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

Clock with 8×10^{-19} Systematic Uncertainty

We report an optical lattice clock with a total systematic uncertainty of 8.1×10^{-19} in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultranarrow ^{1}S_{0}→^{3}P_{0} transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ^{3}D_{1} lifetime, necessitating precise characterization and control of many body effects in the 5s4d ^{3}D_{1} decay. Last, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1×10^{-19}.

Asymmetric Magnon Frequency Comb

We theoretically show the asymmetric spin wave transmission in a coupled waveguide-skyrmion structure, where the skyrmion acts as an effective nanocavity allowing the whispering gallery modes for magnons. The asymmetry originates from the chiral spin wave mode localized in the circular skyrmion wall. By inputting two-tone excitations and mixing them in the skyrmion wall, we observe a unidirectional output magnon frequency comb propagating in the waveguide with a record number of teeth (>50). This coupled waveguide-cavity structure turns out to be a universal paradigm for generating asymmetric magnon frequency combs, where the cavity can be generalized to other magnetic structures that support the whispering gallery mode of magnons. Our results advance the understanding of the nonlinear interaction between magnons and magnetic textures and open a new pathway to exploring the asymmetric spin wave transmission and to steering the magnon frequency comb.

Remote and controlled quantum teleportation network of the polarization squeezed state

Quantum teleportation is a building block in quantum computation and quantum communication. The continuous-variable polarization squeezed state is a key resource in quantum networks, offering advantages for long-distance distribution and direct interfacing of quantum nodes. Although polarization squeezed state has been generated and distributed between remote users, it is a long-standing goal to implement controlled quantum teleportation of the polarization squeezed state with multiple remote users. Here, we propose a feasible scheme to teleport a polarization squeezed state among multiple remote users under control. The polarization state is transferred between different remote quantum networks, and the controlled quantum teleportation of the polarization state can be implemented in one quantum network involving multiple remote users. The results show that such a controlled quantum teleportation can be realized with 36 users through about 6-km free-space or fiber quantum channels, where the fidelity of 0.352 is achieved beyond the classical limit of 0.349 with an input squeezing variance of 0.25. This scheme provides a direct reference for the experimental implementation of remote and controlled quantum teleportation of polarization states, thus enabling more teleportation-based quantum network protocols.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Magnetostriction measurements at milli-kelvin temperatures using a Fabry-Pérot interferometer

This paper demonstrates an optical technique to measure magnetostrictive strain in a cryogenic environment using a Fabry-Pérot resonator spaced by crystal samples. Optical measurement techniques are calibration-free and highly sensitive. This technique was used to measure the magnetostrictive strain of neodymium gallate at a temperature of 49 mK to be λ = 1.3 × 10-5 at 3 T, with a sensitivity of 3.0 × 10-8. We highlight the interesting properties of the crystal's magnetic ordering. The sensitivity of this technique was limited by the wavemeter used to measure the laser frequency, and significant improvements in the sensitivity should be possible.

Excited-Band Coherent Delocalization for Improved Optical Lattice Clock Performance

We implement coherent delocalization as a tool for improving the two primary metrics of atomic clock performance: systematic uncertainty and instability. By decreasing atomic density with coherent delocalization, we suppress cold-collision shifts and two-body losses. Atom loss attributed to Landau-Zener tunneling in the ground lattice band would compromise coherent delocalization at low trap depths for our ^{171}Yb atoms; hence, we implement for the first time delocalization in excited lattice bands. Doing so increases the spatial distribution of atoms trapped in the vertically oriented optical lattice by ∼7 times. At the same time, we observe a reduction of the cold-collision shift by 6.5(8) times, while also making inelastic two-body loss negligible. With these advantages, we measure the trap-light-induced quenching rate and natural lifetime of the ^{3}P_{0} excited state as 5.7(7)×10^{-4}  E_{r}^{-1} s^{-1} and 19(2) s, respectively.

Free space optical link to a tethered balloon for frequency transfer and chronometric geodesy

We present the results of an optical link to a corner cube on board a tethered balloon at 300 m altitude including a Tip/Tilt compensation for the balloon tracking. Our experiment measures the carrier phase of a 1542 nm laser, which is the useful signal for frequency comparison of distant clocks. An active phase noise compensation of the carrier is implemented, demonstrating a fractional frequency stability of 8 × 10-19 after 16 s averaging, which slightly (factor ∼ 3) improves on best previous links via an airborne platform. This state-of-the-art result is obtained with a transportable set-up that enables a fast field deployment.

