A Fermi-degenerate three-dimensional optical lattice clock

Scalable Spin Squeezing from Critical Slowing Down in Short-Range Interacting Systems

Long-range spin-spin interactions are known to generate nonequilibrium dynamics that can squeeze the collective spin of a quantum spin ensemble in a scalable manner, leading to states whose metrologically useful entanglement grows with system size. Here, we show theoretically that scalable squeezing can be produced in 2D U(1)-symmetric systems even by short-range interactions, i.e., interactions that at equilibrium do not lead to long-range order at finite temperatures, but rather to an extended Berezinskii-Kosterlitz-Thouless critical phase. If the initial state is a coherent spin state in the easy plane of interactions, whose energy corresponds to a thermal state in the critical Berezinskii-Kosterlitz-Thouless phase, the nonequilibrium dynamics exhibits critical slowing down, corresponding to a power-law decay of the collective magnetization in time. This slow decay protects scalable squeezing, whose scaling reveals in turn the decay exponent of the magnetization. Our results open the path to realizing massive entangled states of potential metrological interest in many relevant platforms of quantum simulation and information processing-such as Mott insulators of ultracold atoms, or superconducting circuits-characterized by short-range interactions in planar geometries.

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10-19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔  3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

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.

Joint time and frequency transfer through one International Telecommunication Union 100 GHz wavelength division multiplexing channel with commercial devices

We proposed a joint time and frequency transfer scheme over a single International Telecommunication Union 100 GHz wavelength division multiplexing (WDM) channel using a normal commercial WDM device and commercial offset WDM device. A standard 100 GHz WDM channel is divided into three sub-channels with a frequency interval of more than 20 GHz for a time and frequency transfer, which could help to avoid the interference among time, frequency, and data signals in other WDM channels. A joint high-precision time and frequency transfer is, therefore, able to be performed with data transmission over WDM optical communication links without extra requirements on devices. A joint time and frequency transfer in a single 100 GHz WDM channel is experimentally demonstrated over a 60 km fiber link with the communication data transmission in the adjacent channels. The stability of the time transfer can be better than 15 ps at 1 s, and the stability of the frequency transfer can be better than 2.7×10-14 at 1 s, while the bit error rates of the adjacent channels are at the same level as the separate transmission.

Collectively enhanced Ramsey readout by cavity sub- to superradiant transition

When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A π/2-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second π/2-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is an innovative approach to atomic state readout characterized by its speed, simplicity, and highly directional emission of signal photons. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters.

Observation of millihertz-level cooperative Lamb shifts in an optical atomic clock

Collective couplings of atomic dipoles to a shared electromagnetic environment produce a wide range of many-body phenomena. We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions produce spatially dependent cooperative Lamb shifts when spectroscopically interrogating the millihertz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared with nonresonant geometries. Our work demonstrates a platform for precise studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.

Topological Inverse Band Theory in Waveguide Quantum Electrodynamics

Topological phases play a crucial role in the fundamental physics of light-matter interaction and emerging applications of quantum technologies. However, the topological band theory of waveguide QED systems is known to break down, because the energy bands become disconnected. Here, we introduce a concept of the inverse energy band and explore analytically topological scattering in a waveguide with an array of quantum emitters. We uncover a rich structure of topological phase transitions, symmetric scale-free localization, completely flat bands, and the corresponding dark Wannier states. Although bulk-edge correspondence is partially broken because of radiative decay, we prove analytically that the scale-free localized states are distributed in a single inverse energy band in the topological phase and in two inverse bands in the trivial phase. Surprisingly, the winding number of the scattering textures depends on both the topological phase of inverse subradiant band and the odevity of the cell number. Our Letter uncovers the field of the topological inverse bands, and it brings a novel vision to topological phases in light-matter interactions.

