Cumulative fidelity of large-momentum-transfer clock atom interferometers in the presence of laser noise

Abstract We report a systematic uncertainty of 9.2×10 -19 for the USTC Sr1 optical lattice clock, achieving accuracy at the level required for the roadmap of the redefinition of the SI second. A finite-element model with in situ -validated, spatially-resolved chamber emissivity reduced blackbody radiation shift uncertainty to 6.3×10 -19 . Concurrently, the externally mounted lattice cavity, by providing a larger beam waist, reduced the atomic density and thereby suppressed the density shift. Enhanced lattice depth modulation consolidated lattice light shift uncertainty to 6.3×10 -19 by enabling simultaneous determination of key polarizabilities and magic wavelength. Magnetic shifts were resolved below 10 -18 via precision characterization of the second-order Zeeman coefficient. Supported by a clock laser stabilized on an ultralow-expansion glass cavity with crystalline-coated mirrors and refined temperature control suppressing BBR fluctuations, the clock also achieves a frequency stability better than 1×10 -18 at 30,000-s averaging time. These developments collectively establish a new benchmark in USTC Sr1 clock performance and pave the way for high-accuracy applications in metrology and fundamental physics.

I present a Popperian falsification protocol for Ze theory, a framework that derives the Minkowski metric ds2 = Zs2 - k2*Zt2 from a dual-channel binary event counter. Five ordered kill criteria are defined: (Kill-0/1) the normalized Euclidean invariant I_norm = (Zs2+Zt2)/(N-1)2 must be stable across window sizes with std ~ 1/sqrt(N); (Kill-2) the Minkowski form must be preserved under the Ze Lorentz transform; (Kill-3) the Ze velocity limit k = <Zs>/<Zt> must be consistent within the same physical stream; (Kill-4) the Lorentz gamma-factor must be recoverable from counting data; (Kill-5) Ze-derived ds2 must agree with relativistic time dilation from atomic clocks or GPS. Kill-0 through Kill-4 are run numerically on N=10^6 event streams. Ze passes all four: I_norm is flat to <0.6% across window sizes, ds2 is preserved to <5x10^-13%, and gamma is recovered to <3x10^-13%. Non-stationary streams correctly fail Kill-1. Kill-5 remains open. Two errors in the original falsification theses are corrected: the invariant must be normalized by (N-1)2, and the kill condition must compare std(I_norm) to the 1/sqrt(N) baseline.

AlGaN-based deep-ultraviolet vertical-cavity surface-emitting lasers (DUV VCSELs) have shown a great application potential in optical atomic clocks, maskless photolithography, etc. Nevertheless, the uncontrolled cavity length-induced detuning issue, i.e., the difference between the resonance wavelength and gain peak, severely impairs the device performance. Herein, a DUV-VCSEL strategy featuring the uniform nanometer-class control of the cavity length in a 4-in wafer is proposed in the DUV framework based on GaN templates, which ensures the wafer-scale removal of sapphire substrates by laser lift-off, and then provides space for the subsequent deposition of dielectric distributed Bragg reflector (DBR). It is more significant that the strategy brings about a GaN/AlGaN sharp interface with an Al composition difference up to 80%, whereby self-terminated etching with an ultrahigh selectivity of 100:1 is achieved. The cavity length is hence accurately determined by epitaxy itself instead of the fabrication process, so as to minimize the detuning. As such, 285.6-nm optically pumped DUV VCSELs with double dielectric DBRs are fabricated, exhibiting a record low threshold of 0.38 MW cm-2 and a narrow linewidth of 0.11nm. What's more, the lasing wavelength varies within 1.9nm across the 4-in wafer, indicating a cavity length variation of only 0.81%.

Generation of subfemtosecond deep and vacuum UV pulses via two-photon Rabi oscillations in alkali atoms or alkaline-earth ions

This paper proposes a method to generate a low-noise 10.23 MHz time-frequency reference signal based on high-order harmonic locking of the repetition rate (fr) of an optical frequency comb (OFC). An all-polarization-maintaining (PM) Erbium-doped fiber laser with a 122.76 MHz fr is constructed using the nonlinear amplifying loop mirror (NALM) principle. By applying a feedback control to the intracavity piezoelectric actuator (PZT) and electro-optic modulator (EOM), the 10th harmonic of fr is phase-locked to a high-performance rubidium atomic clock (Rb clock), achieving low-noise conversion from the Rb clock to the target signal. Experimental results show that the generated 10.23 MHz signal exhibits residual phase noise of −123.4 dBc/Hz at 1 Hz offset and −158 dBc/Hz at 1 MHz offset, and achieves a residual frequency stability of 3.52 × 10−13 @ 1 s and 3.65 × 10−15 @ 10,000 s. This harmonic locking scheme validates the advantages of photonic microwave generation in achieving ultra-low phase noise while preserving the long-term stability of atomic clocks, providing a strategic solution for next-generation BeiDou Navigation Satellite System (BDS) time-frequency payloads.

