Precision measurement of the Newtonian gravitational constant using cold atoms

Pathfinder experiments with atom interferometry in the Cold Atom Lab onboard the International Space Station

Deployment of ultracold atom interferometers (AI) into space will capitalize on quantum advantages and the extended freefall of persistent microgravity to provide high-precision measurement capabilities for gravitational, Earth, and planetary sciences, and to enable searches for subtle forces signifying physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for fundamental studies of ultracold atoms and to mature space-based quantum technologies. We report on pathfinding experiments utilizing ultracold 87Rb atoms in the CAL AI. A three-pulse Mach-Zehnder interferometer was studied to understand the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL AI was used to remotely measure the Bragg laser photon recoil as a demonstration of the first quantum sensor using matter-wave interferometry in space.

Measuring gravitational attraction with a lattice atom interferometer

Despite being the dominant force of nature on large scales, gravity remains relatively elusive to precision laboratory experiments. Atom interferometers are powerful tools for investigating, for example, Earth's gravity1, the gravitational constant2, deviations from Newtonian gravity3-6 and general relativity7. However, using atoms in free fall limits measurement time to a few seconds8, and much less when measuring interactions with a small source mass2,5,6,9. Recently, interferometers with atoms suspended for 70 s in an optical-lattice mode filtered by an optical cavity have been demonstrated10-14. However, the optical lattice must balance Earth's gravity by applying forces that are a billionfold stronger than the putative signals, so even tiny imperfections may generate complex systematic effects. Thus, lattice interferometers have yet to be used for precision tests of gravity. Here we optimize the gravitational sensitivity of a lattice interferometer and use a system of signal inversions to suppress and quantify systematic effects. We measure the attraction of a miniature source mass to be amass = 33.3 ± 5.6stat ± 2.7syst nm s-2, consistent with Newtonian gravity, ruling out 'screened fifth force' theories3,15,16 over their natural parameter space. The overall accuracy of 6.2 nm s-2 surpasses by more than a factor of four the best similar measurements with atoms in free fall5,6. Improved atom cooling and tilt-noise suppression may further increase sensitivity for investigating forces at sub-millimetre ranges17,18, compact gravimetry19-22, measuring the gravitational Aharonov-Bohm effect9,23 and the gravitational constant2, and testing whether the gravitational field has quantum properties24.

Effect of an aperture in atomic gravimetry

There is a continuous interest in shrinking the dimensions of portable atomic gravimeters. This inevitably ends up truncating the Gaussian wings of the excitation laser beams whose effect has not been properly quantified yet. The diffraction pattern created from this aperture creates ripples in the wavefront in both the phase and the intensity. We calculate the shift in the measured value of an atomic gravimeter introduced by the phase variations in the wavefront. Fortunately, this shift has a Gaussian decay with the aperture size. For extended clouds, we observe a reduction of the effect thanks to an averaging over transverse positions with different values of the shift. Surprisingly, we found that the intensity variations also introduce an important correction to the photon recoil, which contributes at about the same level as the previous shift in the measurement of the gravitational acceleration. Our results should help decide how small an apparatus can be to guarantee a particular accuracy.

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

Measurement of the Earth Tides with a Diamagnetic-Levitated Micro-Oscillator at Room Temperature

The precise measurement of the gravity of Earth plays a pivotal role in various fundamental research and application fields. Although a few gravimeters have been reported to achieve this goal, miniaturization of high-precision gravimetry remains a challenge. In this work, we have proposed and demonstrated a miniaturized gravimetry operating at room temperature based on a diamagnetic levitated micro-oscillator with a proof mass of only 215 mg. Compared with the latest reported miniaturized gravimeters based on microelectromechanical systems, the performance of our gravimetry has substantial improvements in that an acceleration sensitivity of 15  μGal/sqrt[Hz] and a drift as low as 61  μGal per day have been reached. Based on this diamagnetic levitation gravimetry, we observed Earth tides, and the correlation coefficient between the experimental data and theoretical data reached 0.97. Some moderate foreseeable improvements can develop this diamagnetic levitation gravimetry into a chip size device, making it suitable for mobile platforms such as drones. Our advancement in gravimetry is expected to facilitate a multitude of applications, including underground density surveying and the forecasting of natural hazards.

Measuring gravity with milligram levitated masses

Gravity differs from all other known fundamental forces because it is best described as a curvature of space-time. For that reason, it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here, we show gravitational coupling between a levitated submillimeter-scale magnetic particle inside a type I superconducting trap and kilogram source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors.

