Fractional Frequency Instability Research Articles

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.

Dissemination of UTC(NIST) over 20 km of commercial optical fiber with active phase stabilization.

We demonstrate the transfer of a cesium frequency standard steered to UTC(NIST) over 20 km of dark telecom optical fiber. Our dissemination scheme uses an active stabilization technique with a phase-locked voltage-controlled oscillator. Out-of-loop characterization of the optical fiber link performance is done with dual-fiber and single-fiber transfer schemes. We observe a fractional frequency instability of 1.5 × 10-12 and 2 × 10-15 at averaging intervals of 1 s and 105 s, respectively, for the link. Both schemes are sufficient to transfer the cesium clock reference without degrading the signal, with nearly an order of magnitude lower fractional frequency instability than the cesium clocks over all time scales. The simplicity of the two-fiber technique may be useful in future long-distance applications where higher stability requirements are not paramount, as it avoids technical complications involved with the single-fiber scheme.

Operation of a Ramsey-CPT microcell atomic clock with driving current-based power modulation of a VCSEL

We report on the operation of a coherent population trapping (CPT) microcell atomic clock using a pulsed Ramsey-like interrogation. The Ramsey-CPT sequence, defined by two-step optical pulses separated by a free-evolution dark time, is produced by switching on and off the output power of a low-power vertical-cavity surface-emitting laser, through direct modulation of its driving current. High-contrast and narrow Ramsey-CPT fringes are detected without the use of any external optical modulator stage. We demonstrate closed-loop operation of the clock based on high-speed digital signal processing implemented in a field programmable gate array board. The clock's short-term fractional frequency stability is 1.3 × 10−10τ−1/2 until 2000 s. A power light-shift coefficient of 8 × 10−11/μW, in relative value, is obtained for a dark time of 150 μs. This value is about ten times lower than in the continuous regime. These results show the feasibility of fully integrated atomic clocks based on Ramsey spectroscopy, which could provide enhanced long-term stability.

Coherent photo-thermal noise cancellation in a dual-wavelength optical cavity for narrow-linewidth laser frequency stabilisation.

Optical resonators are used for the realisation of ultra-stable frequency lasers. The use of high reflectivity multi-band coatings allows the frequency locking of several lasers of different wavelengths to a single cavity. While the noise processes for single wavelength cavities are well known, the correlation caused by multi-stack coatings has as yet not been analysed experimentally. In our work, we stabilise the frequency of a 729 nm and a 1069 nm laser to one mirror pair and determine the residual-amplitude modulation (RAM) and photo-thermal noise (PTN). We find correlations in PTN between the two lasers and observe coherent cancellation of PTN for the 1069 nm coating. We show that the fractional frequency instability of the 729 nm laser is limited by RAM at 1 × 10-14. The instability of the 1069 nm laser is at 3 × 10-15 close to the thermal noise limit of 1.5 × 10-15.

Terahertz microcomb oscillator stabilized by molecular rotation

Controlling the coherence between light and matter has enabled the radiation of electromagnetic waves with a spectral purity and stability that defines the Système International (SI) second. Transitions between hyperfine levels in atoms are accessible in the microwave and optical domains, but faithfully transferring such stability to other frequency ranges of interest requires additional components such as optical frequency combs. Such spectral purity and stability are specifically sought out for the terahertz domain for both scientific and commercial applications, including precision studies of molecular physics, next-generation wireless communications, quantum sensors, and terahertz frequency standards. Currently, there is a lack of native frequency references in this spectral range, which is essential for the consistency of measurements and traceability. Small-scale terahertz oscillators, which leverage dissipative Kerr soliton microcombs, present a promising avenue for the generation of terahertz waves that rival the spectral purity of electronic alternatives. Here, we experimentally demonstrate the rotational spectroscopy of nitrous oxide (N2O) with a microcomb-based oscillator. To mitigate the frequency drift encompassed in such waves, we lock the frequency of the microcomb terahertz oscillator to that of a rotational transition of N2O, reducing the fractional frequency stability to a level of 5 × 10−12 at 10 s of averaging time. These results constitute a high performance terahertz oscillator that can be scaled down to a compact size while circumventing the need for frequency multiplication or division of frequency standards. This demonstrates a foundational component needed for future terahertz applications.