Node-downloadable frequency transfer system based on a mode-locked laser with over 100 km of fiber

To meet the requirements of time-frequency networks and enable frequency downloadability for nodes along the link, we demonstrated the extraction of stable frequency signals at nodes using a mode-locked laser under the condition of 100 km laboratory fiber. The node consists of a simple structure that utilizes widely used optoelectronic devices and enables plug-and-play applications. In addition, the node can recover frequency signals with multiple frequencies, which are useful for scenarios that require different frequencies. Here, we experimentally demonstrated a short-term frequency instability of 2.83 × 10-13@1 s and a long-term frequency instability of 1.18 × 10-15@10,000 s at the node, which is similar to that at the remote site of the frequency transfer system. At the same time, frequency signals with different frequencies also achieved stable extraction with the same performance at the node. Our results can support the distributed application under large-scale time-frequency networks.

Narrow and Ultranarrow Transitions in Highly Charged Xe Ions as Probes of Fifth Forces

Optical frequency metrology in atoms and ions can probe hypothetical fifth forces between electrons and neutrons by sensing minute perturbations of the electronic wave function induced by them. A generalized King plot has been proposed to distinguish them from possible standard model effects arising from, e.g., finite nuclear size and electronic correlations. Additional isotopes and transitions are required for this approach. Xenon is an excellent candidate, with seven stable isotopes with zero nuclear spin, however it has no known visible ground-state transitions for high resolution spectroscopy. To address this, we have found and measured twelve magnetic-dipole lines in its highly charged ions and theoretically studied their sensitivity to fifth forces as well as the suppression of spurious higher-order standard model effects. Moreover, we identified at 764.8753(16) nm a E2-type ground-state transition with 500 s excited state lifetime as a potential clock candidate further enhancing our proposed scheme.

High power optical frequency comb with 10-19 frequency instability

Optical frequency combs with more than 10 W have paved the way for extreme ultraviolet combs generation by interaction with inert gases, leading to extreme nonlinear spectroscopy and the ultraviolet nuclear clock. Recently, the demand for an ultra-long-distance time and frequency space transfer via optical dual-comb proposes a new challenge for high power frequency comb in respect of power scaling and optical frequency stability. Here we present a frequency comb based on fiber chirped pulse amplification (CPA), which can offer more than 20 W output power. We further characterize the amplifier branch noise contribution by comparing two methods of locking to an optical reference and measure the out-of-loop frequency instability by heterodyning two identical high-power combs. Thanks to the low noise CPA, reasonable locking method, and optical path-controlled amplifiers, the out-of-loop beat note between two combs demonstrates the unprecedented frequency stability of 4.35 × 10-17 at 1s and 6.54 × 10-19 at 1000 s.

An integrated high-flux cold atomic beam source for strontium

We present the design, construction, and characterization of an integrated cold atomic beam source for strontium (Sr), which is based on a compact Zeeman slower for slowing the thermal atomic beam and an atomic deflector for selecting the cold flux. By adopting arrays of permanent magnets to produce the magnetic fields of the slower and the deflector, we effectively reduce the system size and power compared to traditional systems with magnetic coils. After the slower cooling, one can employ additional transverse cooling in the radial direction and improve the atom collimation. The atomic deflectors employ two stages of two-dimensional magnetic-optical trapping (MOT) to deflect the cold flux, whose atomic speed is lower than 50 m/s, by 20° from the thermal atomic beam. We characterize the cold atomic beam flux of the source by measuring the loading rate of a three-dimensional MOT. The loading rates reach up to 109 atoms/s. The setup is compact, highly tunable, lightweight, and requires low electrical power, which addresses the challenge of reducing the complexity of building optical atomic clocks and quantum simulation devices based on Sr.