Continuous frequency tuning of an external cavity diode laser significantly beyond the free spectral range by sweeping the injection current

In this study, the focus is on continuously tuning an external cavity diode laser equipped with an antireflection-coated laser diode over a 14.8 GHz range, 4.5 times larger than the free spectral range, using only injection current sweeps. In contrast, the absence of antireflection coating led to a tuning range of only one-fifth of the free spectral range, accompanied by hysteresis on mode hops. Theoretical analysis of this observed hysteresis suggests that broad tuning can be achieved when the longitudinal modes of the solitary laser diode are eliminated through the antireflection coating.

Effect of atom diffusion on the efficiency of Bragg diffraction in atom interferometers

The transition efficiency of atomic Bragg diffraction as mirrors and beam splitters in Bragg atom interferometers plays an essential role in impacting the fringe contrast and measurement sensitivity. This can be attributed to the properties of atomic sources, Bragg pulse shapes, the pulse duration, and the relative position deviation of the atoms and Bragg pulses. Here, we investigate the effect of the atomic source's diffusion and velocity width on the efficiency of Bragg diffraction of the moving cold atomic cloud. The transfer efficiency of Bragg mirrors and beam splitters are numerically simulated and experimentally measured, which are well consistent in comparison. We quantify these effects of atomic diffusion and velocity width and precisely compute how Bragg pulses' efficiencies vary as functions of these parameters. Our results and methodology allow us to optimize the Bragg pulses at different atomic sources and will help in the design of large momentum transfer mirrors and beam splitters in atom interferometry experiments.

Dependence of the ellipse fitting noise on the differential phase between interferometers in atom gravity gradiometers

Ellipse fitting is widely used in the extraction of the differential phase between atom interferometers amid substantial common phase noise. This study meticulously examines the dependency of extraction noise on the differential phase between atom interferometers during ellipse fitting. It reveals that the minimum extraction noise can manifest at distinct differential phases, contingent upon the dominance of different noise types. Moreover, the outcomes are influenced by whether the interferometers undergo simultaneous detection or not. Our theoretical simulations find empirical validation in a compact horizontal atom gravity gradiometer. The adjustment of the differential phase significantly enhances measurement sensitivity, culminating in a differential gravity resolution of 1.6 × 10-10 g @ 4800 s.

Atom Interferometry with Rb Blue Transitions

We demonstrate a novel scheme for Raman-pulse and Bragg-pulse atom interferometry based on the 5S-6P blue transitions of ^{87}Rb that provides an increase by a factor ∼2 of the interferometer phase due to accelerations with respect to the commonly used infrared transition at 780 nm. A narrow-linewidth laser system generating more than 1 W of light in the 420-422 nm range was developed for this purpose. Used as a cold-atom gravity gradiometer, our Raman interferometer attains a stability to differential acceleration measurements of 1×10^{-8}  g at 1 s and 2×10^{-10}  g after 2000 s of integration time. When operated on first-order Bragg transitions, the interferometer shows a stability of 6×10^{-8}  g at 1 s, averaging to 1×10^{-9}  g after 2000 s of integration time. The instrument sensitivity, currently limited by the noise due to spontaneous emission, can be further improved by increasing the laser power and the detuning from the atomic resonance. The present scheme is attractive for high-precision experiments as, in particular, for the determination of the Newtonian gravitational constant.

Advances in Portable Atom Interferometry-Based Gravity Sensing

Gravity sensing is a valuable technique used for several applications, including fundamental physics, civil engineering, metrology, geology, and resource exploration. While classical gravimeters have proven useful, they face limitations, such as mechanical wear on the test masses, resulting in drift, and limited measurement speeds, hindering their use for long-term monitoring, as well as the need to average out microseismic vibrations, limiting their speed of data acquisition. Emerging sensors based on atom interferometry for gravity measurements could offer promising solutions to these limitations, and are currently advancing towards portable devices for real-world applications. This article provides a brief state-of-the-art review of portable atom interferometry-based quantum sensors and provides a perspective on routes towards improved sensors.

A Ramsey apparatus for proton spins in flowing water

We present an apparatus that applies Ramsey's method of separated oscillatory fields to proton spins in water molecules. The setup consists of a water circuit, a spin polarizer, a magnetically shielded interaction region with various radio frequency elements, and a nuclear magnetic resonance system to measure the spin polarization. We show that this apparatus can be used for Rabi resonance measurements and to investigate magnetic and pseudomagnetic field effects in Ramsey-type precision measurements with a sensitivity below 100 pT.