Quantum-enhanced sensing on optical transitions through finite-range interactions

The control over quantum states in atomic systems has led to the most precise optical atomic clocks so far1-3. Their sensitivity is bounded at present by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can-nevertheless-be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real-world sensors is extremely challenging. Here we illustrate a pathway for harnessing large-scale entanglement in an optical transition using 1D chains of up to 51 ions with interactions that decay as a power-law function of the ion separation. We show that our sensor can emulate many features of the one-axis-twisting (OAT) model, an iconic, fully connected model known to generate scalable squeezing4 and Greenberger-Horne-Zeilinger-like states5-8. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, that is, spin-wave excitations (SWE), at finite momenta, the generation of spin squeezing comparable with OAT (a Wineland parameter9,10 of -3.9 ± 0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of multi-headed cat states in the Q-distribution. We demonstrate the metrological utility of the states in a Ramsey-type interferometer, in which we reduce the measurement uncertainty by -3.2 ± 0.5 dB below the standard quantum limit for N = 51 ions.

A lab-based test of the gravitational redshift with a miniature clock network

Einstein's theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of [ - 12.4 ± 0. 7(stat) ± 2. 5(sys)] × 10-19/cm, consistent with the expected redshift gradient of - 10.9 × 10-19/cm. Our results can also be viewed as relativistic gravitational potential difference measurements with sensitivity to mm scale changes in height on the surface of the Earth. These results highlight the potential of local-oscillator-independent differential clock comparisons for emerging applications of optical atomic clocks including geodesy, searches for new physics, gravitational wave detection, and explorations of the interplay between quantum mechanics and gravity.

Subnatural Linewidth Superradiant Lasing with Cold ^{88}Sr Atoms

Superradiant lasers operate in the bad-cavity regime, where the phase coherence is stored in the spin state of an atomic medium rather than in the intracavity electric field. Such lasers use collective effects to sustain lasing and could potentially reach considerably lower linewidths than a conventional laser. Here, we investigate the properties of superradiant lasing in an ensemble of ultracold ^{88}Sr atoms inside an optical cavity. We extend the superradiant emission on the 7.5 kHz wide ^{3}P_{1}→^{1}S_{0} intercombination line to several milliseconds, and observe steady parameters suitable for emulating the performance of a continuous superradiant laser by fine tuning the repumping rates. We reach a lasing linewidth of 820 Hz for 1.1 ms of lasing, nearly an order of magnitude lower than the natural linewidth.

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.

Pauli blocking of stimulated emission in a degenerate Fermi gas

The Pauli exclusion principle in quantum mechanics has a profound influence on the structure of matter and on interactions between fermions. Almost 30 years ago it was predicted that the Pauli exclusion principle could lead to a suppression of spontaneous emission, and only recently several experiments confirmed this phenomenon. Here we report that this so-called Pauli blockade not only affects incoherent processes but also, more generally, coherently driven systems. It manifests itself as an intriguing sub-Doppler narrowing of a doubly-forbidden transition profile in an optically trapped Fermi gas of ³He. By actively pumping atoms out of the excited state, we break the coherence of the excitation and lift the narrowing effect, confirming the influence of Pauli blockade on the transition profile. This insight into the interplay between quantum statistics and coherent driving is a promising development for future applications involving fermionic systems.

Pauli exclusion principle has fundamental and practical consequences to the structure of matter and particle interaction. Here the authors demonstrate Pauli blocking in a coherently driven system using trapped 3He degenerate Fermi gases.

Hamiltonian engineering of spin-orbit-coupled fermions in a Wannier-Stark optical lattice clock

Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a "magic" lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.

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.

Scalable Spin Squeezing from Spontaneous Breaking of a Continuous Symmetry

Spontaneous symmetry breaking is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the case of quantum spin models with continuous symmetry, we show that this adiabatic process is also accompanied by the suppression of the fluctuations of the symmetry generator-namely, the collective spin component along an axis of symmetry. In systems of S=1/2 spins or qubits, the combination of the suppression of fluctuations along one direction and of the persistence of transverse magnetization leads to spin squeezing-a much sought-after property of quantum states, both for the purpose of entanglement detection as well as for metrological uses. Focusing on the case of XXZ models spontaneously breaking a U(1) [or even SU(2)] symmetry, we show that the adiabatically prepared states have nearly minimal spin uncertainty; that the minimum phase uncertainty that one can achieve with these states scales as N^{-3/4} with the number of spins N; and that this scaling is attained after an adiabatic preparation time scaling linearly with N. Our findings open the door to the adiabatic preparation of strongly spin-squeezed states in a large variety of quantum many-body devices including, e.g., optical-lattice clocks.