Long-range fiber-optic earthquake sensing by active phase noise cancellation

We present a long-range fiber-optic environmental deformation sensor based on active phase noise cancellation (PNC) in metrological frequency dissemination. PNC sensing exploits recordings of a compensation frequency that is commonly discarded. Without the need for dedicated measurement devices, it operates synchronously with metrological services, suggesting that existing phase-stabilized metrological networks can be co-used effortlessly as environmental sensors. The compatibility of PNC sensing with inline amplification enables the interrogation of cables with lengths beyond 1000 km, making it a potential contributor to earthquake detection and early warning in the oceans. Using spectral-element wavefield simulations that accurately account for complex cable geometry, we compare observed and computed recordings of the compensation frequency for a magnitude 3.9 earthquake in south-eastern France and a 123 km fiber link between Bern and Basel, Switzerland. The match in both phase and amplitude indicates that PNC sensing can be used quantitatively, for example, in earthquake detection and characterization.

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.

Erratum: ^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18} [Phys. Rev. Lett. 123, 033201 (2019)]

This corrects the article DOI: 10.1103/PhysRevLett.123.033201.

Loss-tolerant and quantum-enhanced interferometer by reversed squeezing processes

Reversed nonlinear dynamics is predicted to be capable of enhancing the quantum sensing in unprecedented ways. Here, we report the experimental demonstration of a loss-tolerant (external loss) and quantum-enhanced interferometer. Two cascaded optical parametric amplifiers are used to judiciously construct an interferometry with two orthogonal squeezing operation. As a consequence, a weak displacement introduced by a test cavity can be amplified for measurement, and the measured signal-to-noise ratio is better than that of both conventional photon shot-noise limited and squeezed-light assisted interferometers. We further confirm its superior loss-tolerant performance by varying the external losses and comparing with both conventional photon shot-noise limited and squeezed-light assisted configurations, illustrating the potential application in gravitational wave detection.

Evaluating Optical Clock Performance for GNSS Positioning

Atomic clocks are highly precise timing devices used in numerous Positioning, Navigation, and Timing (PNT) applications on the ground and in outer space. In recent years, however, more precise timing solutions based on optical technology have been introduced as current technology capabilities advance. State-of-the-art optical clocks-predicted to be the next level of their predecessor atomic clocks-have achieved ultimate uncertainty of 1 × 10^-18 and beyond, which exceeds the best atomic clock's performance by two orders of magnitude. Hence, the successful development of optical clocks has drawn significant attention in academia and industry to exploit many more opportunities. This paper first provides an overview of the emerging optical clock technology, its current development, and characteristics, followed by a clock stability analysis of some of the successfully developed optical clocks against current Global Navigation Satellite System (GNSS) satellite clocks to discuss the optical clock potentiality in GNSS positioning. The overlapping Allan Deviation (ADEV) method is applied to estimate the satellite clock stability from International GNSS Service (IGS) clock products, whereas the optical clock details are sourced from the existing literature. The findings are (a) the optical clocks are more stable than that of atomic clocks onboard GNSS satellites, though they may require further technological maturity to meet spacecraft payload requirements, and (b) in GNSS positioning, optical clocks could potentially offer less than a 1 mm range error (clock-related) in 30 s and at least 10 times better timing performance after 900 s in contrast to the Galileo satellite atomic clocks-which is determined in this study as the most stable GNSS atomic clock type used in satellite positioning.

Search for Ultralight Dark Matter with Spectroscopy of Radio-Frequency Atomic Transitions

The effects of scalar and pseudoscalar ultralight bosonic dark matter (UBDM) were searched for by comparing the frequency of a quartz oscillator to that of a hyperfine-structure transition in ^{87}Rb, and an electronic transition in ^{164}Dy. We constrain linear interactions between a scalar UBDM field and standard-model (SM) fields for an underlying UBDM particle mass in the range 1×10^{-17}-8.3×10^{-13}  eV and quadratic interactions between a pseudoscalar UBDM field and SM fields in the range 5×10^{-18}-4.1×10^{-13}  eV. Within regions of the respective ranges, our constraints on linear interactions significantly improve on results from previous, direct searches for oscillations in atomic parameters, while constraints on quadratic interactions surpass limits imposed by such direct searches as well as by astrophysical observations.

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.

