laser and a Yb optical lattice clock demonstrates a spectral-hole fractional frequency instability of 1.0×10(-15)τ(-1/2) that averages to 8.5(-1.8)(+4.8)×10(-17) at τ=73 s. Residual amplitude modulation at the frequency of the rf drive applied to the fiber-coupled electro-optic modulator is reduced to less than 1×10(-6) fractional amplitude modulation at τ>1 s by an active servo. The contribution of residual amplitude modulation to the laser-frequency instability is further reduced by digital division of the transmission and incident photodetector signals to less than 1×10(-16) at τ>1 s.

Two-way optical frequency comparisons at5×10−21relative stability over 100-km telecommunication network fibers

By using two-way frequency transfer, we demonstrate ultra-high resolution comparison of optical frequencies over a telecommunication fiber link of 100 km operating simultaneously digital data transfer. We first propose and experiment a bi-directional scheme using a single fiber. We show that the relative stability at 1 s integration time is 7 10^18 and scales down to 5 10^21. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. We also implement a real-time two-way frequency comparison over a uni-directional telecommunication network using a pair of parallel fibers. The relative frequency stability is 10^15 at 1 s integration time and reaches 2 10^17 at 40 000 s. The fractional uncertainty of the frequency comparisons was evaluated for the best case to 2 10^20. These results open the way to accurate and high resolution frequency comparison of optical clocks over intercontinental fiber networks.

Direct comparison of a Ca^+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement

Optical frequency comparison of the (40)Ca(+) clock transition ν(Ca)((2)S(1/2-)(2D(5/2), 729 nm) against the (87)Sr optical lattice clock transition ν(Sr) ((1)S(0)-(3)P(0), 698 nm) has resulted in a frequency ratio ν(Ca) / ν(Sr) = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio ν(Ca) / ν(Sr) to reach 1 × 10(-15) in 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of ν(Ca) using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We note that the absolute frequency of (40)Ca(+) we measure deviates from other published values by more than three times our measurement uncertainty.

When should we change the definition of the second?

The microwave caesium (Cs) atomic clock has formed an enduring basis for the second in the International System of Units (SI) over the last few decades. The advent of laser cooling has underpinned the development of cold Cs fountain clocks, which now achieve frequency uncertainties of approximately 5×10(-16). Since 2000, optical atomic clock research has quickened considerably, and now challenges Cs fountain clock performance. This has been suitably shown by recent results for the aluminium Al(+) quantum logic clock, where a fractional frequency inaccuracy below 10(-17) has been reported. A number of optical clock systems now achieve or exceed the performance of the Cs fountain primary standards used to realize the SI second, raising the issues of whether, how and when to redefine it. Optical clocks comprise frequency-stabilized lasers probing very weak absorptions either in a single cold ion confined in an electromagnetic trap or in an ensemble of cold atoms trapped within an optical lattice. In both cases, different species are under consideration as possible redefinition candidates. In this paper, I consider options for redefinition, contrast the performance of various trapped ion and optical lattice systems, and point to potential limiting environmental factors, such as magnetic, electric and light fields, collisions and gravity, together with the challenge of making remote comparisons of optical frequencies between standards laboratories worldwide.

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.

Precision measurement of the 1S ground-state Lamb shift in atomic hydrogen and deuterium by frequency comparison.

We have measured the hydrogen and deuterium 1S Lamb shift by direct optical frequency comparison of the 1S-2S and 2S-4S/4D two-photon transitions. Our result of 8172.874(60) MHz for the 1S Lamb shift in hydrogen is in agreement with the theoretical value of 8172.802(40) MHz. For the 1S Lamb shift in deuterium, we obtain a value of 8183.807(78) MHz, from which we derive a deuteron matter radium of 1.945(28) fm. The precision of our value for the 1S Lamb shift has surpassed that of radio frequency measurements of the 2S-2P Lamb shift. By comparison with a recent absolute measurement of the hydrogen 1S-2S transition frequency, we deduce a value for the Rydberg constant ${\mathit{R}}_{\mathrm{\ensuremath{\infty}}}$=109 737.315 684 9(30) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.