Short-term Fractional Frequency Stability Research Articles

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.

Microwave phase detection of coherent population trapping resonance in a Cs vapor cell

We report a phase-sensitive microwave detection setup for spectroscopy of coherent population trapping (CPT) resonance in a Cs vapor cell. In this scheme, the optically carried microwave interrogation signal that interacts with atoms is detected by a fast photodiode at the cell output and is then mixed with the local oscillator microwave signal itself. This detection scheme produces at the output of the microwave mixer a dispersive CPT signal that can be directly used for correction of the local oscillator frequency onto the atomic resonance. The evolution of the dispersive CPT resonance signal with the laser power is briefly reported. With this detection scheme, we demonstrate the operation of a CPT atomic clock with a short-term fractional frequency stability of 1 × 10 − 11 at 1 s, which is in good agreement with the slope of the frequency discriminator and the residual microwave phase noise of the setup.

A 500-km Cascaded White Rabbit Link for High-Performance Frequency Dissemination.

We perform experiments exploring the use of white rabbit precision time protocol (WR-PTP) for time and frequency dissemination over long-distance optical fiber links. We use unidirectional links, to ensure compatibility with active telecommunication networks, and White Rabbit equipment with modifications for improved performance. Using fiber spools, we realize a 500 km, four-span cascaded white rabbit link. We show short term fractional frequency stability of 2×10-12 , averaging down to 2×10-15 at one day of integration time, with no frequency shift within the statistical uncertainty. We demonstrate the impact of increasing the White Rabbit SoftPLL bandwidth and the PTP message rate. We show evidence of the effect of thermal fluctuations acting on the fiber, and finally discuss the limitations of the achieved performance. We show comparisons with experimental data acquired with commercial good quality global positioning system (GPS) receivers and show that the medium- and long- term stability and accuracy are more than one order of magnitude better with a WR-PTP link.

Demonstration of a trapped-ion atomic clock in space

Atomic clocks, which lock the frequency of an oscillator to the extremely stable quantized energy levels of atoms, are essential for navigation applications such as deep space exploration1 and global navigation satellite systems2, and are useful toolswith which to address questions in fundamental physics3-6. Such satellite systems use precise measurement of signal propagation times determined by atomic clocks, together with propagation speed, to calculate position. Although space atomic clocks with low instability are an enabling technology for global navigation, they have not yet been applied to deep space navigation and have seen only limited application to space-based fundamental physics, owing to performance constraints imposed by the rigours of space operation7. Methods of electromagnetically trapping and cooling ions have revolutionized atomic clock performance8-13. Terrestrial trapped-ion clocks operating in the optical domain have achieved orders-of-magnitude improvements in performance over their predecessors and have become a key component in national metrology laboratory research programmes13, but transporting this new technology into space has remained challenging. Here we show the results from a trapped-ion atomic clock operating in space. On the ground, NASA's Deep Space Atomic Clock demonstrated a short-term fractional frequency stability of 1.5×10-13/τ1/2 (where τ is the averaging time)14. Launched in 2019, the clock has operated for more than 12months in space and demonstrated there a long-term stability of 3×10-15 at 23days (no drift removal), and an estimated drift of 3.0(0.7)×10-16 per day. Each of these exceeds current space clock performance by up to an order of magnitude15-17. The Deep Space Atomic Clock is particularly amenable to the space environment because of its low sensitivity to variations in radiation, temperature and magnetic fields. This level of space clock performance will enable one-way navigation in which signal delay times are measured in situ, making near-real-time navigation of deep space probes possible18.

Cold-atom clock based on a diffractive optic.

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects 107 87Rb atoms, which are subsequently cooled to 20 µK in optical molasses. We optically probe the microwave atomic ground-state splitting using lin⊥lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only 0.5 mm, the measured short-term fractional frequency stability is 2×10-11/τ.

Electromagnetically induced absorption scheme for vapor-cell atomic clock.

