Atomic Clocks Research Articles

Open-source electronics ecosystem for optical atomic clocks

We present an open-source hardware and software ecosystem for optical atomic clocks. We provide PCB schematics and fabrication files for manufacturing the most important electronic systems together with the required software. The boards are designed for an active bad-cavity superradiant strontium clock and a passive optical lattice strontium clock, but they can be easily adapted to other atomic species’ optical atomic clocks or ultra-cold atoms’ systems like magneto-optical traps or Bose–Einstein condensate setups.

Precision Joint RF Measurement of Inter-Satellite Range and Time Difference and Scalable Clock Synchronization for Multi-Microsatellite Formations.

The rapid development of multi-satellite formations requires inter-satellite radio frequency (RF) measurement to be both precise and scalable. The navigation estimation of multi-satellite formations using a unified time reference demands the simultaneous RF measurement of the inter-satellite range and time difference. However, high-precision inter-satellite RF ranging and time difference measurements are investigated separately in existing studies. Different from the conventional two-way ranging (TWR) method, which is limited by its reliance on a high-performance atomic clock and navigation ephemeris, asymmetric double-sided two-way ranging (ADS-TWR)-based inter-satellite measurement schemes can eliminate such reliance while ensuring measurement precision and scalability. However, ADS-TWR was originally proposed for ranging-only applications. In this study, by fully exploiting the time-division non-coherent measurement characteristic of ADS-TWR, a joint RF measurement method is proposed to obtain the inter-satellite range and time difference simultaneously. Moreover, a multi-satellite clock synchronization scheme is proposed based on the joint measurement method. The experimental results show that when inter-satellite ranges are hundreds of kilometers, the joint measurement system has a centimeter-level accuracy for ranging and a hundred-picosecond-level accuracy for time difference measurement, and the maximum clock synchronization error was only about 1 ns.

Modeling Clock Comparison Experiments to Test Special Relativity

The clock comparison experiments to test special relativity mainly include the Michelson–Morley experiment, Kennedy–Thorndike experiment, Ives–Stilwell experiment and the comparison experiment of atomic clocks in two locations. These experiments can be roughly classified as the comparison of two types of clocks: optical clocks and atomic clocks. Through the comparison of such clocks, Lorentz invariance breaking parameters in the RMS framework can be tested. However, in such experiments, the structural effects of optical clocks have been fully considered, yet the structural effects of atomic clocks have not been carefully studied. Based on this, this paper analyzes the structural effects of atomic clocks in detail and divides the experiments into six types: the comparison of two atomic clocks, two optical clocks, and atomic clocks and optical clocks placed in different and the same locations. Finally, correction parameters for the experimental measurements are given.

Active Suppression of the Light Shift in an Atomic Clock Based on Coherent Population Trapping in 87Rb Vapor Using the Phase Jump Technique

The active suppression of light shift of the reference coherent population trapping (CPT) resonance in 87Rb vapor to improve the long-term stability of compact atomic clocks has been demonstrated experimentally. The approach is based on the phase jump technique used to synthesize an error signal, which is proportional to the light shift of the CPT resonance, from an optical transmission signal. The use of this error signal in an additional feedback loop allows one to stabilize the amplitude of a microwave signal for the phase modulation of laser radiation near a value at which the light shift of the CPT resonance is absent. This technique has made it possible to reduce the long-term instability of CPT atomic clocks in our experiments by a factor of 15 at an integration time of 10 000–20 000 s.

Observation of an Inner-Shell Orbital Clock Transition in Neutral Ytterbium Atoms.

We observe a weakly allowed optical transition of atomic ytterbium from the ground state to the metastable state 4f^{13}5d6s^{2} (J=2) for all five bosonic and two fermionic isotopes with resolved Zeeman and hyperfine structures. This inner-shell orbital transition has been proposed as a new frequency standard as well as a quantum sensor for new physics. We find magic wavelengths through the measurement of the scalar and tensor polarizabilities and reveal that the measured trap lifetime in a three-dimensional optical lattice is 1.9(1)s, which is crucial for precision measurements. We also determine the g factor by an interleaved measurement, consistent with our relativistic atomic calculation. This work opens the possibility of an optical lattice clock with improved stability and accuracy as well as novel approaches for physics beyond the standard model.