Anomaly detection in atomic clocks using machine learning and time series approach

The 1626 nm laser is an essential component for conducting superlattice research on the strontium atomic clock platform. The superlattice constructed with the 1626 nm and 813 nm lasers will facilitate cutting-edge quantum information research focused on topological quantum states transport. We demonstrate an idler-resonant optical parametric oscillator that achieves 1626 nm laser output based on pump enhancement technology. Through a well-designed external cavity, a laser output of 127 mW at 1626 nm has been achieved, with a corresponding pump quantum conversion efficiency of 50% and a pump threshold of 110 mW. The long-term power stability of the output laser is ±1.5% per hour. Variations in the pump cavity modes under different experimental conditions have been measured, and the impedance matching process of the pump light within the cavity has been discussed. The 1626 nm laser and the associated technologies reported in this manuscript will provide optical support for the investigation of superlattice physics on the strontium optical lattice clock platform.

The Ze framework proposes that proper time is not a geometric parameter but a count of effective information updates, with relativistic kinematics emerging statistically from the dynamics of event processing rather than from assumed spacetime structure. This paper presents a comprehensive experimental programme to test four core Ze postulates across multiple domains. The foundational digital experiment employs identical processors receiving identical input streams operating in maximally sequential versus maximally parallel modes, predicting update count ratios τ_B/τ_A = √(1 - v²) where v represents the proportion of parallel correlations—a functional form identical to the Lorentz factor of special relativity. Physical clock experiments compare internal transition counts in systems with different internal complexity (trapped ions, molecular clocks, optical lattice clocks) under identical relativistic conditions, testing whether proper time correlates with update statistics rather than merely with velocity. Non-inertial experiments subject systems to periodic correlation modulation without changing average velocity, predicting that proper time accumulation depends on causal structure rather than path length alone. Quantum-level experiments leverage programmable quantum computers (IBM, IonQ) to test whether interference corresponds to parallel update distribution and whether the quantum Zeno effect reflects mode switching with measurable update deficits. The Ze framework does not claim special relativity is incorrect but seeks to show it arises as an effective theory from deeper informational principles. Structural convergence with causal set theory, twistor theory, and emergent spacetime frameworks provides indirect support. The digital experiment offers the most direct test: if the relativistic curve emerges from pure information dynamics, it demonstrates that relativistic kinematics are not unique to physics but reflect universal constraints on information processing. Independent replication by multiple groups and derivation of relativity without assuming it would constitute sufficient evidence to attract serious scientific engagement. All proposed experiments are feasible with current technology, and their falsification conditions are clearly specified, ensuring the Ze framework meets the highest standards of empirical testability.

Abstract The global navigation satellite system (GNSS) is essential for timing and positioning. In conventional receivers, clock offset is treated as a common error and often lacks careful modeling. However, accurate clock state estimation is crucial in GNSS-based remote timing. Current methods typically model clock error as white noise, which can amplify estimation noise in both the up-coordinate and clock states under certain conditions. Incorporating clock modeling has the potential to mitigate such noise. This study explores the theoretical foundations of clock modeling and examines its influence on GNSS positioning and timing performance. We establish the GNSS timing model and the clock signal model, and clarify the relationship between Allan Variance and the diffusion coefficient. Using a small Rubidium atomic clock and an oven controlled crystal oscillator (OCXO) as examples, we evaluate the effect of clock modeling on frequency offset estimation noise and vertical positioning precision. Theoretical and experimental results demonstrate that clock modeling significantly reduces frequency offset estimation noise, with noise attenuation ranging from 17.19% to 52.83% for OCXO and 87.67% to 97.83% for the Rubidium clock. More stable clocks exhibit greater improvement. Additionally, clock modeling enhances short-term up-coordinate positioning stability, showing improvements of 78.74% for OCXO and 84.23% for the Rubidium clock at 1 s intervals. These findings highlight the potential of clock modeling for rapid online frequency monitoring and improved GNSS timing and positioning performance with OCXOs and compact atomic clocks.

