Long-term Frequency Instability Research Articles

Node-downloadable frequency transfer system based on a mode-locked laser with over 100 km of fiber.

To meet the requirements of time-frequency networks and enable frequency downloadability for nodes along the link, we demonstrated the extraction of stable frequency signals at nodes using a mode-locked laser under the condition of 100 km laboratory fiber. The node consists of a simple structure that utilizes widely used optoelectronic devices and enables plug-and-play applications. In addition, the node can recover frequency signals with multiple frequencies, which are useful for scenarios that require different frequencies. Here, we experimentally demonstrated a short-term frequency instability of 2.83 × 10-13@1 s and a long-term frequency instability of 1.18 × 10-15@10,000 s at the node, which is similar to that at the remote site of the frequency transfer system. At the same time, frequency signals with different frequencies also achieved stable extraction with the same performance at the node. Our results can support the distributed application under large-scale time-frequency networks.

All polarization-maintaining Er:fiber-based optical frequency comb for frequency comparison of optical clocks

We demonstrate an optical frequency comb (OFC) based on a turnkey mode-locked laser with a figure-9-shape structure and polarization-maintaining fibers, for the comparison of frequency among optical clocks with wavelengths of 698 nm, 729 nm, 1068 nm, and 1156 nm. We adopt a multi-branch approach in order to produce high power OFC signals at these specific wavelengths, enabling the signal-to-noise ratio of the beatnotes between the OFC and the clock lasers to exceed 30 dB at a resolution bandwidth of 300 kHz. This approach makes the supercontinuum spectra much easier to be generated than a single branch OFC. However, more out-of-loop fibers degrade the long-term frequency instability due to thermal drift. To minimize the thermal drift effect, we set the fiber lengths of different branches to be similar, and we stabilize the temperature as well. The out-of-loop frequency instability of the OFC due to the incoherence of the multi-branch is about 5.5 × 10−19 for 4000 s, while the in-loop frequency instability of f ceo and that of f beat are 7.5 × 10−18 for 1 s and 8.5 × 10−18 for 1 s, respectively. The turnkey OFC meets the requirement for the comparison of frequency between the best optical clocks.

Frequency instability of a miniature optically pumped cesium-beam atomic frequency standard.

This paper proposes a miniature optically pumped cesium-beam atomic frequency standard with a volume of 38.4 l and a weight of 28 kg and examines the main factors that affect its signal-to-noise ratio (SNR). Methods to improve the SNR are proposed, which improve the short-term frequency instability: installing a collimator at the exit of the cesium oven, using the beam fluorescence spectrum with the fiber-coupled output to stabilize the laser frequency, and using the 4-5 cycling transition of the cesium D2 line for the atomic detection. We also examine several frequency shifts that affect the long-term frequency instability and detail methods to reduce these shifts. At present, the frequency instability achieved by the Peking University miniature optically pumped cesium-beam frequency standard has reached 3.12×10-12/τ.

Femtosecond synchronization of multiple mode-locked lasers and a microwave oscillator by multicolor electro-optic sampling.

Simple multicolor electro-optic sampling-based femtosecond synchronization of multiple mode-locked lasers is demonstrated. Parallel timing error detection between each laser and a common microwave is achieved by wavelength division multiplexing and demultiplexing. The parallel timing error detection enables simultaneous femtosecond synchronization of more than two mode-locked lasers to the microwave oscillator, even when the lasers have different repetition rates. The residual root-mean-square (rms) timing jitter of laser-laser synchronization measured by an optical cross correlator is 2.6 fs (integration bandwidth, 100 Hz-1 MHz), which is limited by the actuator bandwidth in the laser oscillator. The long-term rms timing drift and frequency instability of laser-microwave synchronization are 7.1 fs (over 10,000 s) and 5.5×10-18 (over 2000 s averaging time), respectively. As a versatile and reconfigurable tool for laser-laser and laser-microwave synchronization, the demonstrated method can be used for various applications ranging from ultrafast x-ray and electron science facilities to dual- and triple-comb spectroscopy.

