Atomic Clocks Research Articles

Quantum to classical transport transition and a decoherence detection method in driven optical lattices

Atomic quantum systems such as atomic clocks or qubits with cold atoms in tweezer arrays have attracted enormous interests both in academia and industry. In this work, we report a theoretical study and experimental demonstration of quantum tunneling of atoms in 1D optical lattices with decoherence. In such decoherence process, the expansion of atomic wave packet is suppressed and resonance spectrum is broadened. In this regime, as the decoherence rate L or the modulation time t increases, the evolution of atomic wave packets transitions from coherent tunneling to classical diffusion. We propose a detection method to fast evaluate the degree of decoherence in such systems. Our work benefits the study of decoherence properties of precision measurements based on optical lattice.

High-precision optical time and frequency transfer

High-precision optical time and frequency transfer is accomplished by a collection of laser-based techniques that achieve time dissemination with subpicosecond instabilities and frequency dissemination with instabilities below one part in 1016. The ability to distribute and compare time and frequency at these precisions enables current optical timing networks such as interconnected optical atomic clocks for the redefinition of the second, relativistic geodesy, and fundamental physics tests as well as time and frequency dissemination systems for large-scale scientific instruments. Future optical timing networks promise to expand these applications and enable new advances in distributed coherent sensing, precise navigation, and more. The field of high-precision optical time and frequency transfer has made significant advances over the last 20 years and has begun to transition from technique development to deployment in applications. Here, we present a review of approaches to high-precision optical time and frequency transfer. We first present a brief overview of the metrics used to assess time and frequency transfer. We then provide a discussion of the difference between time transfer and frequency transfer and review the various technical noise sources. We also provide a background on the optical frequency comb and its role in optical time and frequency transfer for additional context. The next sections of the paper cover specific time–frequency transfer techniques and demonstrations beginning with time and frequency transfer over fiberoptic links including continuous-wave (CW) laser-based frequency transfer, CW-laser-based time transfer, and frequency-comb-based time transfer. We then discuss approaches for time and frequency transfer over free-space including pulsed-source time transfer, CW-laser-based frequency transfer, and frequency-comb-based time transfer. Since no known existing review article covers frequency-comb time transfer over free-space, we provide additional details on the technique. Finally, we provide an outlook that outlines outstanding challenges in the field as well as possible future applications.

Coherent evolution of superexchange interaction in seconds-long optical clock spectroscopy.

Scaling up the performance of atomic clocks requires understanding complex many-body Hamiltonians to ensure meaningful gains for metrological applications. Here we use a degenerate Fermi gas loaded into a three-dimensional optical lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, leading to XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy, we map out favorable atomic coherence regimes. We transition through various interaction regimes and observe coherent superexchange, tunable through on-site interaction and site-to-site energy shift, affecting the Ramsey fringe contrast over timescales >1 second. This study lays the groundwork for using a three-dimensional optical lattice clock to probe quantum magnetism and spin entanglement.

Application and accuracy analysis of raw one way inter-satellite link observations of BDS-3 full operational constellation

The Ka-band Inter-Satellite Links (ISL) has been introduced as an innovative measurement technique for orbit determination (OD) and time synchronization (TS) of the global BeiDou Navigation Satellite System (BDS-3), complementing traditional L-band ground-satellite tracking. For the first time, OD and TS have been conducted for the entire full-operational constellation of BDS-3 using raw one-way ISL data. The normal equation (NEQ) accumulation technique is employed to estimate critical parameters, such as the ISL hardware delays (Ka-biases), to derive long-term average solutions. With the support of ISL, an orbital accuracy of 8.0 cm for Medium Earth Orbits (MEOs), 11.6 cm for Inclined Geosynchronous Orbits (IGSOs), and 24.0 cm for Geostationary Orbits (GEO) can be achieved using a ground network consisting of 20 stations. An extended observation model was developed for ISL heterogeneous data at both ends due to the presence of a specialized GEO satellite C61 which exclusively provides ISL data without broadcasting civil L-band signals. Subsequently, the OD and TS capabilities were validated using one-way ISL for GEO C61, resulting in an OD accuracy of approximately 3.7 cm in the radial direction, 7.9 cm in the normal direction, 27.7 cm in the tangential direction, and 29.0 cm in 3-D position; with a TS accuracy of around 0.1 ns. In most cases, one-way ISL transmission and reception Ka-biases remain stable over considerable periods, achieving an accuracy of 0.2 ns. However, apparent abnormal jumps in Ka-bias were observed, which were determined to be sudden changes in L-band hardware delay from navigation signals rather than jumps in ISL hardware delay itself. This finding marks the distinction between L-band hardware delay jumps and atomic clock jumps for navigation satellites. Additionally, the residuals of one-way ISLs exhibit periodic terms. Investigations indicate that these residuals vary with the antenna azimuth and elevation angles of each link and are specific to individual satellites. This variation may be attributed to small deviations in the on-board ISL receivers or antennas. This discovery is valuable for modeling ISL observations.