One- and Two-Axis Squeezing via Laser Coupling in an Atomic Fermi-Hubbard Model

Generation, storage, and utilization of correlated many-body quantum states are crucial objectives of future quantum technologies and metrology. Such states can be generated by the spin-squeezing protocols, i.e., one-axis twisting and two-axis countertwisting. In this Letter, we show activation of these two squeezing mechanisms in a system composed of ultracold atomic fermions in the Mott insulating phase by a position-dependent laser coupling of atomic internal states. Realization of both the squeezing protocols is feasible in the current state-of-the-art experiments.

A High-Precision Transfer of Time and RF Frequency via the Fiber-Optic Link Based on Secure Encryption

This paper presents a high-precision transfer system of time and RF frequency via the fiber optic link based on secure encryption. On the basis of the two-way time transfer of optical fiber, a security strategy composed of an SM2 encryption algorithm is introduced, which can resist the security risk of time information being tampered with. The experimental results show that the developed picosecond-precision fiber-optic time transfer equipment can ensure high stability while realizing the encryption function. Time synchronization stability in terms of time deviation (TDEV) of 1 PPS can reach around 10.7 ps at 1 s and 7.1 ps at 10 s averaging time. The stability of the 10 MHz frequency can reach around 4.7 × 10−12 at 1 s and 1.1 × 10−12 at 10 s averaging time. There is no significant difference in time transfer accuracy, compared with unencrypted conditions. Furthermore, this paper realizes a ring time transfer network via a 150 km fiber-optic link with three nodes using three devices. The TDEV of 1PPS can reach around 20.8 ps at 1s averaging time. This paper provides a reference to establish a high-precision, safe, and stable time synchronization fiber network in the future.

Photoionization cross sections of ultracold 88Sr in 1P1 and 3S1 states at 390 nm and the resulting blue-detuned magic wavelength optical lattice clock constraints

We present the measurements of the photoionization cross sections of the excited ¹P₁ and ³S₁ states of ultracold ⁸⁸Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the ¹S₀-³P₀ clock transition. The photoionization cross section of the ¹P₁ state is determined from the measured ionization rates of ⁸⁸Sr in the magneto-optical trap in the ¹P₁ state to be 2.20(50)×10^-20 m², while the photoionization cross section of ⁸⁸Sr in the ³S₁ state is inferred from the photoionization-induced reduction in the number of atoms transferred through the ³S₁ state in an operating optical lattice clock to be 1.38(66) ×10^-18 m². Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the ³S₁ state would make the use of the ³S₁ state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used ³D_1,2 states during the detection part of the optical clock cycle.

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.

Fiber-optic joint time and frequency transmission with enhanced time precision

We propose a high-precision joint time and frequency transmission scheme based on bidirectional wavelength division multiplexing transmission over an optical fiber link. The time signal is generated based on the phase-stable frequency signal with employment of a dedicated designed low-jitter event generator. Time synchronization is realized by eliminating the time difference between the time signals of the master and slave stations, which is determined by accurate two-way time comparison. In this way, thanks to the high stability of the frequency transmission, low jitter of the dedicated designed event generator, and the high accuracy of the two-way time comparison, a high precision time signal with enhanced time stability and accuracy can be obtained at the slave station, which is synchronized to the master station. Experimentally, a joint time and frequency transmission system is demonstrated over a 62-km urban fiber link. The results show a time stability in terms of time deviation (TDEV) of 3.5 ps/s and 430 fs/10,000 s, and an accuracy of better than 20 ps can be realized.