Abstract High-precision time synchronization is a core technical challenge in modern space science, deep space exploration, and time–frequency metrology. Traditional microwave links struggle to achieve picosecond-level synchronization due to atmospheric delays (tropospheric and ionospheric effects). We propose a novel atmospheric delay correction technique using a triple-frequency microwave link that enables the simultaneous cancellation of atmospheric errors. This technique integrates a three-dimensional ray-tracing algorithm with microwave radiometer measurements to jointly correct both dispersive and non-dispersive tropospheric delays. Simultaneously, first- and second-order ionospheric errors are precisely eliminated via dual-downlink inversion of the slant total electron content. To validate this approach, we developed a theoretical analysis and simulation platform that systematically evaluates various factors—including different satellite types, transmission methods (carrier-phase versus pseudocode), and combinations of onboard and ground atomic clocks—to comprehensively verify the correction technique’s effectiveness. Experimental results show that this method can achieve two-way satellite–ground time synchronization accuracy better than 0.3 picoseconds (RMS) when low-earth orbit satellites and ground stations are both equipped with high-stability optical clocks and carrier-phase transfer is used. The Allan deviation of the transfer link’s clock difference is below 5.17 × 10 − 15 at an averaging time of 100 s. These results highlight the significant potential of our approach, offering an innovative solution for all-weather, high-reliability satellite-to-ground time and frequency transfer systems.

The fundamental nature of time at microscopic scales remains an unsolved problem at the intersection of quantum mechanics and general ‎relativity. This study presents Quantum Chronography, a theoretical framework for analyzing the operational and physical limits of time ‎measurement arising from quantum uncertainty, spacetime curvature, and stochastic metric fluctuations. By integrating the energy–time uncertainty principle with Planck-scale constraints and gravitational backreaction, a lower bound on measurable time intervals is derived. The ‎framework predicts an intrinsic, irreducible temporal uncertainty that grows sublinearly with the measured interval, forming a stochastic ‎lattice of time quanta in regions of significant curvature. Implications for high-precision astronomical timing, including pulsar observations ‎and atomic clock networks, are discussed. Rather than proposing a complete theory of quantum gravity, this work focuses on the physically ‎measurable consequences of quantum and gravitational effects on time. The research results provide a novel operational perspective on the ‎emergent nature of time, bridging concepts from quantum gravity and observational chronometry‎.

This study derives the Lorentz transformation using a third method, distinct from the approaches of Lorentz and Einstein, without introducing Lorentz symmetry or the principle of relativity. First, following Einstein’s operational method, an arbitrary stationary frame is constructed using rigid rulers, atomic clocks, and light signals. Next, the Lorentz transformation is derived solely from the principle of the constancy of the speed of light. This derivation suggests that special relativity does not inherently require the denial of an absolute stationary frame. Accordingly, this study demonstrates that observer relativity and the absoluteness of inertial frames coexist within the Lorentz transformation and its inverse. The former arises from the shared use of light signals and atomic clocks, whereas the latter originates from the operational asymmetry that only the stationary frame employs rigid rulers for spatial measurement. This distinction is evident in the determination of the speed of light: the stationary frame determines it experimentally through round-trip light measurements, whereas moving frames define it axiomatically. Furthermore, while the Doppler effect illustrates observer relativity—where the observed frequency depends on the relative motion and direction—phenomena such as round-trip light experiments and electrostatic interactions between stationary and uniformly moving charges reveal the absoluteness of inertial frames. In conclusion, this study proposes a new theoretical framework—termed absolute relativity—that preserves the empirical successes of special relativity while maintaining physical consistency by restoring the concept of an absolute stationary frame

Abstract Owing to their exceptional performance characteristics, optical atomic clocks enable the generation of time scales that demonstrate superior accuracy and stability compared to conventional microwave clocks. This paper presents an experimental optical time scale based on the NTSC-SrⅡ optical lattice clock as the reference and a hydrogen maser as the flywheel oscillator. The time scale TS(SrⅡ), generated through post-processing analysis over a two-month period, achieves a peak-to-peak time variation of 0.39 ns relative to Coordinated Universal Time (UTC) and reaches frequency stability of 1.94×10-16 at 5 days. In addition, a physical optical time scale TS*(SrⅡ) was realized for approximately one month, the peak-to-peak time difference is 0.3 ns compared to UTC. These results demonstrates that optical time scales maintain competitive performance even when the optical clock operated with limited and non-uniformly distributed uptime. This work constitutes an essential step toward a redefinition of the second of the International System of Units (SI) based on an optical transition.