Quantum-limited optical time transfer for future geosynchronous links

The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity^1-3, dark-matter searches⁴ and gravitational-wave detection⁵. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry^6,7, advanced satellite navigation⁸, clock-based geodesy^2,9,10 and thousandfold improvements in intercontinental time dissemination^11,12. Thus far, only optical clocks have pushed towards quantum-limited performance¹³. By contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches^14-24. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 µW, distant sites are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links in which photons are few and amplification costly: at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits.

Intercombination line frequencies in 171Yb validated with the clock transition

We have carried absolute frequency measurements of the (6s 2) 1 S 0-(6s6p) 3 P 1 transition in 171 Y b (intercombination line), where the spin-1/2 isotope yields two hyperfine lines. The measurements rely on sub-Doppler spectroscopy to yield a discriminator to which a 556 nm laser is locked. The frequency reference for the optical frequency measurements is a high-quality quartz oscillator steered to the GNSS time scale that is bridged with a frequency comb. The reference is validated to ∼3×10-12 by spectroscopy on the 1 S 0- 3 P 0 (clock) line in laser cooled and trapped 171 Y b atoms. From the hyperfine separation between the F=1/2 and F=3/2 levels of 3 P 1, we determine the hyperfine constant to be A(3 P 1)=3957833(28)k H z.

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.

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

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

Compact, portable, thermal-noise-limited optical cavity with low acceleration sensitivity

We develop and demonstrate a compact (less than 6 mL) portable Fabry-Pérot optical reference cavity. A laser locked to the cavity is thermal noise limited at 2 × 10^-14 fractional frequency stability. Broadband feedback control with an electro-optic modulator enables near thermal-noise-limited phase noise performance from 1 Hz to 10 kHz offset frequencies. The additional low vibration, temperature, and holding force sensitivity of our design makes it well suited for out-of-the-lab applications such as optically derived low noise microwave generation, compact and mobile optical atomic clocks, and environmental sensing through deployed fiber networks.

Evaluation of Lattice Light Shift at Low 10^{-19} Uncertainty for a Shallow Lattice Sr Optical Clock

A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. We present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5×10^{-19}.

Mechanical overtone frequency combs

Mechanical frequency combs are poised to bring the applications and utility of optical frequency combs into the mechanical domain. So far, their main challenge has been strict requirements on drive frequencies and power, which complicate operation. We demonstrate a straightforward mechanism to create a frequency comb consisting of mechanical overtones (integer multiples) of a single eigenfrequency, by monolithically integrating a suspended dielectric membrane with a counter-propagating optical trap. The periodic optical field modulates the dielectrophoretic force on the membrane at the overtones of a membrane's motion. These overtones share a fixed frequency and phase relation, and constitute a mechanical frequency comb. The periodic optical field also creates an optothermal parametric drive that requires no additional power or external frequency reference. This combination of effects results in an easy-to-use mechanical frequency comb platform that requires no precise alignment, no additional feedback or control electronics, and only uses a single, mW continuous wave laser beam. This highlights the overtone frequency comb as the straightforward future for applications in sensing, metrology and quantum acoustics.

Entanglement Witness for the Weak Equivalence Principle

The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.

Jet-loaded cold atomic beam source for strontium

We report on the design and characterization of a cold atom source for strontium (Sr) based on a two-dimensional magneto-optical trap (MOT) that is directly loaded from the atom jet of a dispenser. We characterize the atom flux of the source by measuring the loading rate of a three-dimensional MOT. We find loading rates of up to 10⁸ atoms per second. The setup is compact, easy to construct, and has low power consumption. It addresses the longstanding challenge of reducing the complexity of cold beam sources for Sr, which is relevant for optical atomic clocks, quantum simulation, and computing devices based on ultracold Sr.

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298 days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20}  eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28) Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

Distributed quantum sensing with mode-entangled spin-squeezed atomic states

Quantum sensors are used for precision timekeeping, field sensing and quantum communication^1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations^4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network⁹. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes¹⁰. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.

Scalable Quantum Logic Spectroscopy

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of ^{25}Mg^{+} logic ions and ^{27}Al^{+} spectroscopy ions. We observe higher detection efficiency by increasing the number of ^{25}Mg^{+} ions. Applied to multiple ^{27}Al^{+}, this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS.

