Optical clock comparison for Lorentz symmetry testing

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Twin-Field Quantum Key Distribution with Local Frequency Reference

Twin-field quantum key distribution (TFQKD) overcomes the linear rate-loss limit, which promises a boost of secure key rate over long distance. However, the complexity of eliminating the frequency differences between the independent laser sources hinders its practical application. We analyzed and determined the frequency stability requirements for implementing TFQKD using frequency-stabilized lasers. Based on this analysis, we proposed and demonstrated a simple and practical approach that utilizes the saturated absorption spectroscopy of acetylene as an absolute reference, eliminating the need for fast frequency locking to achieve TFQKD. Adopting the 4-intensity sending-or-not-sending TFQKD protocol, we experimentally demonstrated the TFQKD over 502, 301, and 201 km ultralow-loss optical fiber, respectively. We expect this high-performance scheme will find widespread usage in future intercity and free-space quantum communication networks.

Scheme for Quantum-Logic Based Transfer of Accuracy in Polarizability Measurement for Trapped Ions Using a Moving Optical Lattice

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.

Trapped atoms in spatially-structured vector light fields

Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite-Gaussian, Laguerre-Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing. We provide open code to reproduce our results or to evaluate interaction matrix elements for different transition types, beam structures and interaction geometries.

Quantum-Enhanced Metrology for Molecular Symmetry Violation Using Decoherence-Free Subspaces

We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods that have been demonstrated experimentally.

Realizing spin squeezing with Rydberg interactions in an optical clock

Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.

Evaluation of a ^{88}Sr^{+} Optical Clock with a Direct Measurement of the Blackbody Radiation Shift and Determination of the Clock Frequency

We report on an evaluation of an optical clock that uses the ^{2}S_{1/2}→^{2}D_{5/2} transition of a single ^{88}Sr^{+} ion as the reference. In contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well-characterized sensitivity to thermal radiation. We measure the clock output frequency against an independent ^{171}Yb^{+} ion clock, based on the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition, and determine the frequency ratio with a total fractional uncertainty of 2.3×10^{-17}. Relying on a previous measurement of the ^{171}Yb^{+} (E3) clock frequency, we find the absolute frequency of the ^{88}Sr^{+} clock transition to be 444 779 044 095 485.277(59) Hz. Our result reduces the uncertainty by a factor of 3 compared with the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. We also show that for three simultaneously interrogated ^{88}Sr^{+} ions, the increased number causes the expected improvement of the short-term frequency instability of the optical clock without degrading its systematic uncertainty.

Improved Limits on the Coupling of Ultralight Bosonic Dark Matter to Photons from Optical Atomic Clock Comparisons

We present improved constraints on the coupling of ultralight bosonic dark matter to photons based on long-term measurements of two optical frequency ratios. In these optical clock comparisons, we relate the frequency of the ^{2}S_{1/2}(F=0)↔^{2}F_{7/2}(F=3) electric-octupole (E3) transition in ^{171}Yb^{+} to that of the ^{2}S_{1/2}(F=0)↔^{2}D_{3/2}(F=2) electric-quadrupole (E2) transition of the same ion, and to that of the ^{1}S_{0}↔^{3}P_{0} transition in ^{87}Sr. Measurements of the first frequency ratio ν_{E3}/ν_{E2} are performed via interleaved interrogation of both transitions in a single ion. The comparison of the single-ion clock based on the E3 transition with a strontium optical lattice clock yields the second frequency ratio ν_{E3}/ν_{Sr}. By constraining oscillations of the fine-structure constant α with these measurement results, we improve existing bounds on the scalar coupling d_{e} of ultralight dark matter to photons for dark matter masses in the range of about (10^{-24}-10^{-17})  eV/c^{2}. These results constitute an improvement by more than an order of magnitude over previous investigations for most of this range. We also use the repeated measurements of ν_{E3}/ν_{E2} to improve existing limits on a linear temporal drift of α and its coupling to gravity.

