High-accuracy inertial measurements with cold-atom sensors

Remi Geiger; Arnaud Landragin; Sébastien Merlet; Franck Pereira Dos Santos

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High-accuracy inertial measurements with cold-atom sensors

Remi Geiger, Arnaud Landragin, Sébastien Merlet, Franck Pereira Dos Santos

arXiv:2003.12516v1Mar 27, 2020physics.atom-phphysics.app-phphysics.ins-detquant-ph

TL;DR

Cold-atom inertial sensors offer high stability and accuracy across gravitational, inertial, metrological, geophysical, and fundamental-physics measurements, but remain constrained in robustness, dynamic range, and miniaturization. This review synthesizes three decades of developments, emphasizing recent research, system engineering, performance limits, applications, and emerging architectures. It reports strong gravimeter performance and continuing efforts toward field deployment, navigation, and other applications.

Problem
Cold-atom sensors need improved robustness, dynamic range, miniaturization, and integration to extend high-accuracy measurements beyond established laboratory, geoscience, metrology, and fundamental-physics applications.
Method
The article reviews light-pulse atom-interferometer principles, common hardware, instrument developments, performance limitations, applications, and recent research directions.
Results
Gravimeters have achieved inaccuracy better than 2×10^-8 m.s^-2 and stability of 5×10^-10 m.s^-2 in 10^5 s, while alkali sensors using two-photon Raman transitions have delivered the best performances so far.
Takeaways & Limitations
Cold-atom sensors have natural applications in geosciences, metrology, and fundamental-physics tests, with integration and engineering efforts supporting prospective inertial-navigation applications.
Takeaways & Limitations
Cold-atom sensors currently have comparatively weak robustness, dynamic range, and miniaturization, limiting their competitiveness for all inertial-guidance requirements.

Abstract

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The research on cold-atom interferometers gathers a large community of about 50 groups worldwide both in the academic and now in the industrial sectors. The interest in this sub-field of quantum sensing and metrology lies in the large panel of possible applications of cold-atom sensors for measuring inertial and gravitational signals with a high level of stability and accuracy. This review presents the evolution of the field over the last 30 years and focuses on the acceleration of the research effort in the last 10 years. The article describes the physics principle of cold-atom gravito-inertial sensors as well as the main parts of hardware and the expertise required when starting the design of such sensors. It then reviews the progress in the development of instruments measuring gravitational and inertial signals, with a highlight on the limitations to the performances of the sensors, on their applications, and on the latest directions of research.

I. INTRODUCTION

Cold-atom inertial sensing has expanded rapidly, combining light-pulse atom interferometry with increasingly broad applications and engineering objectives. This review introduces the interferometer principle, sensor hardware, performance limits, and application landscape.

Field development: The field has accelerated over the last decade, with about 50 groups worldwide developing atom interferometers for diverse applications as of 2020.Research spans academic and industrial efforts.
Research priorities: Current research pursues better sensor performance, new architectures or generic techniques, and fundamental or field applications.Performance includes sensitivity, stability, accuracy, dynamic range, compactness, transportability, ease of use, and cost.
Interferometer principle: Two-photon Raman or Bragg beamsplitters dominate because they combine high sensitivity and accuracy with a practical compromise in simplicity.Optical transitions provide large momentum transfer and controlled diffraction.
Interferometer principle: Raman interactions couple two atomic ground states while transferring momentum ℏk_eff, enabling controlled matter-wave splitting and inertial sensing.The coupled states undergo coherent Rabi oscillations, with π/2 pulses producing balanced superpositions.
Interferometer principle: A three-pulse π/2−π−π/2 sequence separates, redirects, and recombines atomic wave packets into a Mach-Zehnder interferometer.The output transition probability is modulated by the phase difference accumulated along the two arms.
Limits and system design: Quantum projection noise ultimately limits intrinsic sensitivity, while sensor design must also address hardware integration and environmental disturbances.The review covers vacuum, lasers, control, auxiliary stabilization, and the main performance limitations.

III. SYSTEM ENGINEERING

Cold-atom inertial sensors require coordinated vacuum, atom-source, laser, and control subsystems. The source preparation combines ultrahigh vacuum, laser cooling, and internal-state selection to preserve coherence and interferometer contrast.

System architecture: A cold-atom inertial sensor uses a vacuum chamber, laser system, automated control, and auxiliary stabilization instrumentation.These subsystems support atom interrogation and instrument operation.
Vacuum system and cold-atom source: The vacuum level must remain below 10^-9 hPa so freely evolving atoms retain coherence over hundreds of milliseconds.The chamber is surrounded by magnetic shields and uses standard laser-cooling methods.
Vacuum system and cold-atom source: Microwave, pusher, and Raman pulses prepare atoms in a pure Zeeman-insensitive m_F=0 state with a narrower velocity distribution.This reduces sensitivity to stray magnetic fields and increases interferometer contrast.

B. Laser system

The laser system is a key subsystem because lasers cool, manipulate, and detect the atoms. Its architecture must provide stable Raman phases while accommodating constraints from atomic species, application, environment, and increasing interrogation time.