Atom interferometry with ultracold Mg atoms: frequency standard and quantum sensors

The results of theoretical and experimental studies aimed at the creation of matter wave interferometers with Mg atoms are presented. Atom-optical interferometers based on the Ramsey-Bordé scheme are of great interest for the development of optical frequency standards. Ultracold Mg atoms are promising for the development of an optical frequency standard with relative uncertainty and long-term frequency instability at a level of 10−17 − 10−18. A long-term frequency stability of 3·10−15 is obtained at an averaging time τ = 103 s while stabilizing the frequency of a ‘clock’ laser at 457 nm (1 S 0 → 3 P 1 transition) to narrow Ramsey-Bordé resonances of Mg atoms cooled and localized in a magneto-optical trap. The measured frequency stability is determined by the stability of the measurement system based on an optical frequency comb stabilized to the optical frequency of a Yb:YAG/I2 standard. We also present the results of theoretical studies aimed at the use of Mg atom interferometers based on Bragg diffraction for quantum sensing.

FACTORS AFFECTING THE LONG-TERM STABILITY OF MICROWAVE OSCILLATORS FOR SPACE ELECTRONIC EQUIPMEN

Main factors affecting the long-term stability of microwave oscillator frequency are discussed in this paper. External factors affect the signal frequency at the output of any actual source, causing it to continuously change over time. Long-term frequency instability could be attributed to aging of the material. So, it is necessary to take special environmental factors into account, when designing microwave oscillators for space electronic equipment.

Long-Term Stability Analysis Toward

Long-term frequency instabilities in vapor-cell clocks mainly arise from fluctuations of the experimental and environmental parameters that are converted to clock frequency fluctuations via various physical processes. Here, we discuss the frequency sensitivities and the resulting stability limitations at one-day timescale for a rubidium vapor-cell clock based on a compact magnetron-type cavity operated in air (no vacuum environment). Under ambient laboratory conditions, the external atmospheric pressure fluctuations may dominantly limit the clock stability via the barometric effect. We establish a complete long-term instability budget for our clock operated under stable pressure conditions. Where possible, the fluctuations of experimental parameters are measured via the atomic response. The measured clock instability of at one day is limited by the intensity light-shift effect, which could further be reduced by active stabilization of the laser intensity or stronger optical pumping. The analyses reported here show the way toward simple, compact, and low-power vapor-cell atomic clocks with excellent long-term stabilities ≤ 10-14 at one day when operated in ambient laboratory conditions.

Spectroscopy of the quadrupole clock transition of ytterbium-171 ions for optical frequency standard development

We outline the results of the spectroscopic investigation of the quadrupole transition of a single ytterbium-171 ion as applied to the development of an optical frequency standard with a relative uncertainty and long-term frequency instability of less than 10−17. The spectral width of the resonance recorded at the centre transition frequency amounts to about 30 Hz.

Reduction of light shifts in Ramsey spectroscopy with a combined error signal.

Light-induced frequency shifts can be a key limiting contribution to the mid- and long-term frequency instabilities in atomic clocks. In this letter, we demonstrate the experimental implementation of the combined error signal interrogation protocol to a cold-atom clock based on coherent population trapping (CPT) and Ramsey spectroscopy. The method uses a single error signal that results from the normalized combination of two error signals extracted from two Ramsey sequences of different dark periods. The single combined error signal is used to stabilize the atomic clock frequency. Compared to the standard Ramsey-CPT interrogation, this method reduces the clock frequency sensitivity to light-shift variations by more than one order of magnitude. This method can be applied in various kinds of Ramsey-based atomic clocks, sensors, and instruments.

Simple-structured, subfemtosecond-resolution optical-microwave phase detector.

We demonstrate a simple all-fiber photonic phase detector that can measure the phase (timing) difference between an optical pulse train and a microwave signal with subfemtosecond resolution and -60 dB-level amplitude-to-phase conversion coefficient. It is based on passive phase biasing of a Sagnac loop by the intrinsic phase shift of a symmetric 3×3 fiber coupler. By eliminating the necessity of magneto-optic components or complex radio frequency (RF) electronics for phase biasing of the Sagnac loop, this phase detector has potential to be implemented as an integrated photonic device as well. When using this device for synchronization between a 250MHz mode-locked Er-fiber laser and an 8GHz microwave oscillator, the minimum residual phase noise floor reaches <-154 dBc/Hz (at 8GHz carrier) with integrated root mean square (rms) timing jitter of 0.97fs [1Hz-1MHz]. The long-term rms timing drift and frequency instability are 0.92fs (over 5000s) and 4×10-19 (at 10,000s averaging time), respectively.

Reaching a few 10-15 long-term stability of integrating sphere cold atom clock

We present the long-term stability of the integrating sphere cold atom clock (ISCAC) and analyze its systematic limitations. The relative frequency instability of 2.6×10−15 is reached for an averaging time of 2×105 s. The second-order Zeeman effect and the cavity pulling effect in ISCAC, which would induce the frequency drift from the clock transition, are analyzed. The analytical and experimental results indicate that the cavity pulling effect is the main contribution to the long-term frequency instability of the ISCAC. Further technical improvements to the microwave cavity are also discussed.