Magneto-optical trapping in a near-suface borehole

Borehole gravity sensing can be used in a number of applications to measure features around a well, including rock-type change mapping and determination of reservoir porosity. Quantum technology gravity sensors, based on atom interferometry, have the ability to offer increased survey speeds and reduced need for calibration. While surface sensors have been demonstrated in real world environments, significant improvements in robustness and reductions to radial size, weight, and power consumption are required for such devices to be deployed in boreholes. To realise the first step towards the deployment of cold atom-based sensors down boreholes, we demonstrate a borehole-deployable magneto-optical trap, the core package of many cold atom-based systems. The enclosure containing the magneto-optical trap itself had an outer radius of (60 ± 0.1) mm at its widest point and a length of (890 ± 5) mm. This system was used to generate atom clouds at 1 m intervals in a 14 cm wide, 50 m deep borehole, to simulate how in-borehole gravity surveys are performed. During the survey, the system generated, on average, clouds of (3.0 ± 0.1) × 105 87Rb atoms with the standard deviation in atom number across the survey observed to be as low as 8.9 × 104.

Atom Interferometric Imaging of Differential Potentials Using an Atom Laser

Interferometry is a prime technique for modern precision measurements. Atoms, unlike light, have significant interactions with electric, magnetic, and gravitational fields, making their use in interferometric applications particularly versatile. Here, we demonstrate atom interferometry to image optical and magnetic potential landscapes over an area exceeding 240  μm×600  μm. The differential potentials employed in our experiments generate phase imprints in an atom laser that are made visible through a Ramsey pulse sequence. We further demonstrate how advanced pulse sequences can enhance desired imaging features, e.g., to image steep potential gradients. A theoretical discussion is presented that provides a semiclassical analysis and matching numerics.

Protection of Noise Squeezing in a Quantum Interferometer with Optimal Resource Allocation

Interferometers are crucial for precision measurements, including gravitational waves, laser ranging, radar, and imaging. The phase sensitivity, the core parameter, can be quantum-enhanced to break the standard quantum limit (SQL) using quantum states. However, quantum states are highly fragile and quickly degrade with losses. We design and demonstrate a quantum interferometer utilizing a beam splitter with a variable splitting ratio to protect the quantum resource against environmental impacts. The optimal phase sensitivity can reach the quantum Cramér-Rao bound of the system. This quantum interferometer can greatly reduce the quantum source requirements in quantum measurements. In theory, with a 66.6% loss rate, the sensitivity can break the SQL using only a 6.0 dB squeezed quantum resource with the current interferometer rather than a 24 dB squeezed quantum resource with a conventional squeezing-vacuum-injected Mach-Zehnder interferometer. In experiments, when using a 2.0 dB squeezed vacuum state, the sensitivity enhancement remains at ∼1.6  dB via optimizing the first splitting ratio when the loss rate changes from 0% to 90%, indicating that the quantum resource is excellently protected with the existence of losses in practical applications. This strategy could open a way to retain quantum advantages for quantum information processing and quantum precision measurement in lossy environments.

Compact laser modulation system for a transportable atomic gravimeter

Nowadays, atom-based quantum sensors are leaving the laboratory towards field applications requiring compact and robust laser systems. Here we describe the realization of a compact laser system for atomic gravimetry. Starting with a single diode laser operating at 780 nm and adding only one fiber electro-optical modulator, one acousto-optical modulator and one laser amplifier we produce laser beams at all the frequencies required for a Rb-87 atomic gravimeter. Furthermore, we demonstrate that an atomic fountain configuration can also be implemented with our laser system. The modulated system reported here represents a substantial advance in the simplification of the laser source for transportable atom-based quantum sensors that can be adapted to other sensors such as atomic clocks, accelerometers, gyroscopes or magnetometers with minor modifications.

A Testing Method for Shipborne Atomic Gravimeter Based on the Modulated Coriolis Effect

Shipborne atomic gravimeter (SAG) is an instrument that can directly measure absolute gravity in dynamic environments. As a new type of gravity sensor, a standard method for evaluating its detailed performance has not been proposed and the detailed performance of SAG was rarely reported. In this paper, a system of dynamic gravity measurement, which was integrated with a home-made atomic gravimeter, is demonstrated, and a novel and simple method for testing the performance of SAG on the lake based on the modulated Coriolis effect is put forward. Firstly, in the state of ship mooring, a tilt modulation of the gravity sensor has been realized to make sure the Raman wave vector is parallel to the gravity axis. Moreover, a comparison between the measurement result of CG-5 and SAG has also been carried out to evaluate the accuracy of the SAG. Then, the Coriolis effect modulating experiment is carried out with various routes on lake to test its performance in dynamic environments. In the ship mooring state, the accuracy has been demonstrated to be 0.643 mGal. The internal consistency reliabilities are evaluated to be 0.8 mGal and 1.2 mGal under the conditions of straight line and circle navigation, respectively.