Laser sources: Alkali sensors commonly use semiconductor diode lasers near the 780 nm Rubidium or 852 nm Cesium D2 lines, while telecom-based sources are also being developed.Laser technology is closely linked to the atomic species used.
Laser architecture: 87Rb Raman sensors require five optical frequencies for cooling, detection, and manipulation, with published designs ranging from five lasers to one.Designs are constrained by size, application, measurement environment, and technology evolution.
Raman optics: Raman beams require phase stability in time and space, motivating phase locking, common collimation, retroreflection, large beam waists, and controlled polarization.These choices help maintain a common wavefront for counter-propagating beams.
Control system: Automated control requires tens of analog and digital outputs with sub-microsecond temporal resolution, agile RF and microwave synthesizers, and analog-to-digital converters.Control hardware and software standards evolve rapidly.
Environmental limits: When 2T exceeds a few milliseconds, ground vibration noise typically limits sensitivity to about 10^-5 m.s^-2.τ^-1/2.Isolation platforms, auxiliary seismometers or accelerometers, and vibration-immune schemes are used for rejection.
Applications: Gravity sensors are especially established because their single-axis vertical-accelerometer configuration is relatively simple and serves concrete geoscience applications.They are among the earliest demonstrations of atom-interferometric inertial sensing.

A. Historical context

Cold-atom gravimeters progressed from pioneering fountain interferometers to mature, increasingly compact instruments and differential sensors, with applications beyond laboratory metrology.

The first Raman-pulse atom interferometer used cold sodium atoms in a fountain and targeted competition with classical gravimeters.
The atom gravimeter showed 4 times better stability than a commercial FG5 and agreed on g within a combined uncertainty of 7×10^-8 m.s^-2.
Compact and transportable gravimeter projects began in the early 2000s, while atomic gravity sensing subsequently gained maturity through comparison activities and commercial development.
Vibration noise remains a central sensitivity constraint, although differential measurements reject common vibration noise and can approach detection-noise and quantum-projection-noise limits.
Differential acceleration sensitivities of 3 −4 × 10^-8 m.s^-2.τ^-1/2 corresponded to gravity-gradient sensitivities of 28 and 59 × 10^-9 s^-2.τ^-1/2 for 1.4 m and 0.72 m baselines.

D. Accuracy limits

Atomic gravity sensors offer intrinsically well-defined scale factors, but accuracy is limited by systematic effects, especially Coriolis acceleration and Raman-wavefront aberrations, alongside practical field-use constraints.

The scale factor is tied to time and frequency, providing intrinsic accuracy and long-term stability, but systematic effects must be measured or modeled.
Second-order light shifts, Coriolis acceleration, and laser-wavefront aberrations remain among the most important accuracy effects.
At µK temperatures, residual transverse velocities of order cm.s^-1 can produce Coriolis accelerations as large as 10^-6 m.s^-2.
A 0.1 nm wavefront distortion corresponds to about 1 mrad of Raman phase difference, making wavefront flatness a demanding accuracy requirement.
Ultracold-atom temperature extrapolation reduced the wavefront-aberration uncertainty to 1.3 × 10^-8 m.s^-2.
Many high-performing atomic instruments remain laboratory sensors and require greater robustness, compactness, operational simplicity, and tolerance to environmental changes for field measurements.

A. Gyroscopes

Cold-atom gyroscopes measure rotation through interferometric phase shifts, with sensitivity enhanced by long atom interrogation and a large effective scale factor. The section traces their origins, physical basis, and design trade-offs.

The 1991 pioneering atom-beam experiment resolved rotation-rate differences of about 0.1 rad.s−1.
Atomic-beam gyroscopes retain the best short-term sensitivity, reaching 6×10−10 rad.s−1 at 1 s integration time because of their large atom flux.
The rotation phase follows the Sagnac effect and depends on atomic energy and the interferometer’s oriented area.For non-relativistic atoms, the relevant energy is approximately mc^2, much larger than the photon energy in optical gyroscopes.
Atomic gyroscopes gain scale factor because atoms traverse fixed-size interferometers more slowly than photons, increasing inertial interaction time.
Increasing interrogation time enlarges the physical interferometer area and sensitivity, whereas compact architectures reduce instrument size at the cost of sensitivity.Free-fall distance scales as T^2, constraining the size of long-interrogation designs.

2. Instruments targeting high stability levels with long interrogation times

High-stability cold-atom gyroscopes use architectures and longer interrogation times to improve rotation measurements, while Raman-wavefront imperfections remain a central stability constraint. The latest long-interrogation instrument reaches 3 × 10−10 rad.s−1 after 10 000 s.