A dual-frequency light field scheme, composed of counterpropagating pump and probe light waves with equal circular polarizations and different intensities, is proposed for the detection of subnatural-linewidth electromagnetically induced absorption (EIA) resonances. In this scheme, the bright-type EIA resonance is obtained at fixed static magnetic field by tuning the frequency difference between both optical fields and can be used as a frequency reference in an atomic clock. Using a 5-mm long buffer-gas-filled Cs vapor cell, an EIA-based atomic clock with a short-term fractional frequency stability of 5.8 × 10-12τ-1/2 until 20 s integration time is reported. These performances are found to be in correct agreement with the signal-to-noise/linewidth ratio of the resonance. The proposed EIA scheme can be considered as an alternative approach to the coherent population trapping (CPT) technique for the development of compact atomic clocks and sensors.

Towards a compact, optically interrogated, cold-atom microwave clock

Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $\perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ $5{\times}{10}^{-11}/\sqrt{\tau }$ with a projected quantum projection noise limit at the 10 − 13 / τ ${10}^{-13}/\sqrt{\tau }$ level.

Single-ion, transportable optical atomic clocks

For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below , finding applications in fundamental physics tests, relativistic geodesy and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network have been published, and most of time and frequency metrology institutes have started to develop transportable optical clocks. For the purpose of this special issue, we chose to focus on trapped-ion optical clocks. Even though their short-term fractional frequency stability is impaired by a lower signal-to-noise ratio, they offer a high potential for compactness: trapped ions demand low optical powers and simple loading schemes, and can be trapped in small vacuum chambers. We review recent advances on the clock key components, including ion trap and ultra-stable optical cavity, as well as existing projects and experiments which draw the picture of what future transportable, single-ion optical clocks may resemble.

A high-performance Raman-Ramsey Cs vapor cell atomic clock

We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature, and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed regime. We report also that the central fringe line-width is commonly narrower than the expected Ramsey line-width given by 1/(2TR), with TR the free-evolution time, for short values of TR. The clock demonstrates a short-term fractional frequency stability at the level of 2.3×10−13 τ−1/2 up to 100 s averaging time, mainly limited by the laser amplitude modulation noise. Comparable performances are obtained in the conventional continuous wave regime, with the use of an additional laser power stabilization setup. The pulsed interaction allows to reduce significantly the clock frequency sensitivity to laser power variations, especially for high values of TR. This pulsed CPT clock, ranking among the best microwave vapor cell atomic frequency standards, could find applications in telecommunication, instrumentation, defense or satellite-based navigation systems.

A low power cryocooled autonomous ultra-stable oscillator

We present the design and the preliminary evaluation of a cryostat equipped with a low power pulse-tube cryocooler intended to maintain near 5K a high-Q factor sapphire microwave resonator. This cooled resonator constitutes the frequency reference of an ultra-stable oscillator presenting a short term fractional frequency stability of better than 1×10-15 . The proposed design enables to reach a state-of-the-art frequency stability with a cryogenic oscillator consuming only 3kW of electrical power.

Characterization of commercially available vertical-cavity surface-emitting lasers tuned on Cs D1 line at 894.6 nm for miniature atomic clocks.

We report on the metrological characterization of novel commercially available 894.6nm vertical-cavity surface-emitting lasers (VCSELs), dedicated to Cs D1 line spectroscopy experiments. The thermal behavior of the VCSELs is reported, highlighting the existence of a minimum threshold current and maximum output power in the 55°C-60°C range. The laser relative intensity noise, measured to be -108 dB/Hz at 10Hz Fourier frequency f for a laser power of 25μW, is reduced with increased power. The VCSELs frequency noise is 108 Hz2/Hz at f=100 Hz. The spectral linewidth of the VCSELs is about 30MHz. VCSELs injection current can be directly modulated at 4.596GHz with microwave power in the range of -10 to +0 dBm to generate optical sidebands. A VCSEL was used in a microcell-based Cs atomic clock based on coherent population trapping. A preliminary clock short-term fractional frequency stability of 8×10-11τ-1/2 up to about 100s is reported, demonstrating the suitability of these VCSELs for miniature atomic clock applications.

A CPT-based Cs vapor cell atomic clock with a short-term fractional frequency stability of 3 x 10-13 τ-1/2

This article reports on the development and short-term fractional frequency stability of a continuous-regime (CW) Cs vapor cell atomic clock based on coherent population trapping (CPT). The push-pull optical pumping technique is used to increase the number of atoms that participate to the clock transition, yielding a typical CPT resonance contrast of 25% for a CPT linewidth of about 450 Hz. The clock short-term fractional frequency stability is measured to be 3 x 10-13 τ-1/2 up to 100 seconds averaging time, in correct agreement with the signal-to-noise ratio limit. The mid-term frequency stability results are currently mainly limited by laser power effects. The detection of high-contrast narrow Raman-Ramsey fringes is demonstrated with this setup by making the atoms interact with a light pulse sequence.