Ultra-stable cryogenic sapphire cavity laser with an instability reaching 2 × 10-16 based on a low vibration level cryostat

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of 2(1) × 10^-16. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is optimized by tuning the mixing ratio of the gas-liquid-helium. With this technique, the linear power spectral densities of vibrations at certain frequencies higher than tens of hertz are suppressed by two orders of magnitude in all directions.

176Lu+ clock comparison at the 10-18 level via correlation spectroscopy

The extreme precision of optical atomic clocks has led to an anticipated redefinition of the second by the International System of Units. Furthermore, accuracies pushing the boundary of 1 part in 10¹⁸ and beyond will enable new applications, such as in geodesy and tests of fundamental physics. The ¹S₀ to ³D₁ optical transition in ¹⁷⁶Lu⁺ has exceptionally low sensitivity to external perturbations, making it suitable for practical clock implementations with inaccuracy at or below 10^-18. Here, we perform high-accuracy comparisons between two ¹⁷⁶Lu⁺ references using correlation spectroscopy. A comparison at different magnetic fields is used to obtain a quadratic Zeeman coefficient of -4.89264(88) Hz/mT for the reference frequency. With a subsequent comparison at low field, we demonstrate agreement at the low 10^-18 level, statistically limited by the averaging time of 42 hours. The evaluated uncertainty in the frequency difference is 9 × 10^-19 and the lowest reported in comparing independent optical references.

Towards optical frequency geopotential difference measurements via a flying drone

Geopotential and orthometric height differences between distant points can be measured via timescale comparisons between atomic clocks. Modern optical atomic clocks achieve statistical uncertainties on the order of 10^-18, allowing height differences of around 1 cm to be measured. Frequency transfer via free-space optical links will be needed for measurements where linking the clocks via optical fiber is not possible, but requires line of sight between the clock locations, which is not always practical due to local terrain or over long distances. We present an active optical terminal, phase stabilization system, and phase compensation processing method robust enough to enable optical frequency transfer via a flying drone, greatly increasing the flexibility of free-space optical clock comparisons. We demonstrate a statistical uncertainty of 2.5×10^-18 after 3 s of integration, corresponding to a height difference of 2.3 cm, suitable for applications in geodesy, geology, and fundamental physics experiments.

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.

Controlling of the bidirectional amplifier chain for optical frequency distribution based on a two-dimensional noise detector

In the paper we present a solution for controlling the chain of bidirectional optical amplifiers, intended for long-haul fiber links used to distribute signals produced by optical atomic clocks. The solution is based on a dedicated two-channel noise detector, which allows independent measurement of the noise contributions related to interferometric signal fading and additive wideband noise. New signal quality metrics, based on two-dimensional noise detector, allows to distribute properly the needed gain among the chained amplifiers. Experimental results performed both in laboratory conditions and on a real 600 km-long link, confirming proper operation of proposed solutions, are presented.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

Gravitational redshift test using Rb clocks of eccentric GPS satellites

This paper reports a test of gravitational redshift, which is a consequence of the Einstein equivalence principle, using the Rb clocks of GPS Block IIF satellites. The fractional deviation in the gravitational redshift was measured using 6,640 days of data from three Rb clocks onboard GPS Block IIF satellites. The systematic effects related to orbital uncertainty, temperature, and magnetic field were modeled conservatively. The fractional deviation in the gravitational redshift from the general relativity prediction was measured with ( 0.23 ± 1.34 ) × 10 - 3 at one sigma.