A complete analysis of the link uncertainty budget for pulsed laser time transfer on China space station

High-precision Time-Frequency Rack (HTFR) mission, a part of experiment module II of the China Space Station (CSS), was equipped with a Sr optical clock, H-maser, and laser-cooled microwave clock. To compare time and frequency across widely separated clocks, a microwave link, and a pulsed laser link were both established, which probably enables new possibilities for fundamental science, geodesy, and metrology. Based on the existing relativistic theory for time and frequency transfer, we derive a relativistic model of satellite-ground laser time transfer on CSS (CLT), which can be of direct use in CLT data processing. In addition to first and second-order Sagnac effects, it also includes relativistic rate shifts, atmospheric refraction, and turbulence, laser retroreflector array (LRA) range correction, and position correction between detector and reflector, satisfying the stability evaluation of CSS atomic clocks with fractional frequency stability of 3 × 10−17/10000 s. Additionally, we numerically investigate the link error magnitude and use Monte Carlo simulations to assess the impact of correcting for link errors on the stability of the CLT, taking into account the CSS orbit and attitude determinations as well as the CLT payload calibration parameters. It is shown that the CLT link can be considered to reach a TDEV of approximately 0.1 ps/300 s while meeting the CSS design objectives. The primary factors that influence the stability of the CLT are the position correction between detector and reflector, LRA range correction, and the coupling relation of these two error distributions.

Single-Element Dual-Interferometer for Precision Inertial Sensing: Sub-Picometer Structural Stability and Performance as a Reference for Laser Frequency Stabilization.

Future GRACE-like geodesy missions could benefit from adopting accelerometer technology akin to that of the LISA Pathfinder, which employed laser interferometric readout at the sub-picometer level in addition to the conventional capacitive sensing, which is at best at the level of 100 pm. Improving accelerometer performance holds great potential to enhance the scientific output of forthcoming missions, carrying invaluable implications for research in climate, water resource management, and disaster risk reduction. To reach sub-picometer displacement sensing precision in the millihertz range, laser interferometers rely on suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods are available with varying levels of complexity, size, and performance. In this paper, we describe the performance of a Mach-Zehnder interferometer based on a compact monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in 1013, corresponding to an interferometer pathlength stability better than 1pm/Hz. The prism was designed to host a second interferometer to interrogate the position of a test mass. This optical scheme has been dubbed "single-element dual-interferometer" or SEDI.

Phase-Noise Characterization in Stable Optical Frequency Transfer over Free Space and Fiber Link Testbeds

Time and frequency metrology depends on stable oscillators in both radio-frequency and optical domains. With the increased complexity of the highly precise oscillators also came the demand for delivering the oscillators’ harmonic signals between delocalized sites for comparison, aggregation, or other purposes. Besides the traditional optical fiber networks, free-space optical links present an alternative tool for disseminating stable sources’ output. We present a pilot experiment of phase-coherent optical frequency transfer using a free-space optical link testbed. The experiment performed on a 30 m long link demonstrates the phase-noise parameters in a free-space optical channel under atmospheric turbulence conditions, and it studies the impact of active MEMS mirror stabilization of the received optical wave positioning on the resulting transfer’s performance. Our results indicate that a well-configured MEMS mirror beam stabilization significantly enhances fractional frequency stability, achieving the−14th-order level for integration times over 30 s.

An ultra-stable laser based on molecular iodine with a short-term instability of 3.3 × 10−15 for space based gravity missions

Many space based gravity missions require frequency stabilized lasers with stringent requirements. Toward those requirements, we develop a compact frequency-stabilized laser which is referenced to the R(56)32−0: a1 transition of molecular iodine based on the modulation transfer spectroscopy technique. The stability of the laser is limited by the beam pointing noise, the electronic servo noise, and the residual amplitude modulation (RAM) noise. To improve the beam pointing stability, the system is constructed by gluing most components of the optical system on an ultra-low expansion glass base. We use a pre-amplifier to suppress the electronic servo noise, and use a wedged electro-optic phase modulator to suppress the RAM noise. The fractional frequency instability of the system is evaluated to be 3.3 × 10−15 at 2 s and 4 s averaging time, and is lower than 6 × 10−15 at averaging times from 1 s to 10 000 s. To our knowledge, this is the best short-term (1–4 s) instability reported so far for an iodine stabilized laser. The stability fully meets the requirements of next generation gravity mission and laser interferometer space antenna mission.

Experimental demonstration of weak-light inter-spacecraft clock jitter readout for TianQin.