The Influence of Temperature on Frequency Modulation Spectroscopy in Atom Gravimeter

Atom gravimeters use locked lasers to manipulate atoms to achieve high-precision gravity measurements. Frequency modulation spectroscopy (FMS) is an accurate method of optical heterodyne spectroscopy, capable of the sensitive and rapid frequency locking of the laser. Because of the effective absorption coefficient, Doppler broadening and susceptibility depend on temperature, and the signal-to-noise ratio (SNR) of the spectroscopy could be affected by temperature. We present a detailed study of the influence of the temperature on FMS in atom gravimeters, and the experimental results show that the SNR of the spectroscopy is dependent on temperature. In this paper, the frequency of the reference laser is locked by tracking the set point of the fringe slope of FMS. The influence of the frequency-locking noise of the reference laser on the sensitivity of the atom gravimeter is investigated by changing the temperature of the Rb cell without extra operations. The method presented here could be useful for improving the sensitivity of quantum sensors that require laser spectroscopic techniques.

Tracking the vector acceleration with a hybrid quantum accelerometer triad

Robust and accurate acceleration tracking remains a challenge in many fields. For geophysics and economic geology, precise gravity mapping requires onboard sensors combined with accurate positioning and navigation systems. Cold atom-based quantum inertial sensors can potentially provide these high-precision instruments. However, current scalar instruments require precise alignment with vector quantities. Here, we present the first hybrid three-axis accelerometer exploiting the quantum advantage to measure the full acceleration vector by combining three orthogonal atom interferometer measurements with a classical navigation-grade accelerometer triad. Its ultralow bias permits tracking the acceleration vector over long time scales, yielding a 50-fold improvement in stability (6 × 10^-8 g) over our classical accelerometers. We record the acceleration vector at a high data rate (1 kHz), with absolute magnitude accuracy below 10 μg, and pointing accuracy of 4 μrad. This paves the way toward future strapdown applications with quantum sensors and highlights their potential as future inertial navigation units.

Impact of additional sidebands generated by a tapered amplifier on an atom interferometer

Stimulated Raman transitions are often used in an atom interferometer (AI) for wave packet manipulation. Normally, two lasers with different frequencies contained in a Raman beam are combined first and then amplified by a single tapered amplifier (TA). This configuration can simplify the laser system of the AI, however, additional sidebands will be generated by the TA because of the nonlinear effect in the TA. In this work, the impact of additional sidebands generated with a single TA on the AI is studied. We first observe the additional sidebands in a Raman laser by a Fabry-Pérot interferometer (FPI), and the additional sidebands will be greatly suppressed by reducing the injection laser power of the TA. This is also confirmed by observing the position-dependent Raman transitions induced by additional sidebands at different injection power in an AI. However, the phase shifts induced by additional sidebands are not reduced obviously when the injection power of the TA is reduced. Therefore, it is necessary to separately amplify two lasers contained in the Raman laser by two TAs for a high precision AI. The spectroscopy of Raman laser generated by two TAs is also measured by the FPI, and the impact of additional sidebands on the AI is eliminated. This work has guiding significance for the design of the laser system in a high-precision AI.

A compact cold-atom interferometer with a high data-rate grating magneto-optical trap and a photonic-integrated-circuit-compatible laser system

The extreme miniaturization of a cold-atom interferometer accelerometer requires the development of novel technologies and architectures for the interferometer subsystems. Here, we describe several component technologies and a laser system architecture to enable a path to such miniaturization. We developed a custom, compact titanium vacuum package containing a microfabricated grating chip for a tetrahedral grating magneto-optical trap (GMOT) using a single cooling beam. In addition, we designed a multi-channel photonic-integrated-circuit-compatible laser system implemented with a single seed laser and single sideband modulators in a time-multiplexed manner, reducing the number of optical channels connected to the sensor head. In a compact sensor head containing the vacuum package, sub-Doppler cooling in the GMOT produces 15 μK temperatures, and the GMOT can operate at a 20 Hz data rate. We validated the atomic coherence with Ramsey interferometry using microwave spectroscopy, then demonstrated a light-pulse atom interferometer in a gravimeter configuration for a 10 Hz measurement data rate and T = 0–4.5 ms interrogation time, resulting in Δg/g = 2.0 × 10⁻⁶. This work represents a significant step towards deployable cold-atom inertial sensors under large amplitude motional dynamics.

Cold-atom interferometers have been miniaturized towards fieldable quantum inertial sensing applications. Here the authors demonstrate a compact cold-atom interferometer using microfabricated gratings and discuss the possible use of photonic integrated circuits for laser systems.