Isotope study of the nonlinear pressure shifts of 85Rb and 87Rb hyperfine resonances in Ar, Kr, and Xe buffer gases.

Measurements of the 0-0 hyperfine resonant frequencies of ground-state 85Rb atoms show a nonlinear dependence on the pressure of the buffer gases Ar, Kr, and Xe. The nonlinearities are similar to those previously observed with 87Rb and 133Cs and presumed to come from alkali-metal-noble-gas van der Waals molecules. However, the shape of the nonlinearity observed for Xe conflicts with previous theory, and the nonlinearities for Ar and Kr disagree with the expected isotopic scaling of previous 87Rb results. Improving the modeling alleviates most of these discrepancies by treating rotation quantum mechanically and considering additional spin interactions in the molecules. Including the dipolar-hyperfine interaction allows simultaneous fitting of the linear and nonlinear shifts of both 85Rb and 87Rb in either Ar, Kr, or Xe buffer gases with a minimal set of shared, isotope-independent parameters. To the limit of experimental accuracy, the shifts in He and N2 were linear with pressure. The results are of practical interest to vapor-cell atomic clocks and related devices.

Electro‐Optic Frequency Combs: Theory, Characteristics, and Applications

AbstractOptical frequency combs (OFCs) are a unique kind of light source, which are represented as a series of equally spaced coherent spectral lines in the frequency domain. OFCs can mainly be divided into mode‐locked lasers, Kerr frequency combs, and electro‐optic frequency combs (E‐O combs), which have broad applications in optical communications, frequency metrology, atomic clocks, distance ranging, spectroscopy, and arbitrary waveform generation. Among them, E‐O combs feature some unique advantages, such as fast tunable repetition rate, high sidebands power, and reconfigurability of the comb spectrum. Especially in recent years, with the development of micro–nano processing technology, on‐chip E‐O combs have become a dynamic research topic with many fundamental scientific problems as well as engineering applications for further exploration. To summarize the past development and envision the prosperous future of E‐O combs, the area of E‐O combs is reviewed from the following aspects: development of E‐O combs; theory including the generation process of E‐O combs and the electro‐optic modulation models; important techniques including flattening, broadening, noise, and stability controlling; applications including communications, ranging, spectroscopy, wavelength calibration of astronomical spectrographs, and microwave generation; and pros and cons when compared with other OFCs.

Indigenisation of the Quantum Clock: An Indispensable Tool for Modern Technologies

Time and frequency (T&F) measurement with unprecedented accuracy is the backbone for several sophisticated technologies, commensurate with the evolution of human civilisation in the 20th century in terms of communication, positioning, navigation, and precision timing. This necessity drove researchers in the early 1950s to build atomic clocks that have now evolved to a state-of-the-art level, operating at optical wavelengths as optical atomic clocks, which use cold and trapped samples of atomic/ionic species and various other sophisticated diagnostic test techniques. Such ultrahigh-precision accurate clocks have made it possible to probe fundamental aspects of science through incredibly sensitive measurements. On the other hand, they meet the T&F synchronisation standards for classical and emerging quantum technologies at the desired level of accuracy. Considering the impact of optical atomic clocks in the second quantum revolution (quantum 2.0), they have been identified as an indispensable critical technology in worldwide quantum missions, including in India. This article reviews the present international scenario regarding optical atomic clocks and their related technologies and draws a roadmap for their indigenisation over the next decade.

Dual-frequency fundamental-mode NPRO laser for low-noise microwave generation.