Excitation of an Electric Octupole Transition by Twisted Light

We study the coherent excitation of the ^{2}S_{1/2}→^{2}F_{7/2} electric octupole (E3) transition by twisted light modes with a single ^{171}Yb^{+} ion in the dark center of a vortex beam. The intensity distribution of the beam is mapped as a function of the ion's position by measuring the light shift on an auxiliary electric quadrupole transition. In the center of the vortex beam, we observe excitation of the E3 transition with a fivefold reduced light shift in comparison to excitation by plane wave radiation for the same Rabi frequency. We measure the excitation probabilities for Laguerre-Gaussian twisted light modes of first and second order for different polarization patterns at various orientations of the ion quantization axis with respect to the beam propagation vector. We compare the experimental results with theoretical predictions and find good qualitative agreement.

Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

A way forward for fundamental physics in space

Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

Toward a New Generation of Compact Transportable Yb+ Optical Clocks

Optical atomic clocks are currently one of the most sensitive tools making it possible to precisely test the fundamental symmetry properties of spacetime and Einstein’s theory of relativity. At the same time, the extremely high stability and accuracy of compact transportable optical clocks open new perspectives in important fields, such as satellite navigation, relativistic geodesy, and the global time and frequency network. Our project aimed to develop a compact transportable optical clock based on a single ytterbium ion. We present the first prototype of the Yb+ clock (298 kg in 1 m3) and present several solutions aimed to improve the clock’s robustness to approach the demands of a space-qualified system. We present spectroscopic studies of a 435.5 nm quadrupole clock transition with Fourier-limited spectra of 25 Hz. The estimated instability of the output frequency at 1 GHz, which was down-converted with an optical frequency comb (OFC), is at the level of 9×10−15/τ, and the long-term instability and inaccuracy are at the level of 5×10−16. As the next steps, we present a new design for the clock laser and the OFC.

Measurement of Optical Rubidium Clock Frequency Spanning 65 Days

Optical clocks are emerging as next-generation timekeeping devices with technological and scientific use cases. Simplified atomic sources such as vapor cells may offer a straightforward path to field use, but suffer from long-term frequency drifts and environmental sensitivities. Here, we measure a laboratory optical clock based on warm rubidium atoms and find low levels of drift on the month-long timescale. We observe and quantify helium contamination inside the glass vapor cell by gradually removing the helium via a vacuum apparatus. We quantify a drift rate of 4×10-15/day, a 10 day Allan deviation less than 5×10-15, and an absolute frequency of the Rb-87 two-photon clock transition of 385,284,566,371,190(1970) Hz. These results support the premise that optical vapor cell clocks will be able to meet future technology needs in navigation and communications as sensors of time and frequency.

Resolving the gravitational redshift across a millimetre-scale atomic sample

Einstein's theory of general relativity states that clocks at different gravitational potentials tick at different rates relative to lab coordinates-an effect known as the gravitational redshift¹. As fundamental probes of space and time, atomic clocks have long served to test this prediction at distance scales from 30 centimetres to thousands of kilometres^2-4. Ultimately, clocks will enable the study of the union of general relativity and quantum mechanics once they become sensitive to the finite wavefunction of quantum objects oscillating in curved space-time. Towards this regime, we measure a linear frequency gradient consistent with the gravitational redshift within a single millimetre-scale sample of ultracold strontium. Our result is enabled by improving the fractional frequency measurement uncertainty by more than a factor of 10, now reaching 7.6 × 10^-21. This heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations.

Comparing ultrastable lasers at 7 × 10-17 fractional frequency instability through a 2220 km optical fibre network

Ultrastable lasers are essential tools in optical frequency metrology enabling unprecedented measurement precision that impacts on fields such as atomic timekeeping, tests of fundamental physics, and geodesy. To characterise an ultrastable laser it needs to be compared with a laser of similar performance, but a suitable system may not be available locally. Here, we report a comparison of two geographically separated lasers, over the longest ever reported metrological optical fibre link network, measuring 2220 km in length, at a state-of-the-art fractional-frequency instability of 7 × 10-17 for averaging times between 30 s and 200 s. The measurements also allow the short-term instability of the complete optical fibre link network to be directly observed without using a loop-back fibre. Based on the characterisation of the noise in the lasers and optical fibre link network over different timescales, we investigate the potential for disseminating ultrastable light to improve the performance of remote optical clocks.

Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation

We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}Yb^{+} that is coupled to the ^{2}S_{1/2} ground state via an electric octupole transition. The radiative lifetime is determined to be 4.98(25)×10^{7}  s, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

Compact magneto-optical trap of thulium atoms for a transportable optical clock

We have developed a compact vacuum system for laser cooling and spectroscopy of neutral thulium atoms. Compactness is achieved by obviating a classical Zeeman slower section and placing an atomic oven close to a magneto-optical trap (MOT), specifically at the distance of 11 cm. In this configuration, we significantly gained in solid angle of an atomic beam, which is affected by MOT laser beams, and reached 1 million atoms loaded directly in the MOT with only 15 mW of MOT cooling beams net power. By exploiting Zeeman-like deceleration of atoms with an additional laser beam and tailoring the MOT magnetic field gradient with a small magnetic coil, we demonstrated trapping of up to 13 million atoms. These results show great perspective of the developed setup for realizing a compact high-performance optical atomic clock based on thulium atoms.

Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10⁻¹⁸ level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10⁻¹⁸ in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

There are continuous efforts in improving the stability and systematic shifts of optical clocks. Here the authors demonstrate thulium optical clock utilizing bicolor scheme involving interrogation of both hyperfine levels and they are able to cancel the quadratic Zeeman shift.

An ultralow-noise superconducting radio-frequency ion trap for frequency metrology with highly charged ions

We present a novel ultrastable superconducting radio-frequency (RF) ion trap realized as a combination of an RF cavity and a linear Paul trap. Its RF quadrupole mode at 34.52 MHz reaches a quality factor of Q ≈ 2.3 × 10⁵ at a temperature of 4.1 K and is used to radially confine ions in an ultralow-noise pseudopotential. This concept is expected to strongly suppress motional heating rates and related frequency shifts that limit the ultimate accuracy achieved in advanced ion traps for frequency metrology. Running with its low-vibration cryogenic cooling system, electron-beam ion trap, and deceleration beamline supplying highly charged ions (HCIs), the superconducting trap offers ideal conditions for optical frequency metrology with ionic species. We report its proof-of-principle operation as a quadrupole-mass filter with HCIs and trapping of Doppler-cooled ⁹Be⁺ Coulomb crystals.

Dipole-Dipole Frequency Shifts in Multilevel Atoms

Dipole-dipole interactions lead to frequency shifts that are expected to limit the performance of next-generation atomic clocks. In this work, we compute dipolar frequency shifts accounting for the intrinsic atomic multilevel structure in standard Ramsey spectroscopy. When interrogating the transitions featuring the smallest Clebsch-Gordan coefficients, we find that a simplified two-level treatment becomes inappropriate, even in the presence of large Zeeman shifts. For these cases, we show a net suppression of dipolar frequency shifts and the emergence of dominant nonclassical effects for experimentally relevant parameters. Our findings are pertinent to current generations of optical lattice and optical tweezer clocks, opening a way to further increase their current accuracy, and thus their potential to probe fundamental and many-body physics.

Adaptively controlled fast production of defect-free beryllium ion crystals using pulsed laser ablation

Trapped atomic ions find wide applications ranging from precision measurement to quantum information science and quantum computing. Beryllium ions are widely used due to the light mass and convenient atomic structure of beryllium; however, conventional ion loading from thermal ovens exerts undesirable gas loads for a prolonged duration. Here, we demonstrate a method to rapidly produce pure linear chains of beryllium ions with pulsed laser ablation, serving as a starting point for large-scale quantum information processing. Our method is fast compared to thermal ovens, reduces the gas load to only 10^-12 Torr (10^-10 Pa) level, yields a short recovery time of a few seconds, and also eliminates the need for a deep ultraviolet laser for photoionization. We also study the loading dynamics, which show non-Poissonian statistics in the presence of sympathetic cooling. In addition, we apply feedback control to obtain defect-free ion chains with desirable lengths.