A Truck-Borne System Based on Cold Atom Gravimeter for Measuring the Absolute Gravity in the Field

The cold atom gravimeter (CAG) has proven to be a powerful quantum sensor for the high-precision measurement of gravity field, which can work stably for a long time in the laboratory. However, most CAGs cannot operate in the field due to their complex structure, large volume and poor environmental adaptability. In this paper, a home-made, miniaturized CAG is developed and a truck-borne system based on it is integrated to measure the absolute gravity in the field. The measurement performance of this system is evaluated by applying it to measurements of the gravity field around the Xianlin reservoir in Hangzhou City of China. The internal and external coincidence accuracies of this measurement system were demonstrated to be 35.4 μGal and 76.7 μGal, respectively. Furthermore, the theoretical values of the measured eight points are calculated by using a forward modeling of a local high-resolution digital elevation model, and the calculated values are found to be in good agreement with the measured values. The results of this paper show that this home-made, truck-borne CAG system is reliable, and it is expected to improve the efficiency of gravity surveying in the field.

Soliton Interferometry with Very Narrow Barriers Obtained from Spatially Dependent Dressed States

Bright solitons in atomic Bose-Einstein condensates are strong candidates for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. An analog to a beam splitter is then a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but in a typical realization using a blue-detuned optical dipole potential, the width is limited by the laser wavelength. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal configuration.

Hybrid Electrostatic–Atomic Accelerometer for Future Space Gravity Missions

Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, we propose to study an original concept of a hybrid accelerometer associating a state-of-the-art electrostatic accelerometer (EA) and a promising quantum sensor based on cold atom interferometry. To assess the performance potential of such an instrument, numerical simulations were performed to determine its impact in terms of gravity field retrieval. Taking advantage of the long-term stability of the cold atom interferometer (CAI), it is shown that the reduced drift of the hybrid sensor could lead to improved gravity field retrieval. Nevertheless, this gain vanishes once temporal variations of the gravity field and related aliasing effects are taken into account. Improved de-aliasing models or some specific satellite constellations are then required to maximize the impact of the accelerometer performance gain. To evaluate the achievable acceleration performance in-orbit, a numerical simulator of the hybrid accelerometer was developed and preliminary results are given. The instrument simulator was in part validated by reproducing the performance achieved with a hybrid lab prototype operating on the ground. The problem of satellite rotation impact on the CAI was also investigated both with instrument performance simulations and experimental demonstrations. It is shown that the proposed configuration, where the EA’s proof-mass acts as the reference mirror for the CAI, seems a promising approach to allow the mitigation of satellite rotation. To evaluate the feasibility of such an instrument for space applications, a preliminary design is elaborated along with a preliminary error, mass, volume, and electrical power consumption budget.

Bespoke magnetic field design for a magnetically shielded cold atom interferometer

Quantum sensors based on cold atoms are being developed which produce measurements of unprecedented accuracy. Due to shifts in atomic energy levels, quantum sensors often have stringent requirements on their internal magnetic field environment. Typically, background magnetic fields are attenuated using high permeability magnetic shielding, with the cancelling of residual and introduction of quantisation fields implemented with coils inside the shield. The high permeability shield, however, distorts all magnetic fields, including those generated inside the sensor. Here, we demonstrate a solution by designing multiple coils overlaid on a 3D-printed former to generate three uniform and three constant linear gradient magnetic fields inside the capped cylindrical magnetic shield of a cold atom interferometer. The fields are characterised in-situ and match their desired forms to high accuracy. For example, the uniform transverse field, B_x, deviates by less than 0.2% over more than 40% of the length of the shield. We also map the field directly using the cold atoms and investigate the potential of the coil system to reduce bias from the quadratic Zeeman effect. This coil design technology enables targeted field compensation over large spatial volumes and has the potential to reduce systematic shifts and noise in numerous cold atom systems.

In situ probing and stabilizing the power ratio of electro-optic-modulated laser pairs based on VIPA etalon for quantum sensing

Monitoring and stabilizing the power ratio of laser pairs is significant for high-precision atom interferometers, especially as the compact electro-optic-modulated all-fiber laser system prevails. In this Letter, we demonstrate a novel, to the best of our knowledge, method to in situ probe the relative power of laser pairs and to stabilize the power ratio of two Raman lasers using a high-dispersion virtually imaged phased array (VIPA) etalon. Sub-microsecond resolution on probing laser power transformation during the atom interferometer sequence is achieved and the power ratio of two Raman lasers (PRTR) is tightly locked with high bandwidth despite environmental disturbances, showing an Allan deviation of 4.39 × 10^-5 at 1000 s averaging time. This method provides a novel way to stabilize the PRTR and diagnose multi-frequency laser systems for atom interferometers, and it could find potential applications in broad quantum sensing scenarios.