Laser Cooling Alkaline-earth Atoms for Optical Clock in Chinese Space Station

Abstract This study presents an achievement of laser cooling of alkaline-earth atoms in the Chinese Space Station’s strontium (Sr) atomic space optical clock. The system’s core components, physical unit, optical unit, and electrical unit, have a total volume of 306 L and a total mass of 163.8 kg. These compact and robust units can overcome mechanical vibrations and temperature fluctuations during space launch. The laser sources of the optical unit are composed of diode lasers, and the injection locking of slave lasers is performed automatically by a program. In the experiment, a blue magneto-optical trap of cold atoms was achieved, with the atomic numbers estimated to be approximately (1.50 ± 0.13) × 106 for 87Sr and (8.00 ± 0.56) × 106 for 88Sr. This work establishes a foundation for atomic confinement and high-precision interrogation in space optical clock while expanding the frontiers of cold atom physics in microgravity.

Unidirectional Orbit Determination for Extended Users Based on Navigation Ka-Band Inter-Satellite Links.

Traditional spacecraft orbit determination primarily employs two methodologies: ground station/survey ship-based orbit determination and global navigation satellite system (GNSS)-based orbit determination. The ground tracking measurement system, reliant on multiple tracking stations or ships, presents a less favorable efficiency-to-cost ratio. For high-orbit satellites, GNSS orbit determination is hindered by a limited number of receivable satellites, weak signal strength and suboptimal geometric configurations, thereby failing to meet the demands for the continuous, high-precision orbit measurement of overseas high-orbit satellites. Satellite navigation systems, characterized by global coverage and Ka-band inter-satellite links, offer measurement and communication services to extended users, such as satellites, aircraft, space stations and other spacecraft. With the widespread adoption of navigation satellite systems, particularly in scenarios where ground tracking, telemetry and command (TT&C) stations are out of sight, there is a growing demand among users for Ka-band inter-satellite links for high-precision ranging and orbit determination. This paper introduces an innovative unidirectional orbit-determination technology for extended users, leveraging the navigation Ka-band inter-satellite link. When extended users are constrained by weight and power consumption limitations, preventing the incorporation of high-precision atomic clocks, they utilize their extensive capture capability to conduct distance measurements between navigation satellites. This process involves constructing clock error models, calculating clock error parameters and compensating for these errors, thereby achieving high-precision time-frequency synchronization and bidirectional communication. The technology has enhanced the time and frequency accuracies by three and two orders of magnitude, respectively. Following the establishment of bidirectional communication, unidirectional ranging values are collected daily for one hour. Utilizing these bidirectional ranging values, a mechanical model and state-transfer matrix are established, resulting in orbit-determination calculations with an accuracy of less than 100 m. This approach addresses the challenge of high-precision time-frequency synchronization and orbit determination for users without atomic clocks, utilizing minimal inter-satellite link time slot resources. For the first time in China, extended users can access the navigation inter-satellite link with a minimal allocation of time slot resources, achieving orbit determination at the 100 m level. This advancement significantly enhances the robustness of extended users and provides substantial technical support for various extended users to employ the Ka inter-satellite link for emergency communication and orbit determination.

Electric-field sensing with driven-dissipative time crystals in room-temperature Rydberg vapor