Cross-platform comparison of arbitrary quantum states

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information of executing specific tasks for a single QC. On the other hand, a comparison between different QCs preparing nominally the same arbitrary circuit provides an insight for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform state fidelities.

Efficient protocols for comparing quantum states generated on different quantum computing platforms are becoming increasingly important. Zhu et al. demonstrate cross-platform verification using randomized measurements that allow for scaling to larger systems as compared to full quantum state tomography.

Free-space dissemination of time and frequency with 10-19 instability over 113 km

Networks of optical clocks find applications in precise navigation^1,2, in efforts to redefine the fundamental unit of the 'second'^3-6 and in gravitational tests⁷. As the frequency instability for state-of-the-art optical clocks has reached the 10^-19 level^8,9, the vision of a global-scale optical network that achieves comparable performances requires the dissemination of time and frequency over a long-distance free-space link with a similar instability of 10^-19. However, previous attempts at free-space dissemination of time and frequency at high precision did not extend beyond dozens of kilometres^10,11. Here we report time-frequency dissemination with an offset of 6.3 × 10^-20 ± 3.4 × 10^-19 and an instability of less than 4 × 10^-19 at 10,000 s through a free-space link of 113 km. Key technologies essential to this achievement include the deployment of high-power frequency combs, high-stability and high-efficiency optical transceiver systems and efficient linear optical sampling. We observe that the stability we have reached is retained for channel losses up to 89 dB. The technique we report can not only be directly used in ground-based applications, but could also lay the groundwork for future satellite time-frequency dissemination.

Subrecoil Clock-Transition Laser Cooling Enabling Shallow Optical Lattice Clocks

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the μK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ^{1}S_{0}-^{3}P_{0} clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10^{-19} level.

An elementary quantum network of entangled optical atomic clocks

Optical atomic clocks are our most precise tools to measure time and frequency^1-3. Precision frequency comparisons between clocks in separate locations enable one to probe the space-time variation of fundamental constants^4,5 and the properties of dark matter^6,7, to perform geodesy^8-10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory-the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances^11-16, comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link^17,18 to entangle two ⁸⁸Sr⁺ ions separated by a macroscopic distance¹⁹ (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly [Formula: see text], the value predicted for the Heisenberg limit. Today's optical clocks are typically limited by dephasing of the probe laser²⁰; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques^20-22. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes²³, to other species of trapped particles or-through local operations-to larger entangled systems.

Silicon nitride stress-optic microresonator modulator for optical control applications

Modulation-based control and locking of lasers, filters and other photonic components is a ubiquitous function across many applications that span the visible to infrared (IR), including atomic, molecular and optical (AMO), quantum sciences, fiber communications, metrology, and microwave photonics. Today, modulators used to realize these control functions consist of high-power bulk-optic components for tuning, sideband modulation, and phase and frequency shifting, while providing low optical insertion loss and operation from DC to 10s of MHz. In order to reduce the size, weight and cost of these applications and improve their scalability and reliability, modulation control functions need to be implemented in a low loss, wafer-scale CMOS-compatible photonic integration platform. The silicon nitride integration platform has been successful at realizing extremely low waveguide losses across the visible to infrared and components including high performance lasers, filters, resonators, stabilization cavities, and optical frequency combs. Yet, progress towards implementing low loss, low power modulators in the silicon nitride platform, while maintaining wafer-scale process compatibility has been limited. Here we report a significant advance in integration of a piezo-electric (PZT, lead zirconate titanate) actuated micro-ring modulation in a fully-planar, wafer-scale silicon nitride platform, that maintains low optical loss (0.03 dB/cm in a 625 µm resonator) at 1550 nm, with an order of magnitude increase in bandwidth (DC - 15 MHz 3-dB and DC - 25 MHz 6-dB) and order of magnitude lower power consumption of 20 nW improvement over prior PZT modulators. The modulator provides a >14 dB extinction ratio (ER) and 7.1 million quality-factor (Q) over the entire 4 GHz tuning range, a tuning efficiency of 162 MHz/V, and delivers the linearity required for control applications with 65.1 dB·Hz^2/3 and 73.8 dB·Hz^2/3 third-order intermodulation distortion (IMD3) spurious free dynamic range (SFDR) at 1 MHz and 10 MHz respectively. We demonstrate two control applications, laser stabilization in a Pound-Drever Hall (PDH) lock loop, reducing laser frequency noise by 40 dB, and as a laser carrier tracking filter. This PZT modulator design can be extended to the visible in the ultra-low loss silicon nitride platform with minor waveguide design changes. This integration of PZT modulation in the ultra-low loss silicon nitride waveguide platform enables modulator control functions in a wide range of visible to IR applications such as atomic and molecular transition locking for cooling, trapping and probing, controllable optical frequency combs, low-power external cavity tunable lasers, quantum computers, sensors and communications, atomic clocks, and tunable ultra-low linewidth lasers and ultra-low phase noise microwave synthesizers.