Modular-assembled laser system for a long-baseline atom interferometer

The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new, to the best of our knowledge, type of large-scale atom interferometer facility under construction for the study of gravitation and related problems. To meet the different requirements of the laser system for the atom interferometer using various atoms (including ⁸⁵Rb, ⁸⁷Rb, ⁸⁷Sr, and ⁸⁸Sr), we design and implement a modular assembled laser system. By dividing the laser system into different basic units according to their functions and modularizing each unit, the laser system is made highly scalable while being compact and stable. Its intensity stability is better than 0.1% in 10²s and 0.5% in 10⁴s. We test the performance of the laser system with two experimental systems, i.e., an ⁸⁵Rb-⁸⁷Rb dual-species ultracold atom source and an ⁸⁵Rb atom interferometer. The ⁸⁵Rb-⁸⁷Rb dual-species magneto-optical trap and the ⁸⁵Rb atom interference fringes are realized by using this laser system, indicating that its technical performance can meet the major experimental requirements.

Characterizing atom clouds using a charge-coupled device for atom-interferometry-based G measurements

Precise information of positions and sizes of atom clouds is required for atom-interferometry-based G measurements. In this work, characterizing atom clouds using a charge-coupled device (CCD) is presented. The parameters of atom clouds are extracted from fluorescence images captured by the CCD. For characterization, in-situ calibration of the magnification of the imaging system is implemented using the free-fall distance of atom clouds as the dimension reference. Moreover, influence of the probe beam on measuring the positions of atom clouds is investigated, and a differential measurement by reversing the direction of the probe beam is proposed to suppress the influence. Finally, precision at sub-mm level for characterizing atom clouds is achieved.

Modeling Atom Interferometry Experiments with Bose–Einstein Condensates in Power-Law Potentials

Recent atom interferometry (AI) experiments involving Bose–Einstein condensates (BECs) have been conducted under extreme conditions of volume and interrogation time. Numerical solution of the rotating-frame Gross–Pitaevskii equation (RFGPE), which is the standard mean-field theory applied to these experiments, is impractical due to the excessive computation time and memory required. We present a variational model that provides approximate solutions of the RFGPE for a power-law potential on a practical time scale. This model is well-suited to the design and analysis of AI experiments involving BECs that are split and later recombined to form an interference pattern. We derive the equations of motion of the variational parameters for this model and illustrate how the model can be applied to the sequence of steps in a recent AI experiment where BECs were used to implement a dual-Sagnac atom interferometer rotation sensor. We use this model to investigate the impact of finite-size and interaction effects on the single-Sagnac-interferometer phase shift.

Prospective sensitivities of atom interferometers to gravitational waves and ultralight dark matter

We survey the prospective sensitivities of terrestrial and space-borne atom interferometers to gravitational waves generated by cosmological and astrophysical sources, and to ultralight dark matter. We discuss the backgrounds from gravitational gradient noise in terrestrial detectors, and also binary pulsar and asteroid backgrounds in space-borne detectors. We compare the sensitivities of LIGO and LISA with those of the 100 m and 1 km stages of the AION terrestrial AI project, as well as two options for the proposed AEDGE AI space mission with cold atom clouds either inside or outside the spacecraft, considering as possible sources the mergers of black holes and neutron stars, supernovae, phase transitions in the early Universe, cosmic strings and quantum fluctuations in the early Universe that could have generated primordial black holes. We also review the capabilities of AION and AEDGE for detecting coherent waves of ultralight scalar dark matter. AION-REPORT/2021-04 KCL-PH-TH/2021-61, CERN-TH-2021-116 This article is part of the theme issue 'Quantum technologies in particle physics'.

Quantum sensing for gravity cartography

The sensing of gravity has emerged as a tool in geophysics applications such as engineering and climate research1-3, including the monitoring of temporal variations in aquifers4 and geodesy5. However, it is impractical to use gravity cartography to resolve metre-scale underground features because of the long measurement times needed for the removal of vibrational noise6. Here we overcome this limitation by realizing a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, thermal and magnetic field variations, and instrument tilt. The instrument achieves a statistical uncertainty of 20 E (1 E = 10-9 s-2) and is used to perform a 0.5-metre-spatial-resolution survey across an 8.5-metre-long line, detecting a 2-metre tunnel with a signal-to-noise ratio of 8. Using a Bayesian inference method, we determine the centre to ±0.19 metres horizontally and the centre depth as (1.89 -0.59/+2.3) metres. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. The sensor parameters are compatible with applications in mapping aquifers and evaluating impacts on the water table7, archaeology8-11, determination of soil properties12 and water content13, and reducing the risk of unforeseen ground conditions in the construction of critical energy, transport and utilities infrastructure14, providing a new window into the underground.

