Optical spectrum analyzer with quantum-limited noise floor

Noise characterization of an ultra-stable laser for optical clocks

We report on the development and performance evaluation of an ultra-stable laser for an 27Al+ optical clock. After a series of noise suppressions, especially the vibrational and temperature fluctuation noise, the 30 cm long cavity stabilized laser obtains a frequency instability of 1.3 × 10-16 @1 s. This result is predicted by noise summation and confirmed by the three-cornered hat method. The 27Al+ optical clock transition is also used to characterize the laser frequency noise, and consistent results are yielded. This is the first reported instance of using single ion optical clocks to measure the frequency noise of ultra-stable lasers, as far as we know. With the implementation of the ultra-stable clock laser, an ultra-narrow linewidth clock transition of 2.8 Hz is obtained.

Modeling and optimization of an unbalanced delay interferometer based OPLL system

We present and establish a versatile analytical model that allows overall analysis and optimization for the phase noise performance of the delay interferometer based optical phase-locked loop (OPLL). It allows considering any type of lasers with arbitrary frequency noise properties while taking into account the contributions from various practical noise sources, thus enabling comprehensive investigation for the complicated interaction among underlying limiting factors. The quantitative analysis for their evolution along with the change of the delay of the interferometer unveils the resulting impact on the fundamental limit and dynamics of the output phase noise, leading to a well-balanced loop bandwidth and sensitivity thus enabling the overall optimization in terms of closed-loop noise performance. The tendencies observed and the results predicted in terms of coherence metrics in numerical verification with different lasers have testified to the precision and effectiveness of the proposed model, which is quite capable of acting as a design tool for the insightful analysis and overall optimization with guiding significance for practical applications.

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

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

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.

Quantum Harmonic Oscillator Spectrum Analyzers

Characterization and suppression of noise are essential for the control of harmonic oscillators in the quantum regime. We measure the noise spectrum of a quantum harmonic oscillator from low frequency to near the oscillator resonance by sensing its response to amplitude modulated periodic drives with a qubit. Using the motion of a trapped ion, we experimentally demonstrate two different implementations with combined sensitivity to noise from 500 Hz to 600 kHz. We apply our method to measure the intrinsic noise spectrum of an ion trap potential in a previously unaccessed frequency range.

Precision Metrology Meets Cosmology: Improved Constraints on Ultralight Dark Matter from Atom-Cavity Frequency Comparisons

We conduct frequency comparisons between a state-of-the-art strontium optical lattice clock, a cryogenic crystalline silicon cavity, and a hydrogen maser to set new bounds on the coupling of ultralight dark matter to standard model particles and fields in the mass range of 10^{-16}-10^{-21}  eV. The key advantage of this two-part ratio comparison is the differential sensitivity to time variation of both the fine-structure constant and the electron mass, achieving a substantially improved limit on the moduli of ultralight dark matter, particularly at higher masses than typical atomic spectroscopic results. Furthermore, we demonstrate an extension of the search range to even higher masses by use of dynamical decoupling techniques. These results highlight the importance of using the best-performing atomic clocks for fundamental physics applications, as all-optical timescales are increasingly integrated with, and will eventually supplant, existing microwave timescales.

Demonstration of a Timescale Based on a Stable Optical Carrier

We report on the first timescale based entirely on optical technology. Existing timescales, including those incorporating optical frequency standards, rely exclusively on microwave local oscillators owing to the lack of an optical oscillator with the required frequency predictability and stability for reliable steering. We combine a cryogenic silicon cavity exhibiting improved long-term stability and an accurate ^{87}Sr lattice clock to form a timescale that outperforms them all. Our timescale accumulates an estimated time error of only 48±94  ps over 34 days of operation. Our analysis indicates that this timescale is capable of reaching a stability below 1×10^{-17} after a few months of averaging, making timekeeping at the 10^{-18} level a realistic prospect.

Optical Pumping of TeH+: Implications for the Search for Varying mp/me

Molecular overtone transitions provide optical frequency transitions sensitive to variation in the proton-to-electron mass ratio ( μ ≡ m p / m e ). However, robust molecular state preparation presents a challenge critical for achieving high precision. Here, we characterize infrared and optical-frequency broadband laser cooling schemes for TeH + , a species with multiple electronic transitions amenable to sustained laser control. Using rate equations to simulate laser cooling population dynamics, we estimate the fractional sensitivity to μ attainable using TeH + . We find that laser cooling of TeH + can lead to significant improvements on current μ variation limits.

Imaging Optical Frequencies with 100 μHz Precision and 1.1 μm Resolution

We implement imaging spectroscopy of the optical clock transition of lattice-trapped degenerate fermionic Sr in the Mott-insulating regime, combining micron spatial resolution with submillihertz spectral precision. We use these tools to demonstrate atomic coherence for up to 15 s on the clock transition and reach a record frequency precision of 2.5×10^{-19}. We perform the most rapid evaluation of trapping light shifts and record a 150 mHz linewidth, the narrowest Rabi line shape observed on a coherent optical transition. The important emerging capability of combining high-resolution imaging and spectroscopy will improve the clock precision, and provide a path towards measuring many-body interactions and testing fundamental physics.