Frequency comb-to-comb stabilization over a 1.3-km free-space atmospheric optical link

Stabilizing a frequency comb to an ultra-stable optical frequency reference requires a multitude of optoelectronic peripherals that have to operate under strict ambient control. Meanwhile, the frequency comb-to-comb stabilization aims to synchronize a slave comb to a well-established master comb with a substantial saving in required equipment and efforts. Here, we report an utmost case of frequency comb-to-comb stabilization made through a 1.3 km free-space optical (FSO) link by coherent transfer of two separate comb lines along with a feedback suppression control of atmospheric phase noise. The FSO link offers a transfer stability of 1.7 × 10^-15 at 0.1 s averaging, while transporting the master comb's stability of 1.2 × 10^-15 at 1.0 s over the entire spectrum of the slave comb. Our remote comb-to-comb stabilization is intended to expedite diverse long-distance ground-to-ground or ground-to-satellite applications; as demonstrated here for broadband molecular spectroscopy over a 6 THz bandwidth as well as ultra-stable microwaves generation with phase noise of -80 dBc Hz^-1 at 1 Hz.

Coherent frequency transfer with < 5*10-21 stability via a multi-branch comb with noise cancellation

We demonstrate a multi-branch frequency comb for spectral purity transfer incorporating hardware enabled noise cancellation based on a cw noise transfer laser. We verify coherent frequency transfer at stabilities ≈ 2×10^-18 in 1 second and < 5×10^-21 in 10,000 seconds without any reference cavity.

Continuous Bose-Einstein condensation

Bose-Einstein condensates (BECs) are macroscopic coherent matter waves that have revolutionized quantum science and atomic physics. They are important to quantum simulation¹ and sensing^2,3, for example, underlying atom interferometers in space⁴ and ambitious tests of Einstein's equivalence principle^5,6. A long-standing constraint for quantum gas devices has been the need to execute cooling stages time-sequentially, restricting these devices to pulsed operation. Here we demonstrate continuous Bose-Einstein condensation by creating a continuous-wave (CW) condensate of strontium atoms that lasts indefinitely. The coherent matter wave is sustained by amplification through Bose-stimulated gain of atoms from a thermal bath. By steadily replenishing this bath while achieving 1,000 times higher phase-space densities than previous works^7,8, we maintain the conditions for condensation. Our experiment is the matter wave analogue of a CW optical laser with fully reflective cavity mirrors. This proof-of-principle demonstration provides a new, hitherto missing piece of atom optics, enabling the construction of continuous coherent-matter-wave devices.

Laser-cooled 171Yb+ microwave frequency standard with a short-term frequency instability of 8.5 × 10-13/√τ

We report on the development of a microwave frequency standard based on a laser-cooled ¹⁷¹ Y b ⁺ ion trap system. The electronics , lasers, and magnetic shields are integrated into a single physical package. With over 10⁵ ions are stably trapped, the system offers a high signal-to-noise ratio Ramsey line-shape. In comparison with previous work, the frequency instability of a ¹⁷¹ Y b ⁺ microwave clock was further improved to 8.5×10^-13/τ for averaging times between 10 and 1000 s. Essential systematic shifts and uncertainties are also estimated.

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.