Monolithic nonplanar ring oscillators (NPROs) have achieved great success in industry, scientific applications and space missions due to their excellent narrow-linewidth, low-noise, high beam-quality, lightweight and compact performances. Here, we show that stable dual-frequency or multi-frequency fundamental-mode (DFFM or MFFM) laser can be stimulated directly by tunning pump divergence-angle and beam-waist injected to NPRO. The DFFM laser has a frequency deviation of one free spectral range of the resonator and thus can be utilized for pure microwave generation by common-mode-rejection. To demonstrate the purity of the microwave signal, a theoretical phase noise model is established, and the phase noise and the frequency tunability of the microwave signal are experimentally studied. Single sideband phase noise for a 5.7 GHz carrier is measured as low as -112 dBc/Hz at 10 kHz offset, and -150 dBc/Hz at 10 MHz offset in the free running condition of the laser, which outperforms its counterparts from dual-frequency Laguerre-Gaussian (LG) modes. The frequency of the microwave signal can be efficiently tunned through two channels, with frequency tunning coefficients of 15 Hz/V by piezo, and -60.5 kHz/K by temperature, respectively. We expect that such compact, tunable, low-cost and low-noise microwave sources can facilitate multiple applications including miniaturized atomic clocks, communication and radar, etc.

Integrating planar photonics for multi-beam generation and atomic clock packaging on chip

The commercialization of atomic technologies requires replacing laboratory-scale laser setups with compact and manufacturable optical platforms. Complex arrangements of free-space beams can be generated on chip through a combination of integrated photonics and metasurface optics. In this work, we combine these two technologies using flip-chip bonding and demonstrate an integrated optical architecture for realizing a compact strontium atomic clock. Our planar design includes twelve beams in two co-aligned magneto-optical traps. These beams are directed above the chip to intersect at a central location with diameters as large as 1 cm. Our design also includes two co-propagating beams at lattice and clock wavelengths. These beams emit collinearly and vertically to probe the center of the magneto-optical trap, where they will have diameters of ≈100 µm. With these devices we demonstrate that our integrated photonic platform is scalable to an arbitrary number of beams, each with different wavelengths, geometries, and polarizations.

Active Suppression of the Light Shift in an Atomic Clock Based on Coherent Population Trapping in 87Rb Vapor Using the Phase Jump Technique

The active suppression of light shift of the reference coherent population trapping (CPT) resonance in 87Rb vapor to improve the long-term stability of compact atomic clocks has been demonstrated experimentally. The approach is based on the phase jump technique used to synthesize an error signal, which is proportional to the light shift of the CPT resonance, from an optical transmission signal. The use of this error signal in an additional feedback loop allows one to stabilize the amplitude of a microwave signal for the phase modulation of laser radiation near a value at which the light shift of the CPT resonance is absent. This technique has made it possible to reduce the long-term instability of CPT atomic clocks in our experiments by a factor of 15 at an integration time of 10 000–20 000 s.

Continuous outcoupling of ultracold strontium atoms combining three different traps

We have demonstrated the continuous outcoupling of ultracold 88Sr atoms using a moving optical lattice. While Sr atoms are Zeeman-slowed and magneto-optically trapped on the 1S0–1P1 transition, the atoms relaxed to the 5s5p 3P2 metastable state are magnetically trapped and Doppler cooled on the 5s5p 3P2–5s4d 3D3 transition at 2.92 μm. By optically pumping the atoms to the 5s5p 3P0 state, we outcouple the atoms by a moving optical lattice. Such a continuous atomic source enables superradiant lasers and the zero-dead-time operation of atom interferometers and optical lattice clocks.

Be optical lattice clocks with the fractional Stark shift up to the level of 10−19

The energy levels and electric dipole () matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic , magnetic dipole () and electric quadrupole () polarizabilities as well as the hyperpolarizabilities of the and states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.

Chaos in coupled atom–molecular Bose–Einstein condensates

We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.

The maximum weight in UTC: proposal for a new approach.

The goal of this work is the improvement of the long-term stability of Coordinated Universal Time (UTC). To achieve this purpose a comprehensive analysis of the atomic clocks participating in the calculation of UTC is presented. We focus our analysis on the hydrogen masers, the only clocks reaching the maximum weight in UTC. We observed that the present weighting algorithm fails to assign the maximum weight to H-masers with the best stability (predictability) only and too many clocks reach the maximum weight. To improve the process, we present a new way to generalize the maximum weight in the weighting algorithm of UTC based on the Karush-Kuhn-Tucker conditions. The method succeeds in improving the long-term stability of UTC.