Watt-level blue light for precision spectroscopy, laser cooling and trapping of strontium and cadmium atoms

High-power and narrow-linewidth laser light is a vital tool for atomic physics, being used for example in laser cooling and trapping and precision spectroscopy. Here we produce Watt-level laser radiation at 457.75 nm and 460.86 nm of respective relevance for the cooling transitions of cadmium and strontium atoms. This is achieved via the frequency doubling of a kHz-linewidth vertical-external-cavity surface-emitting laser (VECSEL), which is based on a novel gain chip design enabling lasing at > 2 W in the 915-928 nm region. Following an additional doubling stage, spectroscopy of the ¹S₀ → ¹P₁ cadmium transition at 228.87 nm is performed on an atomic beam, with all the transitions from all eight natural isotopes observed in a single continuous sweep of more than 4 GHz in the deep ultraviolet. The absolute value of the transition frequency of ¹¹⁴Cd and the isotope shifts relative to this transition are determined, with values for some of these shifts provided for the first time.

Doubly Modulated Optical Lattice Clock: Interference and Topology

The quantum system under periodical modulation is the simplest path to understand the quantum nonequilibrium system because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase cannot be gauged out so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to the ultrahigh precision and ultrastability of the OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigenenergies, we demonstrate the relation between the effective Floquet Hamiltonian and the one-dimensional topological insulator with a high winding number. Our experiment not only provides a direction for detecting the phase effect but also paves a way in simulating the quantum topological phase in the OLC platform.

Microscale whispering-gallery-mode light sources with lattice-confined atoms

Microlasers, relying on the strong coupling between active particles and optical microcavity, exhibit fundamental differences from conventional lasers, such as multi-threshold/thresholdless behavior and nonclassical photon emission. As light sources, microlasers possess extensive applications in precision measurement, quantum information processing, and biochemical sensing. Here we propose a whispering-gallery-mode microlaser scheme, where ultracold alkaline-earth metal atoms, i.e., gain medium, are tightly confined in a two-color evanescent lattice that is in the ring shape and formed around a microsphere. To suppress the influence of the lattice-induced ac Stark shift on the moderately-narrow-linewidth laser transition, the red-detuned trapping beams operate at a magic wavelength while the wavelength of the blue-detuned trapping beam is set close to the other magic wavelength. The tiny mode volume and high quality factor of the microsphere ensure the strong atom-microcavity coupling in the bad-cavity regime. As a result, both saturation photon and critical atom numbers, which characterize the laser performance, are substantially reduced below unity. We explore the lasing action of the coupled system by using the Monte Carlo approach. Our scheme may be potentially generalized to the microlasers based on the forbidden clock transitions, holding the prospect for microscale active optical clocks in precision measurement and frequency metrology.

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.

Fast Control of Atom-Light Interaction in a Narrow Linewidth Cavity

We propose a method to exploit high-finesse optical resonators for light-assisted coherent manipulation of atomic ensembles, overcoming the limit imposed by the finite response time of the cavity. The key element of our scheme is to rapidly switch the interaction between the atoms and the cavity field with an auxiliary control process as, for example, the light shift induced by an optical beam. The scheme is applicable to other atomic species, both in trapped and free fall configurations, and can be adopted to control the internal and/or external atomic degrees of freedom. Our method will open new possibilities in cavity-aided atom interferometry and in the preparation of highly nonclassical atomic states.

Interferometric Constraints on Spacelike Coherent Rotational Fluctuations

Precision measurements are reported of the cross-spectrum of rotationally induced differential position displacements in a pair of colocated 39 m long, high-power Michelson interferometers. One arm of each interferometer is bent 90° near its midpoint to obtain sensitivity to rotations about an axis normal to the plane of the instrument. The instrument achieves quantum-limited sensing of spatially correlated signals in a broad frequency band extending beyond the 3.9-MHz inverse light travel time of the apparatus. For stationary signals with bandwidth Δf>10  kHz, the sensitivity to rotation-induced strain h of classical or exotic origin surpasses CSD_{δh}<t_{P}/2, where t_{P}=5.39×10^{-44}  s is the Planck time. This measurement is used to constrain a semiclassical model of nonlocally coherent rotational degrees of freedom of spacetime, which have been conjectured to emerge in holographic quantum geometry but are not present in a classical metric.