Improved Bounds on Lorentz Symmetry Violation from High-Energy Astrophysical Sources

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent γ-ray telescope data allow the Lorentz-violating electron cνμ parameters to be constrained extremely well, so that all bounds are at the level of 7×10−16 or better.

Scalable Codes for Precision Calculations of Properties of Complex Atomic Systems

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that enables computations that were not previously possible due to system complexity. This code package also allows much quicker computations to be run with higher accuracy for simple systems. We explored different methods of load-balancing matrix element calculations for many-electron systems, which are very difficult due to the intrinsic nature of the computational methods used to calculate them. Furthermore, dynamic memory allocation and MPI parallelization have been implemented to optimize and accelerate the computations. We have achieved near-perfect linear scalability and efficiency with the number of processors used for calculation, paving the way towards the future where most open-shell systems will finally be able to be treated with good accuracy. We present several examples illustrating new capabilities of the newly developed codes, specifically correlating up to all 60 electrons in the highly charged Ir17+ ion and predicting certain properties of Fe16+.

Frequency ratio measurements at 18-digit accuracy using an optical clock network

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics¹. Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10^-18 level, two orders of magnitude beyond their microwave predecessors². Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained largely unchanged for more than a decade^3-5. Here we operate a network of optical clocks based on ²⁷Al⁺ (ref. ⁶), ⁸⁷Sr (ref. ⁷) and ¹⁷¹Yb (ref. ⁸), and measure their frequency ratios with fractional uncertainties at or below 8 × 10^-18. Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields^9,10. Our optical clock network utilizes not just optical fibre¹¹, but also a 1.5-kilometre free-space link^12,13. This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws¹, perform relativistic geodesy¹⁴ and substantially improve international timekeeping¹⁵.

Observation of an Electric Quadrupole Transition in a Negative Ion: Experiment and Theory

The first direct experimental observation of an electric quadrupole (E2) absorption transition between bound states of an atomic negative ion has been made. The transition was observed in the negative ion of bismuth by resonant (1+1) photon detachment from Bi^{-} via ^{3}P_{2}→^{3}P_{0} excitation. The E2 transition properties were completely independently calculated using a hybrid theoretical approach to account for the strong multilevel electron interactions and relativistic effects. The experimental and ab initio theoretical results are in excellent agreement, providing valuable new insight into this complex system and forbidden transitions in negative ions more generally.

Demonstration of the Systematic Evaluation of an Optical Lattice Clock Using the Drift-Insensitive Self-Comparison Method

The self-comparison method is a powerful tool in the uncertainty evaluation of optical lattice clocks, but any drifts will cause a frequency offset between the two compared clock loops and thus lead to incorrect measurement result. We propose a drift-insensitive self-comparison method to remove this frequency offset by adjusting the clock detection sequence. We also experimentally demonstrate the validity of this method in a one-dimensional 87Sr optical lattice clock. As the clock laser frequency drift exists, the measured frequency difference between two identical clock loops is (240 ± 34) mHz using the traditional self-comparison method, while it is (−15 ± 16) mHz using the drift-insensitive self-comparison method, indicating that this frequency offset is cancelled within current measurement precision. We further use the drift-insensitive self-comparison technique to measure the collisional shift and the second-order Zeeman shift of our clock and the results show that the fractional collisional shift and the second-order Zeeman shift are 4.54(28) × 10−16 and 5.06(3) × 10−17, respectively.

Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons

We compare two optical clocks based on the ^{2}S_{1/2}(F=0)→^{2}D_{3/2}(F=2) electric quadrupole (E2) and the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition of ^{171}Yb^{+} and measure the frequency ratio ν_{E3}/ν_{E2}=0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ν_{E3}=642121496772645.10(8)  Hz, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1)×10^{-18}/yr and of the proton-to-electron mass ratio μ to -8(36)×10^{-18}/yr. Using the annual variation of the Sun's gravitational potential at Earth Φ, we improve limits for a potential coupling of both constants to gravity, (c^{2}/α)(dα/dΦ)=14(11)×10^{-9} and (c^{2}/μ)(dμ/dΦ)=7(45)×10^{-8}.

Rugged mHz-Linewidth Superradiant Laser Driven by a Hot Atomic Beam

We propose a new type of superradiant laser based on a hot atomic beam traversing an optical cavity. We show that the theoretical minimum linewidth and maximum power are competitive with the best ultracoherent clock lasers. Also, our system operates naturally in continuous wave mode, which has been elusive for superradiant lasers so far. Unlike existing ultracoherent lasers, our design is simple and rugged. This makes it a candidate for the first widely accessible ultracoherent laser, as well as the first to realize sought-after applications of ultracoherent lasers in challenging environments.

Non-Minimal Lorentz Violation in Macroscopic Matter

The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and non-minimal violations. The hamiltonian and modified Newton’s second law for a test body are derived. The framework is applied to free-fall and torsion-balance tests of the weak equivalence principle and to orbital motion. The effects on continuous media are studied, and the frequency shifts in acoustic resonators are calculated.

Calculation of Polarizabilities for Atoms with Open Shells

A version of the configuration interaction method for atoms with open shells (the Configuration Interaction with Perturbation Theory—CIPT method, PRA 95, 012503 (2017)) is extended for calculation of static and dynamic polarizabilities. Its use is demonstrated by calculation of the polarizabilities for the ground and excited states of Er, Tm and Yb. It is proved to be an useful tool in designing a new generation of optical atomic clocks sensitive to new physics.

Prospects and challenges for squeezing-enhanced optical atomic clocks

Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.

Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol

We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.

Sub-kelvin temperature management in ion traps for optical clocks

The uncertainty of the ac Stark shift due to thermal radiation represents a major contribution to the systematic uncertainty budget of state-of-the-art optical atomic clocks. In the case of optical clocks based on trapped ions, the thermal behavior of the rf-driven ion trap must be precisely known. This determination is even more difficult when scalable linear ion traps are used. Such traps enable a more advanced control of multiple ions and have become a platform for new applications in quantum metrology, simulation, and computation. Nevertheless, their complex structure makes it more difficult to precisely determine its temperature in operation and thus the related systematic uncertainty. We present here scalable linear ion traps for optical clocks, which exhibit very low temperature rise under operation. We use a finite-element model refined with experimental measurements to determine the thermal distribution in the ion trap and the temperature at the position of the ions. The trap temperature is investigated at different rf-drive frequencies and amplitudes with an infrared camera and integrated temperature sensors. We show that for typical trapping parameters for In+, Al+, Lu+, Ca+, Sr+, or Yb+ ions, the temperature rise at the position of the ions resulting from rf heating of the trap stays below 700 mK and can be controlled with an uncertainty on the order of a few 100 mK maximum. The corresponding uncertainty of the trap-related blackbody radiation shift is in the low 10-19 and even 10-20 regime for 171Yb+(E3) and 115In+, respectively.

Coherent Excitation of the Highly Forbidden Electric Octupole Transition in ^{172}Yb^{+}

We report on the first coherent excitation of the highly forbidden ^{2}S_{1/2}→^{2}F_{7/2} electric octupole (E3) transition in a single trapped ^{172}Yb^{+} ion, an isotope without nuclear spin. Using the transition in ^{171}Yb^{+} as a reference, we determine the transition frequency to be 642 116 784 950 887.6(2.4) Hz. We map out the magnetic field environment using the forbidden ^{2}S_{1/2}→^{2}D_{5/2} electric quadrupole (E2) transition and determine its frequency to be 729 476 867 027 206.8(4.4) Hz. Our results are a factor of 1×10^{5} (3×10^{5}) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable ^{2}F_{7/2} state of Yb^{+}.