Mode competition in nonequilibrium Rydberg gases enables the exploration of emergent many-body phases. This work leverages this emergent phase for electric field detection at room temperature. Sensitive frequency-resolved electric field measurements at very low-frequencies (VLF) are of central importance in a wide range of applications where deep-penetration is required in communications, navigation and imaging or surveying. The long wavelengths on order of 10–100 km (3–30 kHz) limit the efficiency, sensitivity, and bandwidth of compact classical detectors that are constrained by Chu’s limit. Rydberg-atom electrometers are an attractive approach for microwave electric-field sensors but have reduced sensitivity at lower-frequencies. Very recent efforts to advance the standard Rydberg-atoms approach is based on DC electric-field (E-field) Stark shifting and have resulted in sensitivities between 67.9 and 2.2 uVcm-1Hz-1/2 (0.1–10 kHz) by fine optimization of the DC E-field. A major challenge in these approaches is the need for embedded electrodes or plates due to DC E-field Stark screening effect, which can perturb coupling of VLF signals when injected from external sources. In this article, it is demonstrated that state-of-art sensitivity ((1.60 ± 0.23) uVcm-1Hz-1/2) can instead be achieved using limit-cycle oscillations in driven-dissipative Rydberg atoms by using a magnetic field (B-field) to develop mode-competition between nearby Rydberg states. The mode-competition between nearby Rydberg-states develop an effective transition centered at the oscillation frequency capable of supporting external VLF E-field coupling in the ~ 10–15kHz regime without the requirement for fine optimization of the B-field magnitude.

Resolving gravitational redshift with sub-millimeter height differences using spin-squeezed optical clocks

Abstract The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential, also known as gravitational redshift, is one of the classical tests of Einstein’s theory of general relativity. Owing to their ultra-high accuracy and stability, state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference. Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing. Here, we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of 171Yb atoms. The numerical results illustrate that for a sample of 104 atoms, the atomic-collision-limited resolution of the vertical separation between the two clocks can reach 0.48 mm, corresponding to a fractional gravitational redshift at the 10-20 level. In addition, the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms. Our work opens a door to the future spin-squeezing-enhanced test of general relativity.

Broadband Visible Wavelength Microcomb Generation In Silicon Nitride Microrings Through Air‐Clad Dispersion Engineering

AbstractThe development of broadband microresonator frequency combs at visible wavelengths is pivotal for the advancement of compact and fieldable optical atomic clocks and spectroscopy systems. Yet, their realization necessitates resonators with anomalous dispersion, an arduous task due to the prevailing normal dispersion regime of materials within the visible spectrum. In this work, it is evinced that silicon nitride microring resonators with air cladding on top and sides—a deviation from the frequently employed silica‐embedded resonators—allows for the direct generation of broadband microcombs in the visible range. Combs pumped at 1060 nm (283 THz) are experimentally demonstrated that reach wavelengths as short as 680 nm (440 THz), and combs pumped at 780 nm (384 THz) reach wavelengths as short as 630 nm (475 THz). Simulations show that microcombs extending to wavelengths as low as 461 nm (650 THz) should be accessible in this platform.

Low-noise extraction of a single frequency comb line by fiber Brillouin amplification.

We present a low-noise extraction of individual frequency lines from an optical frequency comb based on fiber Brillouin amplification. The phase and intensity noise properties of this extraction process are comprehensively investigated. The excess phase noise introduced by the extraction process under various conditions is studied in detail and found to be determined by environmental disturbances on the Brillouin gain fiber, which is reduced in our short-fiber, all-polarization-maintaining (PM) scheme. The simplicity and low phase noise characteristics of this approach demonstrate its capability in maintaining the coherence of a frequency comb line with ultra-narrow linewidth. Furthermore, the intensity noise of the extracted comb line is found to be strongly dependent on amplified spontaneous Brillouin scattering, further emphasizing the benefits of the all-PM design. These findings underscore the potential of this comb line extraction technique as a robust low-noise single-frequency laser generator or optical frequency synthesizer required in demanding fields such as cold atomic physics, optical communications, and optical clocks.

Ticking toward an advanced atomic clock

Long shelf-life shows mini-microwave ion clocks may soon outperform vapor cell-based clocks

A High-Precision Frequency Synchronization Method Based on a Novel Geostationary Communication Satellite Phase-Locked Transponder

Equipping satellites with a series of high-precision frequency references is essential; however, even advanced active hydrogen masers can often be too heavy and expensive for the current satellite payload constraints. Moreover, in geostationary Earth-orbit communication satellites lacking atomic clocks, onboard oscillators can degrade the performance of time–frequency transmission methods. To address these challenges, this study proposes a novel phase-locked transponder that leverages Einstein’s synchronization theory and real-time carrier-phase compensation to improve the transmission performance of satellite frequency transfer systems while mitigating the noise from onboard satellite oscillators. Notably, this requires only simple modifications to the existing transponder structure. By replicating the high-precision atomic frequency standards from ground stations to satellites, the proposed system achieves enhanced frequency synchronization without additional onboard clocks. The feasibility of the satellite-to-ground link was validated through both a theoretical analysis and an experimental verification. Specifically, ground experiments demonstrated a reproducibility of 6.33 ps (1σ) over a 24 h period, with a long-term frequency stability of 3.36 × 10−16 at an average time of 10,000 s under dynamic conditions, showcasing the potential of this approach for advanced frequency synchronization. This paper presents a cost-effective and scalable solution for enhancing frequency synchronization in geostationary satellites, improving communication reliability, supporting advanced scientific and navigational applications, and enabling the development of high-precision, space-air-ground integrated time–frequency synchronization networks.