Quantum friction on a rotating pair of atomic oscillators at all temperatures and all distances

Abstract We report the SrII optical lattice clock at the National Time Service Center (NTSC). In this system, a blackbody radiation shield with movable lattice mitigates blackbody radiation shifts through active temperature control. A shallow optical lattice with minimal tunneling minimizes AC Stark shifts. Phase-locked counter-propagating lattice beams and conductive vacuum viewports further reduce systematic uncertainties and a novel initial-state preparation method simplifies the system. Clock transition spectra achieve a linewidth of 2.5 Hz with a 400 ms clock pulse, and self-comparison stability reaches 5.1 × 10 −16 at 1 s. These advancements give this clock the potential to be a critical platform for realizing outstanding systematic uncertainties in the future.

The Lorentz transformations of mass and time are derived and explained within the framework of quantum-process thermodynamics. To this end, various notions of quantum work are employed to describe the behavior of an accelerated particle, such as an electron, which consists of a core wave and a guiding wave. We find that, during acceleration, a particle changes not only its velocity but also its internal structure and energies. While the mass and frequency of its guiding wave increase, the mass and frequency of its core wave decrease. As the wavelength of the core wave increases, the rate at which an accelerated atomic clock accumulates time is reduced. This is a dynamical process, rather than an observational effect formulated in terms of relations between inertial frames. We present a new equation for a form of energy that provides a unified description of particle motion and electromagnetic energy. We compare our results with special relativity and discuss a range of microscopic and macroscopic experiments. On this basis, quantum-process thermodynamics emerges as a promising framework for exploring deterministic aspects of quantum dynamics.

Narrow-linewidth vertical-cavity surface-emitting lasers (VCSELs) are key enablers for chip-scale atomic clocks and quantum sensors, yet conventional designs suffer from short cavity lengths and excess spontaneous emission, resulting in broad linewidths and degraded frequency stability. Here, we demonstrate a monolithically integrated VCSEL operating at the cesium D1 line (894.6 nm) that achieves intrinsic linewidth compression to ~1 MHz, without requiring external optical feedback. This performance is enabled by embedding a passive cavity adjacent to the active region, which spatially redistributes the optical field into a low-loss region, extending photon lifetime while suppressing higher-order transverse and longitudinal modes. The resulting device exhibits robust single-mode operation over a wide current and temperature range, with side-mode suppression ratio (SMSR) > 35 dB, orthogonal polarization suppression ratio (OPSR) > 25 dB and a beam divergence of ~7°. Integrated into a Cesium vapor-cell atomic clock, the VCSEL supports a frequency stability of 1.89 × 10-12 τ-1/2. These results position this VCSEL architecture as a compact, scalable solution for next-generation quantum-enabled frequency references and sensing platforms.

Optical lattice clocks of fermionic strontium offer a versatile platform for probing fundamental physics and developing quantum technologies. The bivalent electronic structure of strontium gives rise to a doubly forbidden atomic transition that is accessible due to hyperfine mixing in fermionic strontium-87, thus resulting in a submillihertz natural linewidth. Currently, the most accurate optical lattice clocks operate on this narrow transition by tightly trapping strontium-87 atoms in a optical lattice at 813 nm. Magic wavelengths occur where the Stark shifts of both the ground and excited states are equal, thus eliminating any position- and intensity-dependent broadening of the corresponding transition. Theoretical calculations of the electronic structure of strontium-87 have also predicted another magic wavelength of the clock transition at 497.01(57) nm. In this work, we experimentally measure the magic wavelength to be 497.4364(4) nm. Compared to the 813-nm magic wavelength, 497 nm is closer to the strong 461-nm dipolar transition of strontium, resulting in an order-of-magnitude increase in atomic polarizability and deeper traps with less optical power. The proximity to the 461-nm transition also leads to an enhanced sensitivity of 334(10) Hz/(nm E R ) at the magic wavelength.

Achieving superradiant lasing with an ultranarrow linewidth is crucial for enhancing atomic clock stability in quantum precision measurement. By employing the exceptional point (EP) property of the system, we demonstrate theoretically superradiant lasing with linewidths in the μHz range, sustained at the high-power level. This is achieved by incoherently pumping optical lattice clock transitions with ultracold alkaline-earth strontium-87 atoms in the EP of a PT-symmetric system. Physically, the atomic coherence reaches a maximum in the EP, significantly amplifying the superradiance effect and resulting in superradiant lasing with an ultranarrow linewidth. This linewidth is even three orders of magnitude smaller than that of superradiant lasing in the systems without EP. Our Letter extends the realm of superradiant lasing by introducing the EP property, and offers promising applications for developing atomic clocks with exceptional stability and accuracy.