The space-based gravitational wave detection mission, TianQin, requires high-level synchronization between independent clocks of all spacecrafts to extract the gravitational wave signals. It is necessary to measure the inter-spacecraft relative clock jitter based on laser phase-sideband clock transfer. The main challenge is the tracking and locking of clock sideband beatnote signals with low signal-to-noise ratio and frequency variation. In this paper, a systematic scheme of inter-spacecraft clock jitter readout is reported. The requirement of the clock transfer link for TianQin based on the time-delay interferometry algorithm is derived. A bi-directional laser interferometer system with a transmission optical power below 1 nW and a time delay of ∼50 µs is built up to demonstrate the weak-light clock transfer. In this scheme, frequency modulation is performed on the laser to simulate the inter-spacecraft Doppler frequency shift and its variation. Based on electrical and optical clock transfer comparison experiments, it is demonstrated that the GHz frequency synthesizer is the main noise source below the 50 mHz frequency range. The residual clock jitter noise introduced by the optical transfer link is below 40 fs/Hz1/2 above the 6 mHz frequency range, and the fractional frequency instability is less than 6.7 × 10-17 at 1000 s, which meets the requirement of the TianQin mission. Ultimately, The carrier phase measurement accuracy reaches 1 × 10-4 cycles/Hz1/2 above 6 mHz after differential clock noise correction using measured clock jitter.

Ultra-stable microwave cryogenic oscillator operated with a Gifford-McMahon cryocooler

We demonstrate for the first time an ultra-stable microwave cryogenic oscillator operated with a Gifford-McMahon (GM) cryocooler. Despite the high level of vibration generated by the GM, we show that an optimised design, with simple passive solutions, enables a sufficient mechanical decoupling to achieve a state-of-the-art frequency stability. The implemented 10 GHz cryogenic oscillator features a fractional frequency stability (ADEV, Allan deviation) σy(τ)<3×10−15 for 1s≤τ≤104s.

Multiple-Branch Optical Frequency Transfer Without the Frequency Allocation Constraints

We report on the realization of a multiple-branch optical frequency transfer method, which can be adopted to deliver an optical reference to multiple independent remote sites. In comparison with the previous techniques, the proposed technique mitigates the frequency allocation constraints of the driving frequencies for the acousto-optic modulators (AOMs) at the remote sites by adding a short loop fiber link at the local site. The end-to-end optical path phase noise detection and compensation for each remote site is simultaneously performed at the remote site, which significantly simplifies the configuration at the local site, and can improve the signal-to-noise ratio (SNR) and reduce the cycle slip rate. We also conduct theoretical analysis for the effect of frequency aliasing from the perspective of different refractive index in triple-pass optical frequency transfer, analyze the effect of the SNR and cycle slips on the fractional frequency instability, and present a comprehensive equation for calculating noise contributions from end-to-end optical frequency transfer over the multiple-branch fiber network, demonstrating that the implementation of the fiber noise cancellation (FNC) for the each branch consisting of two fiber topologies with the single FNC setup is practical. This technique paves the way to integrate the optical frequency networks into the existing fiber communication networks with the higher compatibility and reliability.

Realizing spin squeezing with Rydberg interactions in an optical clock.

Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.

Photonic millimeter-wave transfer with balanced dual-heterodyne phase noise detection and cancellation.

We report on the realization of long-haul and high-precision millimeter-wave (mm-wave) transfer through a fiber-optic link based on balanced dual-heterodyne phase noise detection. The balanced dual-heterodyne detection is achieved by detecting the fiber phase noise superimposed two intermediate frequency (IF) signals without requiring a local synchronization signal and its output is used to compensate the fiber-induced phase noise by actuating the frequency of the one optical carrier. The proposed scheme can effectively get rid of the effect of the local reference, largely simplifying the configuration at the local site. Additionally, we model and experimentally study the noise contribution coming from the out-of-band, which can be effectively suppressed to the below of the system noise floor with a fractional frequency instability of 1.9 × 10-17 at 10,000 s by designing and implementing a high-precision temperature control module with a peak-to-peak temperature fluctuation of no more than 0.002 K. We experimentally demonstrate that a 100 GHz mm-wave signal to be transmitted over a 150 km fiber-optic link can achieve the fractional frequency instabilities of less than 3.4 × 10-14 at 1 s and 3.5 × 10-17 at 10,000 s.