Enhanced observation time of magneto-optical traps using micro-machined non-evaporable getter pumps

We show that micro-machined non-evaporable getter pumps (NEGs) can extend the time over which laser cooled atoms can be produced in a magneto-optical trap (MOT), in the absence of other vacuum pumping mechanisms. In a first study, we incorporate a silicon-glass microfabricated ultra-high vacuum (UHV) cell with silicon etched NEG cavities and alumino-silicate glass (ASG) windows and demonstrate the observation of a repeatedly-loading MOT over a 10 min period with a single laser-activated NEG. In a second study, the capacity of passive pumping with laser activated NEG materials is further investigated in a borosilicate glass-blown cuvette cell containing five NEG tablets. In this cell, the MOT remained visible for over 4 days without any external active pumping system. This MOT observation time exceeds the one obtained in the no-NEG scenario by almost five orders of magnitude. The cell scalability and potential vacuum longevity made possible with NEG materials may enable in the future the development of miniaturized cold-atom instruments.

Coherent Suppression of Tensor Frequency Shifts through Magnetic Field Rotation

We introduce a scheme to coherently suppress second-rank tensor frequency shifts in atomic clocks, relying on the continuous rotation of an external magnetic field during the free atomic state evolution in a Ramsey sequence. The method retrieves the unperturbed frequency within a single interrogation cycle and is readily applicable to various atomic clock systems. For the frequency shift due to the electric quadrupole interaction, we experimentally demonstrate suppression by more than two orders of magnitude for the ^{2}S_{1/2}→^{2}D_{3/2} transition of a single trapped ^{171}Yb^{+} ion. The scheme provides particular advantages in the case of the ^{171}Yb^{+} ^{2}S_{1/2}→^{2}F_{7/2} electric octupole (E3) transition. For an improved estimate of the residual quadrupole shift for this transition, we measure the excited state electric quadrupole moments Θ(^{2}D_{3/2})=1.95(1)ea_{0}^{2} and Θ(^{2}F_{7/2})=-0.0297(5)ea_{0}^{2} with e the elementary charge and a_{0} the Bohr radius, improving the measurement uncertainties by one order of magnitude.

Detection of metastable electronic states by Penning trap mass spectrometry

State-of-the-art optical clocks¹ achieve precisions of 10^-18 or better using ensembles of atoms in optical lattices^2,3 or individual ions in radio-frequency traps^4,5. Promising candidates for use in atomic clocks are highly charged ions⁶ (HCIs) and nuclear transitions⁷, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range⁸ that are accessible to frequency combs⁹. However, insufficiently accurate atomic structure calculations hinder the identification of suitable transitions in HCIs. Here we report the observation of a long-lived metastable electronic state in an HCI by measuring the mass difference between the ground and excited states in rhenium, providing a non-destructive, direct determination of an electronic excitation energy. The result is in agreement with advanced calculations. We use the high-precision Penning trap mass spectrometer PENTATRAP to measure the cyclotron frequency ratio of the ground state to the metastable state of the ion with a precision of 10^-11-an improvement by a factor of ten compared with previous measurements^10,11. With a lifetime of about 130 days, the potential soft-X-ray frequency reference at 4.96 × 10¹⁶ hertz (corresponding to a transition energy of 202 electronvolts) has a linewidth of only 5 × 10^-8 hertz and one of the highest electronic quality factors (10²⁴) measured experimentally so far. The low uncertainty of our method will enable searches for further soft-X-ray clock transitions^8,12 in HCIs, which are required for precision studies of fundamental physics⁶.