A high-overtone bulk acoustic wave resonator-oscillator-based 4.596 GHz frequency source: Application to a coherent population trapping Cs vapor cell atomic clock.

This article reports on the design and characterization of a high-overtone bulk acoustic wave resonator (HBAR)-oscillator-based 4.596 GHz frequency source. A 2.298 GHz signal, generated by an oscillator constructed around a thermally controlled two-port aluminum nitride-sapphire HBAR resonator with a Q-factor of 24,000 at 68 °C, is frequency multiplied by 2-4.596 GHz, half of the Cs atom clock frequency. The temperature coefficient of frequency of the HBAR is measured to be -23 ppm/ °C at 2.298 GHz. The measured phase noise of the 4.596 GHz source is -105 dB rad(2)/Hz at 1 kHz offset and -150 dB rad(2)/Hz at 100 kHz offset. The 4.596 GHz output signal is used as a local oscillator in a laboratory-prototype Cs microcell-based coherent population trapping atomic clock. The signal is stabilized onto the atomic transition frequency by tuning finely a voltage-controlled phase shifter implemented in the 2.298 GHz HBAR-oscillator loop, preventing the need for a high-power-consuming direct digital synthesis. The short-term fractional frequency stability of the free-running oscillator is 1.8 × 10(-9) at one second integration time. In locked regime, the latter is improved in a preliminary proof-of-concept experiment at the level of 6.6 × 10(-11) τ(-1/2) up to a few seconds and found to be limited by the signal-to-noise ratio of the detected CPT resonance.

A coherent population trapping Cs vapor cell atomic clock based on push-pull optical pumping

This article reports on the characterization of a compact coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique. This method allows to detect high-contrast CPT resonances on the 0-0 magnetic-field insensitive clock transition. The clock short-term fractional frequency stability is measured to be 3×10−13 τ−1/2 up to 100 s averaging time, in correct agreement with the signal-to-noise ratio limit. These results are among the best performances ever reported for a CPT-based clock. The noise budget is detailed. A preliminary study is reported to evaluate limitations to the clock mid-term frequency stability. The clock performances are found to be presently mainly limited in the mid-term by laser power effects.

Simple-design ultra-low phase noise microwave frequency synthesizers for high-performing Cs and Rb vapor-cell atomic clocks.

We report on the development and characterization of novel 4.596 GHz and 6.834 GHz microwave frequency synthesizers devoted to be used as local oscillators in high-performance Cs and Rb vapor-cell atomic clocks. The key element of the synthesizers is a custom module that integrates a high spectral purity 100 MHz oven controlled quartz crystal oscillator frequency-multiplied to 1.6 GHz with minor excess noise. Frequency multiplication, division, and mixing stages are then implemented to generate the exact output atomic resonance frequencies. Absolute phase noise performances of the output 4.596 GHz signal are measured to be -109 and -141 dB rad(2)/Hz at 100 Hz and 10 kHz Fourier frequencies, respectively. The phase noise of the 6.834 GHz signal is -105 and -138 dB rad(2)/Hz at 100 Hz and 10 kHz offset frequencies, respectively. The performances of the synthesis chains contribute to the atomic clock short term fractional frequency stability at a level of 3.1 × 10(-14) for the Cs cell clock and 2 × 10(-14) for the Rb clock at 1 s averaging time. This value is comparable with the clock shot noise limit. We describe the residual phase noise measurements of key components and stages to identify the main limitations of the synthesis chains. The residual frequency stability of synthesis chains is measured to be at the 10(-15) level for 1 s integration time. Relevant advantages of the synthesis design, using only commercially available components, are to combine excellent phase noise performances, simple-architecture, low-cost, and to be easily customized for signal output generation at 4.596 GHz or 6.834 GHz for applications to Cs or Rb vapor-cell frequency standards.