Simple and robust architecture of a laser system for atom interferometry

We report a compact and robust architecture of a versatile laser system that allows the implementation of several advanced atom interferometry techniques, such as Bragg diffraction, Bloch oscillations, or single and double Raman diffraction. A low noise, frequency tunable fiber-laser (λ = ~1560 nm) serves as the seed. A couple of fiber-coupled amplifiers followed by two fibered second-harmonic generators produce a pair of phase-locked, frequency-controllable laser beams at 780 nm. Manipulating frequencies of individual laser beams at λ = 1560 nm before the amplifiers, facilitates achieving a maximum relative detuning of ± 20 MHz, while maintaining a constant output power. We present the scheme to implement Raman spectroscopy using our laser system and discuss its advantages. Finally, the overall performance of the laser setup has been evaluated by realizing interferometers in copropagating Ramsey-Raman and counterpropagating Bragg configuration.

Quantum probe of space-time curvature

An atom interferometer measures the quantum phase due to gravitational time dilation.

Observation of a gravitational Aharonov-Bohm effect

Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.

Effects and Prospects of the Vibration Isolation Methods for an Atomic Interference Gravimeter

An atomic interference gravimeter (AIG) is of great value in underwater aided navigation, but one of the constraints on its accuracy is vibration noise. For this reason, technology must be developed for its vibration isolation. Up to now, three methods have mainly been employed to suppress the vibration noise of an AIG, including passive vibration isolation, active vibration isolation and vibration compensation. This paper presents a study on how vibration noise affects the measurement of an AIG, a review of the research findings regarding the reduction of its vibration, and the prospective development of vibration isolation technology for an AIG. Along with the development of small and movable AIGs, vibration isolation technology will be better adapted to the challenging environment and be strongly resistant to disturbance in the future.

Eliminating the phase shifts arising from additional sidebands in an atom gravimeter with a phase-modulated Raman laser

The additional sidebands (ASBs) in a Raman laser will have a significant effect on the performance of atom gravimeters (AGs) based on phase-modulated Raman lasers. We propose a method of modulating the sideband-to-carrier ratio in Raman lasers to determine the magic time intervals where the phase shift induced by the ASB effect is minimized, and this method is demonstrated by experiments. Among these magic time intervals, some noise-immunity points are predicted. Based on the prediction and the result of the ASB effect changing with the interval time T between adjacent Raman pulses, an optimal magic time interval is selected. Therefore, the uncertainty to the gravity measurement induced by the ASB effect when the AG works at the magic time interval is reduced to 0.5 μGal. Furthermore, the ASB effect and its zero-phase points in four-pulse atom interferometers are also discussed. This work provides a clear way to eliminate the phase shift induced by the ASB effect in high-precision AGs employing phase-modulated Raman lasers.

Effects related to the temperature of atoms in an atom interferometry gravimeter based on ultra-cold atoms

The temperature of atoms, coupled to several effects, plays an important role in high precision atom interferometry gravimeters. In this work, we present an ultra-cold ⁸⁷Rb atom interferometry gravimeter, in which the atom source is produced by evaporative cooling in an all optical dipole trap to investigate the effects related to atom temperature. A condensate containing 4 × 10⁴ atoms can be prepared within 3.2 s through an all-optical dipole trap composed of two reservoirs and a dimple. The fringe contrast of our atom interferometry gravimeter reaches up to 76(4)% due to the advantage of ultra-cold atom source even at a free evolution time of T=80 ms. A resolution of 6 μGal (1 μGal=1×10^-8 m/s²) after 3000 s integration time with a sampling rate of 0.25 Hz is achieved in this atom gravimeter. The relationship between the fringe contrast and the atom temperature in the atom gravimeter is studied; in addition, the wavefront aberration effect in the atom gravimeter is also investigated by varying the temperature of atoms.

Collective-Mode Enhanced Matter-Wave Optics

In contrast to light, matter-wave optics of quantum gases deals with interactions even in free space and for ensembles comprising millions of atoms. We exploit these interactions in a quantum degenerate gas as an adjustable lens for coherent atom optics. By combining an interaction-driven quadrupole-mode excitation of a Bose-Einstein condensate (BEC) with a magnetic lens, we form a time-domain matter-wave lens system. The focus is tuned by the strength of the lensing potential and the oscillatory phase of the quadrupole mode. By placing the focus at infinity, we lower the total internal kinetic energy of a BEC comprising 101(37) thousand atoms in three dimensions to 3/2 k_{B}·38_{-7}^{+6}  pK. Our method paves the way for free-fall experiments lasting ten or more seconds as envisioned for tests of fundamental physics and high-precision BEC interferometry, as well as opens up a new kinetic energy regime.

CODATA Recommended Values of the Fundamental Physical Constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice

We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.