Integrated multiple wavelength stabilization on a multi-channel cavity for a transportable optical clock

We present a simple, compact, and efficient scheme for integrated multiple wavelength stabilization and continuous operation of a transportable ⁴⁰Ca⁺ optical clock using a multi-channel cavity. The fractional frequency instability of 729 nm clock laser is ∼ 1.5 ×10^-15 at 10 s with an approximate linewidth of 1 Hz. Meanwhile, frequency fluctuations of all the other lasers are less than ± 330 kHz/day. The one-day stability of this clock is measured as ∼ 5 ×10^-17 through 72 h continuous operation. This scheme is potentially useful for the realization of next-generation transportable optical clocks and other metrological systems.

Optical frequency distribution using laser repeater stations with planar lightwave circuits

We report a cascaded optical fiber link which connects laboratories in RIKEN, the University of Tokyo, and NTT within a 100-km region using a transfer light at 1397 nm, a subharmonic of the Sr clock frequency. The multiple cascaded link employing several laser repeater stations benefits from a wide feedback bandwidth for fiber noise compensation, which allows constructing optical lattice clock networks based on the master-slave configuration. We developed the laser repeater stations based on planar lightwave circuits to significantly reduce the interferometer noise for improved link stability. We implemented a 240-km-long cascaded link in a UTokyo-NTT-UTokyo loop using light sent from RIKEN via a 30-km-long link. In environments with large fiber noise, the link instability is 3 × 10^-16 at an averaging time of 1 s and reaches 1 × 10^-18 at 2,600 s.

Hyperfine Averaging by Dynamic Decoupling in a Multi-Ion Lutetium Clock

We propose and experimentally demonstrate a scheme that realizes hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with autobalanced Ramsey spectroscopy, which facilitates the elimination of residual shifts due to imperfect implementation and ac stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the ^{1}S_{0}↔^{3}D_{1} clock transition in a three-ion Lu^{+} clock. From the demonstration we are able to provide a measurement of the ^{3}D_{1} quadrupole moment, Θ(^{3}D_{1})=0.634(9)ea_{0}^{2}.

Cavity-enhanced non-destructive detection of atoms for an optical lattice clock

We demonstrate a new method of cavity-enhanced non-destructive detection of atoms for a strontium optical lattice clock. The detection scheme is shown to be linear in atom number up to at least 2×10⁴ atoms, to reject technical noise sources, to achieve signal to noise ratio close to the photon shot noise limit, to provide spatially uniform atom-cavity coupling, and to minimize inhomogeneous ac Stark shifts. These features enable detection of atoms with minimal perturbation to the atomic state, a critical step towards realizing an ultra-high-stability, quantum-enhanced optical lattice clock.

End-to-end topology for fiber comb based optical frequency transfer at the 10-21 level

We introduce a simple and robust scheme for optical frequency transfer of an ultra-stable source light field via an optical frequency comb to a field at a target optical frequency, where highest stability is required, e.g., for the interrogation of an optical clock. The scheme relies on a topology for end-to-end suppression of the influence of optical path-length fluctuations, which is attained by actively phase-stabilized delivery, combined with common-path propagation. This approach provides a robust stability improvement without the need for additional isolation against environmental disturbances such as temperature, pressure or humidity changes. We measure residual frequency transfer instabilities by comparing the frequency transfers carried out with two independent combs simultaneously. Residual fractional frequency instabilities between two systems of 8 × 10^-18 at 1 s and 3 × 10^-21 at 10⁵ s averaging time are observed. We discuss the individual noise contributions to the residual instability. The presented scheme is technically simple, robust against environmental parameter fluctuations and enables an ultra-stable frequency transfer, e.g., to optical clock lasers or to lasers in gravitational wave detectors.

Overview of the Phenomenology of Lorentz and CPT Violation in Atomic Systems

This is an overview of recent publications on the prospects of searching for nonminimal Lorentz-violating effects in atomic spectroscopy experiments. The article discusses the differences in the signals for Lorentz violation in the presence of minimal and nonminimal operators and what systems are more sensitive to certain types of Lorentz-violating operators.