Optical Stabilization of a Microwave Oscillator for Fountain Clock Interrogation.

We describe an optical frequency stabilization scheme of a microwave oscillator that is used for the interrogation of primary cesium fountain clocks. Because of its superior phase noise properties, this scheme, which is based on an ultrastable laser and a femtosecond laser frequency comb, overcomes the frequency instability limitations of fountain clocks given by the previously utilized quartz-oscillator-based frequency synthesis. The presented scheme combines the transfer of the short-term frequency instability of an optical cavity and the long-term frequency instability of a hydrogen maser to the microwave oscillator and is designed to provide continuous long-term operation for extended measurement periods of several weeks. The utilization of the twofold stabilization scheme on the one hand ensures the referencing of the fountain frequency to the hydrogen maser frequency and on the other hand results in a phase noise level of the fountain interrogation signal, which enables fountain frequency instabilities at the 2.5 ×10-14 (τ/s)-1/2 level that are quantum projection noise limited.

Distribution of a phase-stabilized 100.02 GHz millimeter-wave signal over a 160 km optical fiber with 4.1 × 10-17 instability.

We report a long-distance phase-stabilized millimeter-wave distribution over optical fibers, where the optical-link-induced phase noise is compensated with a high-precision photonic-generated millimeter-wave (mm-wave) voltage-controlled oscillator (VCO). The mm-wave VCO is realized based on pre-filtering and re-modulating optical spectral lines of an optical frequency comb (OFC). By adjusting the frequency spacing of the optical spectral lines extracted from the OFC, the phase error of the transmitted optical mm-wave signal can be compensated precisely. Using the mm-wave VCO, we demonstrate a distribution of a 100.02 GHz signal over spooled optical fibers and the fractional frequency instability of the system at different transmission distances is exhibited. The residual phase noise of the remote mm-wave signal after being transferred through a 160-km fiber link is measured to be -59 dBc/Hz at 1 Hz frequency offset from the carrier, and the RMS timing jitter in the frequency range from 0.01 Hz to 1 MHz reaches 62 fs. The long-term fractional frequency instability of 4.1 × 10-17 at 10000 s averaging time is achieved, and the maximum timing drift is within 0.93 ps (peak to peak) during 4 hours.

Working for a mobile high accuracy (10&amp;lt;sup&amp;gt;-15&amp;lt;/sup&amp;gt;) rubidium atomic fountain clock

Fountain clocks, including cesium fountains and rubidium fountains, are the most accurate running atomic clocks in the world. A mobile rubidium clock prototype has been researching at SIOM since 2003, the unique features of the fountain clocks are: less cold-atom loss, higher SNR and less collision-shift were acquired by operating with rubidium, a fold optical path decreased laser power by 2/3, which also made the whole device be more stable, compact, and easier to manufacture. The Ramsey finger of microwave-transition in the fountain clock has been obtained with its SNR of about 100. The fountain clock has been lock to a H-maser, Allan Deviation calculating had shown that the short-term fractional frequency instability was 8×10^-13 at 1 s, and long-term fractional frequency instability was better than 6×10^-15 in 4×10⁴ s. Errors evaluating and system optimizing are in process, the total fractional uncertainties are expected to be less than 4×10^-15 when it is evaluated recently.

Long-term frequency instability of atomic frequency references based on coherent population trapping and microfabricated vapor cells

We present an evaluation of the long-term frequency instability and environmental sensitivity of a chip-scale atomic clock based on coherent population trapping, particularly as affected by the light-source subassembly. The long-term frequency stability of this type of device can be dramatically improved by judicious choice of operating parameters of the light-source subassembly. We find that the clock frequency is influenced by the laser-injection current, the laser temperature, and the rf modulation index. The sensitivity of the clock frequency to changes in the laser-injection current or the substrate temperature can be significantly reduced through adjustment of the rf modulation index. This makes the requirements imposed on the laser-temperature stabilization, in order to achieve a given frequency stability, less severe. The clock-frequency instability due to variations in local oscillator power is shown to be reduced through the choice of an appropriate light intensity inside the cell. The importance of these parameters with regard to the long-term stability of such systems is discussed.