Ultra-stable 1064-nm neodymium-doped yttrium aluminum garnet lasers with 2.5 × 10-16 frequency instability

Cavity-stabilized ultra-stable optical oscillators are one of the core ingredients in the ground-based or spaceborne precision measurements such as optical frequency metrology, test of special relativity, and gravitational wave observation. We report in detail the development of two ultra-stable systems based on 1064-nm neodymium-doped yttrium aluminum garnet lasers and 20-cm optical cavities. The optical cavities adopt ultra-low-loss silica mirrors with compensating rings. An electro-optic crystal with a wedged angle is used to reduce the residual amplitude modulation. Using two-stage thermal control, long-term stabilities of 100 µK are achieved for the outer wall of the vacuum chamber housing the optical cavity. Two additional thermal shields increased the time constant of the optical cavities to 70 h. By operating the optical cavity at the temperature of zero coefficient of thermal expansion, the frequency stability reaches 2.5 × 10^-16 at 10 s averaging time and remains below 5 × 10^-16 with an extended time of 1000 s after removing the first- and second-order drifts. The dependence of the laser linewidth on the measurement time is tested against a simplified theoretical model.

Spin-Twisted Optical Lattices: Tunable Flat Bands and Larkin-Ovchinnikov Superfluids

Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.

Sub-ps resolution clock-offset measurement over a 114 km fiber link using linear optical sampling

We demonstrate a sub-ps resolution clock-offset measurement based on linear optical sampling technique via a 114 km fiber link by transferring a dual optical frequency comb. The time deviation between two distance clocks is 110 fs at 1 s and 22 fs at 100 s averaging, and the standard deviation of the measured clock offset is 237 fs. This sub-ps level of clock offset measurement should benefit many time synchronization applications via long fiber links.

Half-minute-scale atomic coherence and high relative stability in a tweezer clock

The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology¹, simulation² and information³. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems^2,4-7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms^8-10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 10¹⁶. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel^11,12. The result is a relative fractional frequency stability of 5.2(3) × 10^-17τ^-1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition¹³ in tailored atom arrays.

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.

Frequency division using a soliton-injected semiconductor gain-switched frequency comb

With optical spectral marks equally spaced by a frequency in the microwave or the radio frequency domain, optical frequency combs have been used not only to synthesize optical frequencies from microwave references but also to generate ultralow-noise microwaves via optical frequency division. Here, we combine two compact frequency combs, namely, a soliton microcomb and a semiconductor gain-switched comb, to demonstrate low-noise microwave generation based on a novel frequency division technique. Using a semiconductor laser that is driven by a sinusoidal current and injection-locked to microresonator solitons, our scheme transfers the spectral purity of a dissipative soliton oscillator into the subharmonic frequencies of the microcomb repetition rate. In addition, the gain-switched comb provides dense optical spectral emissions that divide the line spacing of the soliton microcomb. With the potential to be fully integrated, the merger of the two chipscale devices may profoundly facilitate the wide application of frequency comb technology.

The emergence of picokelvin physics

The frontier of low-temperature physics has advanced to the mid-picokelvin (pK) regime but progress has come to a halt because of the problem of gravity. Ultracold atoms must be confined in some type of potential energy well: if the depth of the well is less than the energy an atom gains by falling through it, the atom escapes. This article reviews ultracold atom research, emphasizing the advances that carried the low-temperature frontier to 450 pK. We review microgravity methods for overcoming the gravitational limit to achieving lower temperatures using free-fall techniques such as a drop tower, sounding rocket, parabolic flight plane and the International Space Station. We describe two techniques that promise further advancement-an atom chip and an all-optical trap-and present recent experimental results. Basic research in new regimes of observation has generally led to scientific discoveries and new technologies that benefit society. We expect this to be the case as the low-temperature frontier advances and we propose some new opportunities for research.

Physical Implications of a Fundamental Period of Time

If time is described by a fundamental process rather than a coordinate, it interacts with any physical system that evolves in time. The resulting dynamics is shown here to be consistent provided the fundamental period of the time system is sufficiently small. A strong upper bound T_{C}<10^{-33}  s of the fundamental period of time, several orders of magnitude below any direct time measurement, is obtained from bounds on dynamical variations of the period of a system evolving in time.