Recent improvements on the atomic fountain clock at SIOM**Project supported by the National Natural Science Foundation of China (Grant Nos. 61275204 and 91336105).

We report the recent advance in our rubidium atomic fountain clock (AFC). The parameters of the Ramsey cavity are optimized by balancing the coupling from the two ports. The temperature control system of the Ramsey interaction region is renovated, and the resonant temperature of the Ramsey cavity is regulated to be slightly above the room temperature. The quality of magnetic environment in the Ramsey interaction region is also improved. A new digital-to-analog converter (DAC) circuit that controls the local oscillator is adopted to decrease the noise of the oven-controlled crystal oscillator output. As a result, the short-term fractional frequency stability of 2.7 × 10−13τ−1/2 and the long-term fractional frequency stability of 1.6 × 10−15 at the average time of 32800 s are achieved.

Residual frequency drift in an atomic fountain clock

We report a locking mode in which the local oscillator (LO) is locked to an atomic fountain and calibration of the residual frequency drift (RFD). In this running mode, the locked LO outputs a standard frequency signal, and a short-term fractional frequency stability of 2.7 \times 10-13τ-1/2 is achieved. Due to the frequency drift of the LO in free running mode, a systematic frequency bias, or RFD, exists after being locked by the atomic fountain. We analyze and measure the RFD with a value of -3(2) \times 10-16. A sectionalized post-process method is adopted to calibrate the RFD.

Performance of a prototype atomic clock based on lin‖lin coherent population trapping resonances in Rb atomic vapor

We report on the performance of the first table-top prototype atomic clock based on coherent population trapping (CPT) resonances with parallel linearly polarized optical fields (lin||lin configuration). Our apparatus uses a vertical cavity surface emitting laser (VCSEL) tuned to the D1 line of 87Rb with current modulation at the 87Rb hyperfine frequency. We demonstrate cancellation of the first-order light shift by proper choice of rf modulation power, and further improve our prototype clock stability by optimizing the parameters of the microwave lock loop. Operating in these optimal conditions, we measured a short-term fractional frequency stability (Allan deviation) 2*10^{-11} tau^{-1/2} for observation times 1s<tau< 20s. This value is limited by large VCSEL phase noise and environmental temperature fluctuation. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated lin||lin CPT resonance clock with environmental impacts minimized.

A compensated multi-pole linear ion trap mercury frequency standard for ultra-stable timekeeping

The multi-pole linear ion trap frequency standard (LITS) being developed at the Jet Propulsion Laboratory (JPL) has demonstrated excellent short- and long-term stability. The technology has now demonstrated long-term field operation providing a new capability for timekeeping standards. Recently implemented enhancements have resulted in a record line Q of 5 x 10(12) for a room temperature microwave atomic transition and a short-term fractional frequency stability of 5 x 10(-14)/tau(1/2). A scheme for compensating the second order Doppler shift has led to a reduction of the combined sensitivity to the primary LITS systematic effects below 5 x 10(-17) fractional frequency. Initial comparisons to JPL's cesium fountain clock show a systematic floor of less than 2 x 10(-16). The compensated multi-pole LITS at JPL was operated continuously and unattended for a 9-mo period from October 2006 to July 2007. During that time it was used as the frequency reference for the JPL geodetic receiver known as JPLT, enabling comparisons to any clock used as a reference for an International GNSS Service (IGS) site. Comparisons with the laser-cooled primary frequency standards that reported to the Bureau International des Poids et Mesures (BIPM) over this period show a frequency deviation less than 2.7 x 10(-17)/day. In the capacity of a stand-alone ultra-stable flywheel, such a standard could be invaluable for long-term timekeeping applications in metrology labs while its methodology and robustness make it ideal for space applications as well.

Cancellation of light shifts in an N-resonance clock

We demonstrate that first-order light shifts can be canceled for an all-optical, three-photon-absorption resonance (N-resonance) on the D1 transition of 87Rb. This light-shift cancellation facilitates improved frequency stability for an N-resonance clock. For example, by using a tabletop apparatus designed for N-resonance spectroscopy, we measured a short-term fractional frequency stability (Allan deviation) of approximately/= 1.5 x 10(-11) tao1/2 for observation times of 1 s < or = tao < or = 50 s. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated N-resonance clock.