Vibration sensitivity minimization of an ultra-stable optical reference cavity based on orthogonal experimental design

Abstract The ultra-stable optical reference cavity (USORC) is a key element for a variety of applications. In this work, based on the orthogonal experimental design method, we study the vibration sensitivity optimization of a classical USORC with a 100 mm length. According to a test of 4 levels and 3 factors, the L 16 (43) orthogonal table is established to design orthogonal experiments. The vibration sensitivities under different parameters are simulated and analyzed. The vibration sensitivities in three directions of the USORC are used as three single-object values, and the normalized sum of the three vibration sensitivities is selected as comprehensive object values. Through the range analysis of the object values, the influence degrees of the parameters on the three single objects and the comprehensive object are determined. The optimal parameter combination schemes are obtained by using the comprehensive balance method and the comprehensive evaluation method, respectively. Based on the corresponding fractional frequency stability of ultra-stable lasers, the final optimal parameter combination scheme A1B3C3 is determined and verified. This work is the first to use an orthogonal experimental design method to optimize vibration sensitivities, providing an approach to vibration sensitivities optimization and is also beneficial for the vibration sensitivity design of a transportable USORC.

A cryogenic sapphire resonator oscillator with 10−16 mid-term fractional frequency stability

We report in this Letter the outstanding frequency stability performance of an autonomous cryogenic sapphire oscillator (CSO) presenting a flicker frequency noise floor below 2×10−16 near 1000 s of integration time and a long-term Allan deviation limited by a random walk process of ∼1×10−18τ. The frequency stability qualification at this level called for the implementation of sophisticated instrumentation associated with ultra-stable frequency references. This result is technologically sound as it demonstrates the potentiality of the CSO technology. From the physical point of view, it sets an upper limit to the ultimate noise floor of the cryogenic microwave resonator that is competitive to that of the ultra-stable optical Fabry–Pérot cavities.

Stabilized free space optical frequency transfer using digitally enhanced heterodyne interferometry.

Free-space continuous-wave laser interferometry using folded links has applications in precision measurement for velocimetry, vibrometry, optical communications, and verification of frequency transfer for metrology. However, prompt reflections from the transceiver optics degrade the performance of these systems, especially when the power of the returning signal is equal to or less than the power of the prompt reflections. We demonstrate phase stabilized free-space continuous-wave optical frequency transfer that exploits the auto-correlation properties of pseudo-random binary sequences to filter out prompt reflections. We show that this system significantly improves the stability and robustness of optical frequency transfer over a 750 m turbulent free-space channel, achieving a best fractional frequency stability of 8 × 10-20 at an integration time of τ = 512 s, and cycle-slip-free periods up to 162 min.

A chip-scale atomic beam clock

Atomic beams are a longstanding technology for atom-based sensors and clocks with widespread use in commercial frequency standards. Here, we report the demonstration of a chip-scale microwave atomic beam clock using coherent population trapping (CPT) interrogation in a passively pumped atomic beam device. The beam device consists of a hermetically sealed vacuum cell fabricated from an anodically bonded stack of glass and Si wafers in which lithographically defined capillaries produce Rb atomic beams and passive pumps maintain the vacuum environment. A prototype chip-scale clock is realized using Ramsey CPT spectroscopy of the atomic beam over a 10 mm distance and demonstrates a fractional frequency stability of ≈1.2 × 10−9/sqrt{tau } for integration times, τ, from 1 s to 250 s, limited by detection noise. Optimized atomic beam clocks based on this approach may exceed the long-term stability of existing chip-scale clocks, and leading long-term systematics are predicted to limit the ultimate fractional frequency stability below 10−12.

Active whispering-gallery microclock in pulsed-operation mode

A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at ${10}^{3}$ s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.

Broadband optical frequency comb covering spectral regions at UV, VIS, and NIR

Herein, we present a compact, robust, self-referenced optical frequency comb (OFC) ranging from ultraviolet (UV) to near-infrared (NIR) light. The OFC system employs an all-polarization-maintained fiber figure-9 fiber oscillation as a seed laser, which is separated into two branches at the same repetition rate of approximately 100 MHz. One branch is adopted to implement frequency stabilization. Herewith, the repetition rate and the carrier-envelope phase are separately stabilized while the residual phase noises are reduced to 504 μrad and 1.12 rad (ranging from 1 Hz to 3 MHz), corresponding to fractional frequency stabilities of 1.91 × 10−12 and 1.44 × 10−17, respectively. The other branch is used to implement supercontinuum generation and quadruplicate frequency nonlinear processes, thus achieving an OFC system in the ranges of 266, 532, and 600–2200 nm. The precise frequency transferring characteristics of this OFC system exhibit great potential for precision measurement applications and optical frequency synchronization.