E-band widely tunable, narrow linewidth heterogeneous laser on silicon

We demonstrate a heterogeneously integrated laser on silicon exhibiting a sub-20 kHz Lorentzian linewidth over a wavelength tuning range of 58 nm from 1350 to 1408 nm, which are record values to date for E-band integrated lasers in the literature. Wide wavelength tuning is achieved with an integrated Si ring-resonator-based Vernier mirror, which also significantly reduces the Lorentzian linewidth. Such a record performance leverages a mature heterogeneous III–V/Si platform and marks an important milestone in E-band optical fiber communications and in reaching visible wavelengths via second harmonic generation for optical atomic clock applications.

Quantum-enhanced differential atom interferometers and clocks with spin-squeezing swapping

Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here we show that differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Our protocol uses a single spin-squeezed state that is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.

A Real-Time Linear Prediction Algorithm for Detecting Abnormal BDS-2/BDS-3 Satellite Clock Offsets

Due to space environment interference, imperfect data processing model, and the performance of atomic clocks, real-time satellite clock products often contain outliers or irregular biases. We propose a real-time linear moving short-term prediction algorithm to predict clock offsets and detect abnormalities. The proposed algorithm mainly includes phase/frequency anomaly detection and real-time prediction part. Both the phase and frequency domains are used to detect abnormal clock offsets with previous epochs for building the clock prediction model accurately. The real-time moving prediction module utilizes the high short-term prediction performance to check the clock abnormality. The performance of the algorithm is then evaluated for all satellites with real-time estimated satellite clock offsets. To verify the feasibility and effectiveness of the proposed linear moving model and algorithm, the results of the grey model GM(1,1) and the ARIMA model are also compared. The experimental results indicated that the algorithm can detect clock outliers, frequency modulation, and phase jumps, and the linear model has a better clock performance improvement. After the abnormalities are removed with the proposed algorithm, the average STD accuracy of the real-time clock offsets for all satellites is improved by 15.5%, compared to an improvement of 11.4% by the GM(1,1) model and 11.5% by the ARIMA model. The PPP results demonstrate that the proposed clock prediction algorithm improves the positioning accuracy by 8.1%, 13.3%, and 16.9% in the east, north, and up components, respectively.

Comparative Performance Analysis of Femtosecond-Laser-Written Diode-Pumped Pr:LiLuF4 Visible Waveguide Lasers

In this work, we present the operation of a femtosecond-laser-written diode-pumped visible waveguide laser based on praseodymium-doped lithium lutetium fluoride. The refractive index modification induced by the femtosecond laser in the crystal exhibits an anisotropic behavior, thus enabling the fabrication of different types of waveguides from single-track structures to stress-induced waveguides and depressed cladding structures. All the waveguides were characterized by realizing transmission measurements and the waveguide design was optimized to obtain extremely low propagation losses, equal to 0.12 dB/cm. Lasing has been achieved at 604 nm and 721 nm from different waveguides. In addition, stable continuous-wave lasing at 698 nm has been obtained in a depressed cladding waveguide. This wavelength corresponds to the one needed for the transition of the atomic clock based on the neutral strontium atom. In the end, we report the observation of laser emission at 645 nm from a depressed cladding waveguide.

Exploiting the two-dimensional magneto-optical trapping of Hg199 for a mercury optical lattice clock

Two-dimensional magneto-optical trapping (2D-MOT) is an efficient tool for generating a high flux of precooled atoms. A 2D-MOT for mercury (Hg) is so far missing despite the potential of this atomic species in several areas. Here, we present the characterization of a 2D-MOT for Hg enabled by addressing the ${}^{1}{S}_{0}$- ${}^{3}{P}_{1}$ laser cooling transition at 254 nm. The laser source based on an ytterbium-doped fiber amplifier has low-frequency noise and high reliability. Parameters affecting the efficiency of the 2D-MOT are studied, i.e., optical trapping power, push beam power, cooling laser frequency detuning, and magnetic-field gradient. When used with a Hg optical lattice clock, the 2D-MOT increases by a factor of 4.5, the rate of preparation of the atomic samples, yielding an improved clock short term stability of $6.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ at 1 s.