Locally sealed microfabricated vapor cells filled from an ex situ Cs source

Microfabricated alkali vapor cells are key to enable miniature devices such as atomic clocks and optically pumped magnetometers with reduced size, weight, and power. Yet, more versatile fabrication methods are still needed to further expand their use cases. Here, we demonstrate an approach to collectively fill and seal microfabricated cesium cells using locally sealed microchannels patterned within one of the glass substrates comprising the cells. Unlike current methods that rely on wafer-level anodic bonding as the last sealing step, an approach based on local sealing opens the path to features so far limited to traditional glass-blown cells, including the ability to deposit temperature-sensitive antirelaxation coatings, reaching lower background gas pressure without an additional gettering material or filling with diverse atomic or molecular species.

Deep-ultraviolet second harmonic generation down to 150 nm in a quartz crystal with chirped dual-periodic superstructure.

Deep-ultraviolet (DUV) second harmonic generation (SHG) can realize the coherent sources for some modern equipment and optical spectroscopy measurements, however, that with nonlinear crystals is still a long-standing challenge due to the difficulty in phase-matching dependent on refractive dispersion relationship ruled by Lorentz model. Herein, we originally introduced the chirp into the additional periodic phase (APP) phase-matching and realized novel phase-matching conditions with the chirped additional periodic phase (CAPP) for DUV SHG with a CAPP quartz. The unprecedented tunable DUV SHG was realized with a wavelength from 150 to 203 nm (corresponding to a photon energy of 8.26∼6.1 eV). The developed light source presents the first SHG below 165 nm and would find promising applications in modern equipment such as angle-resolved photoemission spectroscopy (ARPES), optical atomic clocks, and DUV photodissociation dynamics. This strategy breaks the limitation of the Lorentz model for SHG and would be applicable for the extreme SHG approaching the transmittance edge of the nonlinear solid media.

On possibilities of improving the accuracy of the geocentric gravitational constant GM by combining SLR and atomic clocks measurements

Nowadays, the geocentric gravitational constant GM is determined by solving equations of motion for trajectories of artificial satellites measured by Satellite Laser Ranging (SLR). The estimated value of GM and its uncertainty 398600441.8 ± 0.8×106 m3s−2 are currently adopted by the International Astronomical Union. In this study, we investigate possibility of improving the accuracy of GM by integrating atomic clocks measurements with SLR. The functional model defines GM in terms of geopotential differences observed by atomic clocks at two points in space and their distance measured by SLR. Two types of observation equations are established. The first equation defines geopotential differences with respect to the geoidal geopotential value W0. The second equation defines distances with respect to the geocentric position of ground-based station determined from GNSS measurements. With the improving stability of atomic clocks to 10−18, it will be possible to measure geopotential differences with the accuracy ±0.1 m2s−2 (equivalent to ±1 cm in terms of the geoidal heights), while SLR measurements can currently be carried out with sub-centimetre accuracy under optimal conditions and applying advanced corrections and numerical procedures. Taking into consideration both, accuracy characteristics and their expected improvement, we conduct sensitivity analysis to assess accuracy requirements needed to improve the accuracy GM (±0.8×106 m3s−2). Error analysis indicates that combination of relativistic measurements with SLR cannot improve the accuracy of GM due to insufficient stability of atomic clocks. Nevertheless, the accuracy improvement by an order of magnitude might be feasible if relativistic measurements are carried out by atomic clocks with stability 10−20 (or better), while also achieving sub-millimetre accuracy of SLR. Integration of relativistic measurements with SLR could improve the accuracy of GM, while the critical aspect is determination of the geoidal geopotential value W0 with sub-millimetre accuracy in terms of geoidal heights that could be achievable.