Differential clock comparisons with a multiplexed optical lattice clock

Rapid progress in optical atomic clock performance has advanced the frontiers of timekeeping, metrology and quantum science^1-3. Despite considerable efforts, the instabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves^4,5. Here we implement a 'multiplexed' one-dimensional optical lattice clock, in which spatially resolved strontium atom ensembles are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser and read-out in parallel. In synchronous Ramsey interrogations of ensemble pairs we observe atom-atom coherence times of 26 s, a 270-fold improvement over the measured atom-laser coherence time, demonstrate a relative instability of [Formula: see text] (where τ is the averaging time) and reach a relative statistical uncertainty of 8.9 × 10^-20 after 3.3 h of averaging. These results demonstrate that applications involving optical clock comparisons need not be limited by the instability of the local oscillator. We further realize a miniaturized clock network consisting of 6 atomic ensembles and 15 simultaneous pairwise comparisons with relative instabilities below [Formula: see text], and prepare spatially resolved, heterogeneous ensemble pairs of all four stable strontium isotopes. These results pave the way for multiplexed precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, the development of clock-based gravitational wave and dark matter detectors^6-12 and new tests of relativity in the lab^13-16.

Floquet Engineering Hz-Level Rabi Spectra in Shallow Optical Lattice Clock

Quantum metrology with ultrahigh precision usually requires atoms prepared in an ultrastable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultracold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive a shallow ^{87}Sr optical lattice clock. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4 Hz linewidth. With careful comparison between the theory and experiment, we demonstrate that the Rabi frequency and the Bloch bands can be tuned, simultaneously and independently. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phases of matter by engineering exotic spin orbit couplings.

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.

Coherent fibre link for synchronization of delocalized atomic clocks

Challenging experiments for tests in fundamental physics require highly coherent optical frequency references with suppressed phase noise from hundreds of kHz down to μHz of Fourier frequencies. It can be achieved by remote synchronization of many frequency references interconnected by stabilized optical fibre links. Here we describe the path to realize a delocalized optical frequency reference for spectroscopy of the isomeric state of the nucleus of Thorium-229 atom. This is a prerequisite for the realization of the next generation of an optical clock - the nuclear clock. We present the established 235 km long phase-coherent stabilized cross-border fibre link connecting two delocalized metrology laboratories in Brno and Vienna operating highly-coherent lasers disciplined by active Hydrogen masers through optical frequency combs. A significant part (up to tens of km) of the optical fibre is passing urban combined collectors with a non-negligible level of acoustic interference and temperature changes, which results in a power spectral density of phase noise over 10⁵ rad²· Hz^-1. Therefore, we deploy a digital signal processing technique to suppress the fibre phase noise over a wide dynamic range of phase fluctuations. To demonstrate the functionality of the link, we measured the phase noise power spectral density of a remote beat note between two independent lasers, locked to high-finesse stable resonators. Using optical frequency combs at both ends of the link, a long-term fractional frequency stability in the order of 10^-15 between local active Hydrogen masers was measured as well. Thanks to this technique, we have achieved reliable operation of the phase-coherent fibre link with fractional stability of 7 × 10^-18 in 10³ s.

Digital Doppler-Cancellation Servo for Ultrastable Optical Frequency Dissemination Over Fiber

Progress made in optical references, including ultrastable Fabry-Perot cavities, optical frequency combs, and optical atomic clocks, has driven the need for ultrastable optical fiber networks. Telecom-wavelength ultrapure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this article, we present a Doppler-cancellation setup based on a digital phase-locked loop (PLL) for ultrastable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the software-defined radio (SDR) implementation of the PLL is based on a compact commercial board embedding a field-programmable gate array and analog-to-digital and digital-to-analog converters. Using three different configurations, including an undersampling method, we demonstrate a 20-m-long fiber link with residual fractional frequency instability as low as 10^-18 at 1000 s and optical phase noise of -70 dBc/Hz at 1 Hz with a telecom frequency carrier.

Radium Ion Optical Clock

We report the first operation of a Ra^{+} optical clock, a promising high-performance clock candidate. The clock uses a single trapped ^{226}Ra^{+} ion and operates on the 7s ^{2}S_{1/2}→6d ^{2}D_{5/2} electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1×10^{-13}/sqrt[τ], where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν=9×10^{-16}. Using the clock, we realize the first measurement of the ratio of the D_{5/2} state to the S_{1/2} state Landé g-factors: g_{D}/g_{S}=0.598 805 3(11). A Ra^{+} optical clock could improve limits on the time variation of the fine structure constant, α[over ˙]/α, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.