A Fermi-degenerate three-dimensional optical lattice clock

Strontium optical lattice clocks have the potential to simultaneously interrogate millions of atoms with a high spectroscopic quality factor of 4 × 10¹⁷ Previously, atomic interactions have forced a compromise between clock stability, which benefits from a large number of atoms, and accuracy, which suffers from density-dependent frequency shifts. Here we demonstrate a scalable solution that takes advantage of the high, correlated density of a degenerate Fermi gas in a three-dimensional (3D) optical lattice to guard against on-site interaction shifts. We show that contact interactions are resolved so that their contribution to clock shifts is orders of magnitude lower than in previous experiments. A synchronous clock comparison between two regions of the 3D lattice yields a measurement precision of 5 × 10^-19 in 1 hour of averaging time.

Ultrastable Silicon Cavity in a Continuously Operating Closed-Cycle Cryostat at 4 K

We report on a laser locked to a silicon cavity operating continuously at 4 K with 1×10^{-16} instability and a median linewidth of 17 mHz at 1542 nm. This is a tenfold improvement in short-term instability, and a 10^{4} improvement in linewidth, over previous sub-10-K systems. Operating at low temperatures reduces the thermal noise floor and, thus, is advantageous toward reaching an instability of 10^{-18}, a long-sought goal of the optical clock community. The performance of this system demonstrates the technical readiness for the development of the next generation of ultrastable lasers that operate with an ultranarrow linewidth and long-term stability without user intervention.

1.5 μm Lasers with Sub-10 mHz Linewidth

We report on two ultrastable lasers each stabilized to independent silicon Fabry-Pérot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of 4×10^{-17} for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.

Quantum lock-in force sensing using optical clock Doppler velocimetry

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator, thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single-trapped ⁸⁸Sr⁺ ion as a force sensor. The ion is electrically driven at a frequency much lower than the trap resonance frequency. We measure small amplitude of motion by measuring the periodic Doppler shift of an atomic optical clock transition, enhanced using the quantum lock-in technique. We report frequency force detection sensitivity as low as 2.8 × 10⁻²⁰ NHz^−1/2.

Existing force sensors are designed for driving frequencies above tens of kHz due to heating and sensitivity loss. Here the authors demonstrate precise force metrology for below kHz frequency range by combining the Doppler-shifted optical transition in trapped ion and quantum lock-in technique.

Precision measurement and frequency metrology with ultracold atoms

Precision measurement and frequency metrology have pushed many scientific and technological frontiers in the field of atomic, molecular and optical physics. In this article, we provide a brief review on the recent development of optical atomic clocks, with an emphasis placed on the important inter-dependence between measurement precision and systematic effects. After presenting a general discussion on the motivation and techniques behind the development of optical lattice clocks, where the use of many atoms greatly enhances the measurement precision, we present the JILA strontium optical lattice clock as the leading system of frequency metrology with the lowest total uncertainty, and we describe other related research activities. We discuss key ingredients that have enabled the optical lattice clocks with ultracold atoms to reach the 18th digit in both precision and accuracy. Furthermore, we discuss extending the power of precision clock spectroscopy to study quantum many-body physics and to provide control for atomic quantum materials. In addition, we explore future research directions that have the potential to achieve even greater precision.

Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty

The pursuit of better atomic clocks has advanced many research areas, providing better quantum state control, new insights in quantum science, tighter limits on fundamental constant variation and improved tests of relativity. The record for the best stability and accuracy is currently held by optical lattice clocks. Here we take an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Our (87)Sr optical lattice clock now achieves fractional stability of 2.2 × 10(-16) at 1 s. With this improved stability, we perform a new accuracy evaluation of our clock, reducing many systematic uncertainties that limited our previous measurements, such as those in the lattice ac Stark shift, the atoms' thermal environment and the atomic response to room-temperature blackbody radiation. Our combined measurements have reduced the total uncertainty of the JILA Sr clock to 2.1 × 10(-18) in fractional frequency units.

Observation of motion-dependent nonlinear dispersion with narrow-linewidth atoms in an optical cavity

As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.

An optical lattice clock with accuracy and stability at the 10(-18) level

Progress in atomic, optical and quantum science has led to rapid improvements in atomic clocks. At the same time, atomic clock research has helped to advance the frontiers of science, affecting both fundamental and applied research. The ability to control quantum states of individual atoms and photons is central to quantum information science and precision measurement, and optical clocks based on single ions have achieved the lowest systematic uncertainty of any frequency standard. Although many-atom lattice clocks have shown advantages in measurement precision over trapped-ion clocks, their accuracy has remained 16 times worse. Here we demonstrate a many-atom system that achieves an accuracy of 6.4 × 10(-18), which is not only better than a single-ion-based clock, but also reduces the required measurement time by two orders of magnitude. By systematically evaluating all known sources of uncertainty, including in situ monitoring of the blackbody radiation environment, we improve the accuracy of optical lattice clocks by a factor of 22. This single clock has simultaneously achieved the best known performance in the key characteristics necessary for consideration as a primary standard-stability and accuracy. More stable and accurate atomic clocks will benefit a wide range of fields, such as the realization and distribution of SI units, the search for time variation of fundamental constants, clock-based geodesy and other precision tests of the fundamental laws of nature. This work also connects to the development of quantum sensors and many-body quantum state engineering (such as spin squeezing) to advance measurement precision beyond the standard quantum limit.

Zero-dead-time operation of interleaved atomic clocks

We demonstrate a zero-dead-time operation of atomic clocks. This clock reduces sensitivity to local oscillator noise, integrating as nearly 1/τ whereas a clock with dead time integrates as 1/τ(1/2) under identical conditions. We contend that a similar scheme may be applied to improve the stability of optical clocks.