Generating Multipartite Spin States with Fermionic Atoms in a Driven Optical Lattice

We propose a protocol for generating generalized Greenberger-Horne-Zeilinger (GHZ) states using ultracold fermions in 3D optical lattices or optical tweezer arrays. The protocol uses the interplay between laser driving, on site interactions and external trapping confinement to enforce energetic spin- and position-dependent constraints on the atomic motion. These constraints allow us to transform a local superposition into a GHZ state through a stepwise protocol that flips one site at a time. The protocol requires no site-resolved drives or spin-dependent potentials, exhibits robustness to slow global laser phase drift, and naturally makes use of the harmonic trap that would normally cause difficulties for entanglement-generating protocols in optical lattices. We also discuss an improved protocol that can compensate for holes in the loadout at the cost of increased generation time. The state can immediately be used for quantum-enhanced metrology in 3D optical lattice clocks, opening a window to push the sensitivity of state-of-the-art sensors beyond the standard quantum limit.

State-Dependent Optical Lattices for the Strontium Optical Qubit

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than 4 orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits

Modern navigation systems integrate the global positioning system (GPS) with an inertial navigation system (INS), which complement each other for correct attitude and velocity determination. The core of the INS integrates accelerometers and gyroscopes used to measure forces and angular rate in the vehicular inertial reference frame. With the help of gyroscopes and by integrating the acceleration to compute velocity and distance, precision and compact accelerometers with sufficient accuracy can provide small-error location determination. Solid-state implementations, through coherent readout, can provide a platform for high performance acceleration detection. In contrast to prior accelerometers using piezoelectric or capacitive readout techniques, optical readout provides narrow-linewidth high-sensitivity laser detection along with low-noise resonant optomechanical transduction near the thermodynamical limits. Here an optomechanical inertial sensor with an 8.2 μg Hz-1/2 velocity random walk (VRW) at an acquisition rate of 100 Hz and 50.9 μg bias instability is demonstrated, suitable for applications, such as, inertial navigation, inclination sensing, platform stabilization, and/or wearable device motion detection. Driven into optomechanical sustained-oscillation, the slot photonic crystal cavity provides radio-frequency readout of the optically-driven transduction with an enhanced 625 μg Hz-1 sensitivity. Measuring the optomechanically-stiffened oscillation shift, instead of the optical transmission shift, provides a 220× VRW enhancement over pre-oscillation mode detection.

Microscope objective for imaging atomic strontium with 0.63 micrometer resolution

Imaging and manipulating individual atoms with submicrometer separation can be instrumental for quantum simulation of condensed matter Hamiltonians and quantum computation with neutral atoms. Here we present an open-source design of a microscope objective for atomic strontium, consisting solely of off-the-shelf lenses, that is diffraction-limited for 461 nm light. A prototype built with a simple stacking design is measured to have a resolution of 0.63(4) µm, which is in agreement with the predicted value. This performance, together with the near diffraction-limited performance for 532 nm light, makes this design useful for both quantum gas microscopes and optical tweezer experiments with strontium. Our microscope can easily be adapted to experiments with other atomic species such as erbium, ytterbium, and dysprosium, as with rubidium Rydberg atoms.

Laser with 10-13 short-term instability for compact optically pumped cesium beam atomic clock

We realize a high-stability laser by modulation transfer spectroscopy and apply it to implement a high-performance compact optically pumped cesium beam atomic clock. Evaluated by the optical heterodyne method with two identical frequency-stabilized lasers, the frequency instability of the 852 nm laser directly referenced on thermal atoms is 2.6×10^-13 at the averaging time of 5 s. Factors degrading the frequency stability of the laser are analyzed, and we will further control it to reduce the frequency noise of the laser. By comparing with a Hydrogen maser, the measured Allan deviation of the high-stability-laser-based cesium beam atomic clock is 2×10^-12/τ, dropping to 1×10^-14 in less than half a day of averaging time. To our knowledge, the Allan deviation of our cesium clock is better than that of any reported compact cesium beam atomic clocks at the averaging time of half-day. The high-performance atomic clock can promote the fields in metrology and timekeeping, and the high-stability laser additionally possesses great potential to be a compact optical frequency standard.