The influence of polarization misalignment for modulation transfer spectrum in atom gravimeter

The accuracy of atom gravimeters is directly related to the Raman laser, which is used to manipulate the atomic wave packet, and the frequency of the Raman laser could be affected by temperature when the laser polarization is not along the preferred axis of the electro-optic crystal employed in the modulation transfer spectrum (MTS). This effect has been researched by modulating the laser polarization in the MTS in this work. The experimental results show that both the laser frequency and gravity measurement results have a sinusoidal dependence on temperature, and the period of the fluctuation is 0.8 °C. The systematic effect can reach 12.4 μGal when the polarization misalignment is 15°, which is a remarkable contribution to the absolute gravity measurement. The amplitude of this effect could be reduced by adjusting the laser polarization to the crystal's preferred axis. According to the result, the included angle between the laser polarization and the crystal's preferred axis should be smaller than 5° if 2 μGal accuracy is required.

All acousto-optic modulator laser system for a 12 m fountain-type dual-species atom interferometer

We design and implement a laser system for ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometers based on acousto-optic frequency shift and tapered amplifier laser technologies. We use eight-pass acousto-optic modulators to generate repumping lasers for ⁸⁵Rb and ⁸⁷Rb atoms. The maximum frequency shift of the laser is 2.8 GHz, and the diffraction efficiency is higher than 20%. We use high-frequency acousto-optic modulators to generate the Raman lasers. This laser system uses only two seed lasers to provide the various frequencies required by ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometers, which greatly improves laser usage. The laser system is applied in the equivalence principle test experiment using an ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometer. The signal of atoms launched to 12 meters is successfully observed, and the resolution of gravity differential measurement is improved from 8×10^-9 g to 1×10^-10g.

Transverse Confinement of Photon Position in the Light-Atom Interaction

In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.

Gravitational Decoherence and the Possibility of Its Interferometric Detection

We present a general master equation describing the quantum dynamics of a scalar bosonic field interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence both in position and in energy momentum. We show how the master equation reproduces, thus generalizing, the previous results in the literature by taking appropriate limits. We estimate the effect of gravitational decoherence in atom interferometers, providing also a straightforward way to assess the magnitude of the effect.

Twin-lattice atom interferometry

Inertial sensors based on cold atoms have great potential for navigation, geodesy, or fundamental physics. Similar to the Sagnac effect, their sensitivity increases with the space-time area enclosed by the interferometer. Here, we introduce twin-lattice atom interferometry exploiting Bose-Einstein condensates of rubidium-87. Our method provides symmetric momentum transfer and large areas offering a perspective for future palm-sized sensor heads with sensitivities on par with present meter-scale Sagnac devices. Our theoretical model of the impact of beam splitters on the spatial coherence is highly instrumental for designing future sensors.

Atom interferometers can be useful for precision measurement of fundamental constants and sensors of different type. Here the authors demonstrate a compact twin-lattice atom interferometry exploiting Bose-Einstein condensates (BECs) of 87 Rb atoms.

A dual-magneto-optical-trap atom gravity gradiometer for determining the Newtonian gravitational constant

As part of a program to determine the gravitational constant G using multiple independent methods in the same laboratory, an atom gravity gradiometer is being developed. The gradiometer is designed with two magneto-optical traps to ensure both the fast simultaneous launch of two atomic clouds and an optimized configuration of source masses. Here, the design of the G measurement by atom interferometry is detailed, and the experimental setup of the atom gravity gradiometer is reported. A preliminary sensitivity of 3 × 10^-9 g/Hz to differential gravity acceleration is obtained, which corresponds to 99 E/Hz (1 E = 10^-9 s^-2) for the gradiometer with a baseline of 0.3 m. This provides access to measuring G at the level of less than 200 parts per million in the first experimental stage.

CODATA recommended values of the fundamental physical constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

Measurement of gravitational coupling between millimetre-sized masses

Gravity is the weakest of all known fundamental forces and poses some of the most important open questions to modern physics: it remains resistant to unification within the standard model of physics and its underlying concepts appear to be fundamentally disconnected from quantum theory^1-4. Testing gravity at all scales is therefore an important experimental endeavour^5-7. So far, these tests have mainly involved macroscopic masses at the kilogram scale and beyond⁸. Here we show gravitational coupling between two gold spheres of 1 millimetre radius, thereby entering the regime of sub-100-milligram sources of gravity. Periodic modulation of the position of the source mass allows us to perform a spatial mapping of the gravitational force. Both linear and quadratic coupling are observed as a consequence of the nonlinearity of the gravitational potential. Our results extend the parameter space of gravity measurements to small, single source masses and low gravitational field strengths. Further improvements to our methodology will enable the isolation of gravity as a coupling force for objects below the Planck mass. This work opens the way to the unexplored frontier of microscopic source masses, which will enable studies of fundamental interactions^9-11 and provide a path towards exploring the quantum nature of gravity^12-15.

Precision measurement of the Newtonian gravitational constant

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10-11 m3 kg-1 s-2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.