A cryogenic open-cavity sapphire reference oscillator with low spurious mode density

In this paper, we describe the implementation of a microwave cryogenic sapphire oscillator (CSO) at the Laboratoire de Physique et Métrologie des Oscillateurs. In our realization we solved the problem of the spurious modes by operating the sapphire resonator in an open cavity. The CSO compared to a hydrogen maser demonstrates a frequency stability better than 3 x 10(-14) at short term. Its long-term frequency instability of the order of 3 x 10(-12)/day is limited by a random walk process. A first attempt to use this reference oscillator to characterize other signal sources is presented.

Instability in self-pulsation in laser diodes and its effect on all-optical synchronization

The effect of short- and long-term frequency instability in self- pulsation on all-optical synchronization using a twin-section laser diode is experimentally investigated. Short-term frequency instability broadens the unlocked full width at half maximum (FWHM) of the fundamental of the ii spectrum of the self-pulsating laser diode. We show experimentally that the value of the unlocked FWHM, and thus the level of short-term instability, has a direct effect on the optical power required to maintain synchronization. A novel means of reducing the FWHM is presented, based on a reflective transmission line stub connected to the absorber of the twin-section self-pulsating laser diode in use. A reduction of up to 5 dB in the average optical power required for effective synchronization is observed. Long-term frequency instability can prevent synchronization from taking place because of the limited lock-in frequency range of a self-pulsating laser diode. It is shown that for the devices used here, the dominant cause of long-term instability is temperature. A new method of sensing the temperature in a twin-section laser, called absorber current temperature sensing, which reduces the measured unsycnchronized frequency drift by more than 5:1, is demonstrated. The results have important implications for the design of new all-optical synchronization subsystems, based on self-pulsating laser diodes.

Automatic thermal frequency control of microwave oscillator with dielectric disk resonator

Microwave oscillators that are stabilized by sapphire disk resonators have good short-term relative frequency stability (σ(τ)=10−10 over averaging time τ∼1 sec) but inadequate long-term stability. This is mainly due to the high temperature coefficient of frequency of the disk resonator. An automatic frequency-control system based on thermal control of the frequency of the disk resonator was developed to improve the long-term frequency stability of the oscillators. The parameters of the automatic frequency-control system were optimized by computer, which involved solution of the nonstationary problem of the temperature distribution in the disk resonator and examination of the stability of the automatic control system for diffuse propagation of the control signal. Recommendations are given for selection of the heater geometry and frequency-control method. An oscillator with the thermal frequencecy-control system had a long-term relative frequency instability of (0.3–1)·10−8 per day, which was determined by the stability of the crystal-controlled reference oscillator. The automatic frequency-control system did not appreciably change the noise characteristics of the oscillator.

A frequency stabilized compact high repetition rate TEA-CO&lt;inf&gt;2&lt;/inf&gt;laser

A compact atmospheric-pressure hybrid CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> laser utilizing a transverse double-discharge technique has been constructed and operated at moderate repetition rates. A pulse output energy of 80 mJ has been obtained under single-mode conditions at repetition frequencies of 100 Hz. Using the hybrid technique to obtain single-longitudinal-mode operation, we have been able to reach a 7 kHz long-term relative frequency instability between the TEA laser and a local oscillator. Measurements of the frequency sweeping during the pulse tail (chirp) are also presented along with a direct measurement of the resonant frequency pulling effect associated with the real part of the electric susceptibility of the gas. Limitations on the pulse repetition frequency for this laser configuration are also discussed.

Cryogenic high-frequency stable systems with mode-conversion cavities

The mode conversion conditions, under which the frequency characteristics of the cavity are optimal for the transmission-type discriminator, are determined. Both theoretical and experimental results are described. From a comparative analysis one can see that using such a discriminator for frequency stabilization has some advantages over the usual systems. The possible applications of cryogenic mode-conversion cavities to the frequency stabilization problem are considered, including long-term and short-term frequency stabilizing systems. Taking into account the frequency characteristics of the tapered-mode-conversion cavities, it is possible to get frequency stability of stabilized oscillators at nitrogen temperatures, which would be almost the same as that at helium temperatures. It is shown that in the superconducting state the parametric generation, by means of nonlinear impedance of superconductors, is very useful for getting frequency stability as high as that for quantum frequency standards. It is shown experimentally that a mode-conversion-cavity stabilized oscillator has a long-term frequency instability Δf f ⩽ 10 −9 per hour at nitrogen temperature and short-term instability Δf f ∼ 10 −8 for an averaged time of 10 −7 s at the same temperature. A combination of these long-term and short-term systems in a single device permits still higher parameters to be achieved.