Development of an Interference Filter-Stabilized External-Cavity Diode Laser for Space Applications

The National Time Service Center of China is developing a compact, highly stable, 698 nm external-cavity diode laser (ECDL) for dedicated use in a space strontium optical clock. This article presents the optical design, structural design, and preliminary performance of this ECDL. The ECDL uses a narrow-bandwidth interference filter for spectral selection and a cat’s-eye reflector for light feedback. To ensure long-term stable laser operation suitable for space applications, the connections among all the components are rigid and the design avoids any spring-loaded adjustment. The frequency of the first lateral rocking eigenmode is 2316 Hz. The ECDL operates near 698.45 nm, and it has a current-controlled tuning range over 40 GHz and a PZT-controlled tuning range of 3 GHz. The linewidth measured by the heterodyne beating between the ECDL and an ultra-stable laser with 1 Hz linewidth is about 180 kHz. At present, the ECDL has been applied to the principle prototype of the space ultra-stable laser system.

PyLCP: A Python package for computing laser cooling physics

We present a Python object-oriented computer program for simulating various aspects of laser cooling physics. Our software is designed to be both easy to use and adaptable, allowing the user to specify the level structure, magnetic field profile, or the laser beams' geometry, detuning, and intensity. The program contains three levels of approximation for the motion of the atom, applicable in different regimes offering cross checks for calculations and computational efficiency depending on the physical situation. We test the software by reproducing well-known phenomena, such as damped Rabi flopping, electromagnetically induced transparency, stimulated Raman adiabatic passage, and optical molasses. We also use our software package to quantitatively simulate recoil-limited magneto-optical traps, like those formed on the narrow ¹S₀ → ³P₁ transition in ⁸⁸Sr and ⁸⁷Sr.

Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors

Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.

Cold-atom clock based on a diffractive optic

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects 10^{7 87}Rb atoms, which are subsequently cooled to 20 µK in optical molasses. We optically probe the microwave atomic ground-state splitting using lin⊥lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only 0.5 mm, the measured short-term fractional frequency stability is 2×10^-11/τ.

Reciprocity of propagation in optical fiber links demonstrated to 10-21

We present a study of the fundamental limit of fiber links using dedicated link architecture. We use an experimental arrangement that enables us to detect the forward and backward propagation noise independently and simultaneously in optical fiber and where the optical phase evolution is expected to be driven by the only contribution of the reference arms of the Michelson interferometer ensemble. In this article, we demonstrate indeed the high correlation between the optical phase evolution and the temperature variation of the interferometer ensemble, leading to a frequency offset of (4.4±2.3)×10^-21. Using a simple temperature model and a Bayesian analysis to evaluate the model parameters, we show that the temperature effect can be compensated with post-processing, removing the frequency offset down to (0.5±2.0)×10^-21. The residual slope of the optical phase evolution over 33 days is 350 yoctosecond/s. Using a global temperature parameter, we divide these 33 days dataset in four subsets and analyse their uncertainties. We show that they are self-consistent when the temperature is taken into account. This provides an alternative method to evaluate the accuracy of a fiber link, especially when the dataset includes large dead times. The result is finally interpreted as a test of the reciprocity of the propagation delay in an optical fiber. This unprecedented transfer capability could enable the comparisons of future optical clocks with expected performance at 10^-20 level and open new possibilities for stringent tests of special and general relativity.

Superradiant cooling, trapping, and lasing of dipole-interacting clock atoms

A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.

Demonstration of slow light in rubidium vapor using single photons from a trapped ion

Practical implementation of quantum networks is likely to interface different types of quantum systems. Photonically linked hybrid systems, combining unique properties of each constituent system, have typically required sources with the same photon emission wavelength. Trapped ions and neutral atoms both have compelling properties as nodes and memories in a quantum network but have never been photonically linked because of vastly different operating wavelengths. Here, we demonstrate the first interaction between neutral atoms and photons emitted from a single trapped ion. We use slow light in ⁸⁷Rb vapor to delay photons originating from a trapped ¹³⁸Ba⁺ ion by up to 13.5 ± 0.5 ns, using quantum frequency conversion to overcome the frequency difference between the ion and neutral atoms. The delay is tunable and preserves the temporal profile of the photons. This result showcases a hybrid photonic interface usable as a synchronization tool-a critical component in any future large-scale quantum network.