Polarization‐Stable Wavelength‐Tunable Single‐Mode Vertical‐Cavity Surface‐Emitting Lasers with a Monolithic High‐Refractive‐Index‐Contrast Grating Top Coupling Mirror

AbstractVertical cavity surface emitting lasers (VCSELs) are high performance quality and low cost light sources in many optoelectronic components. Polarization stable single mode (SM) emission over a large spectral bandwidth at high ambient temperatures is an important prerequisite for many applications such as microscale atomic clocks, gas sensing, optical coherence tomography, and optical interconnects. At the same time, it is important to maintain a simple and robust VCSEL device design concept. A hybrid monolithic high index contrast grating (MHCG) distributed Bragg reflector (DBR) VCSEL design showing mono‐linearly polarized, true single mode (SM) emission over a thermally tuned wavelength range >9 nm and excellent performance at ambient temperatures up to 80 °C is reported. Spectral tuning is achieved solely by intrinsic heating induced by the injection current, offering a low power budget and robust tuning mechanism compared to other wavelength‐swept devices, while achieving about double the tuning range of standard single‐mode VCSELs. The devices are fabricated by conventional nanoprocessing techniques, and the device architecture exhibits the robustness of standard VCSELs with a simple monolithic one‐mesa structure.

Algorithm for Taming Rubidium Atomic Clocks Based on Longwave (Loran-C) Timing Signals

This paper explores effective methods for taming rubidium atomic clocks with longwave timing signals. In an in-depth analysis of the time-difference data between the 1PPS timing signal output from the ground-wave signal received by a long-wave receiver and the 1PPS signal from UTC, we observe that the time-difference data has significant short-term jitter and long-term periodicity effects. To meet this challenge, we adopt several innovative strategies. First, we use the Fourier transform algorithm to analyse the time-frequency characteristics of the time-difference data in detail and accordingly propose a de-jittering correction algorithm for the long-wave timing data, which is aimed at improving the stability of the long-wave timing signals. Secondly, the time difference model of the rubidium clock is innovatively modified, and a quadratic polynomial superimposed with a periodic fluctuation term is constructed, which can accurately solve and eliminate the periodic components and obtain smoother time difference data. Finally, the parameters of the rubidium clock are accurately estimated by the least-squares method using the corrected smoother time difference data, and the output frequency of the rubidium clock is adjusted accordingly so that the rubidium clock is tamed effectively by the long-wave timing signal successfully. The experimental results show that the long-term stability of the tamed rubidium clock is significantly improved to 3.52 × 10−13/100,000 s; meanwhile, the phase deviation of the output 1PPS from the UTC of the tamed rubidium clock after entering the stabilisation period is kept within 25 ns.

Dual wavelength Brillouin laser terahertz source stabilized to carbonyl sulfide rotational transition

Optical-based terahertz sources are important for many burgeoning scientific and technological applications. Among such applications is precision spectroscopy of molecules, which exhibit rotational transitions at terahertz frequencies. Stemming from precision spectroscopy is frequency discrimination (a core technology in atomic clocks) and stabilization of terahertz sources. Because many molecular species exist in the gas phase at room temperature, their transitions are prime candidates for practical terahertz frequency references. We demonstrate the stabilization of a low phase-noise, dual-wavelength Brillouin laser (DWBL) terahertz oscillator to a rotational transition of carbonyl sulfide (OCS). We achieve an instability of 1.2×10−12/τ, where τ is the averaging time in seconds. The signal-to-noise ratio and intermodulation limitations of the experiment are also discussed. We thus demonstrate a highly stable and spectrally pure terahertz frequency source. Our presented architecture will likely benefit metrology, spectroscopy, precision terahertz studies, and beyond.

Realization of Landau-Zener Rabi oscillations on an optical lattice clock

Realization of Landau-Zener Rabi oscillations on an optical lattice clock

Improved absolute frequency measurement of 171Yb at NMIJ with uncertainty below 2×10−16

Abstract We report improved absolute frequency measurement of the 1S 0 − 3 P0 transition of 171Yb at National Metrology Institute of Japan (NMIJ) by comparing the 171Yb optical lattice clock NMIJ-Yb1 with 13 Cs primary frequency standards via International Atomic Time from August 2021 to May 2023. The measured absolute frequency is 518 295 836 590 863.62(10) Hz with a fractional uncertainty of 1.9 × 10 − 16 , in good agreement with the recommended frequency of 171Yb as a secondary representation of the second. This uncertainty is 2.6 times lower than our previous measurement uncertainty, and slightly lower than any uncertainties of the absolute frequency measurements of 171Yb that have so far been reported by other institutes. We also estimate correlation coefficients between our present and previous measurements, which is important for updating the recommended frequency.