First generations of cold-atom gyroscopes: 2.4 × 10−7 rad.s−1.τ −1/2 sensitivity and 1 × 10−8 rad.s−1 stability at 4000 s were demonstrated by the first SYRTE cold-atom gyroscope.The 80 ms total interrogation experiment was limited by quantum projection noise, while trajectory and Raman-wavefront fluctuations constrained stability.
First generations of cold-atom gyroscopes: The Stanford four-pulse configuration overcame accuracy and dynamic-range limitations and enabled latitude, azimuth, and Earth-rotation measurements.Time asymmetry suppressed spurious noise from multiple-path interferences and increased signal-to-noise ratio.
First generations of cold-atom gyroscopes: 1.2 × 10−7 rad.s−1.τ −1/2 short-term sensitivity was achieved with composite light pulses in the Hannover gyroscope architecture.The instrument used separated counter-propagating atomic sources and a 19 mm2 Sagnac area.
Second generation of cold-atom gyroscopes: Wavefront aberrations coupled to atomic-trajectory fluctuations constrain long-term stability, producing an estimated 7×10−8 rad.s−1 level in a representative case.For T = 50 ms, δλ = λ/50, and δv0 < 1 µm.s−1, the bias is about 15 mrad against a 16 rad Earth-rotation signal.
Second generation of cold-atom gyroscopes: 3 × 10−10 rad.s−1 stability after 10 000 s was reached by the second-generation SYRTE gyroscope with 800 ms interrogation and an 11 cm2 Sagnac area.The measured stability remained above the 2 × 10−10 rad.s−1.τ −1/2 quantum projection noise limit; 10−12 rad.s−1 is anticipated if trajectory bias is controlled.

3. Example of gyroscope simplification effort

Researchers are simplifying cold-atom gyroscopes through centimeter-scale point-source interferometry and compact hardware, but reduced interrogation time and scale-factor instability limit performance. These efforts support potential field and scientific applications.

Example of gyroscope simplification effort: A NIST point-source interferometer occupies a 1 cm2 glass-chamber area and has a 0.03 mm2 Sagnac area.Its rotation and acceleration measurements use the root-mean-square atomic velocities to define the Sagnac area.
Example of gyroscope simplification effort: The compact setup’s sensitivity is limited by T = 8 ms Raman interrogation, technical noise, initial cloud size, and measurement dead time.The instrument was also demonstrated for gyro-compassing.
Example of gyroscope simplification effort: Point-source interferometry has a scale factor dependent on initial cloud size, causing instabilities when compact designs have small expansion ratios.
Example of gyroscope simplification effort: Using image-derived contrast and cloud-size information suppresses scale-factor drifts by a factor of 10 without degrading short-term sensitivity.
Applications: Cold-atom gyroscopes may first address high-stability applications in quiet environments, such as underwater navigation, while integration, dynamic range, robustness, and industrialization remain important requirements.

B. Accelerometers and progress for a complete inertial measurement unit

Cold-atom accelerometers are being adapted for inertial navigation by increasing data rates, hybridizing with classical sensors, and extending dynamic range, but dead times, vibrations, and phase ambiguity remain central challenges.

B. Accelerometers and progress for a complete inertial measurement unit: Single-axis atom accelerometers are simpler than gyroscopes but mobile operation is hindered by carrier vibrations and dead times between measurements.An isolation platform does not solve the problem for airborne operation.
B. Accelerometers and progress for a complete inertial measurement unit: 50 to 100 measurements per second were achieved by recapturing atoms after each interferometer sequence in a dual-axis accelerometer and gyroscope.Cold ensemble exchange maintains a large atom number at high data rates.
B. Accelerometers and progress for a complete inertial measurement unit: Vapor-cell atom interferometry avoids cold-ensemble production, but its sensitivity remains far from competitive with the best MEMS accelerometers.The reported comparison concerns MEMS sensitivities reaching 10^-6 m.s^-2.τ^-1/2.
B. Accelerometers and progress for a complete inertial measurement unit: Hybridization uses classical sensors during atomic dead times while retaining the cold-atom sensor’s long-term stability.A demonstrated hybrid accelerometer combined bandwidth from DC to 430 Hz with long-term stability.
B. Accelerometers and progress for a complete inertial measurement unit: 50-fold improvement in the trade-off between high sensitivity and limited dynamic range was obtained using composite fringes from varying interrogation times.Related approaches also provide quadrature phase detection and real-time systematic phase cancellation.

4. Multi-axis measurements

Multi-axis and multi-signal architectures address the phase ambiguity, dynamic-range, and dead-time limitations that complicate mobile cold-atom inertial sensing, while broader inertial applications motivate increasingly integrated designs.

4. Multi-axis measurements: Complete inertial measurement units require three-axis accelerometers and three-axis gyroscopes, yet simultaneous measurement of all inertial components remains challenging.Existing multi-axis demonstrations often rely on successive measurements over the three directions.
4. Multi-axis measurements: Three-dimensional atom optics have been proposed to sense three acceleration and rotation components simultaneously and isolate them in a single shot.The proposal uses coherent superpositions of atomic wave packets along three spatial directions.
4. Multi-axis measurements: Cold-atom inertial sensors support applications including fundamental-constant measurements, exotic-force searches, dark matter detection, and gravitational-wave detection.These applications exploit the sensors’ sensitivity to inertial forces.
4. Multi-axis measurements: Relative uncertainties below 10^-9 were achieved in a fine-structure-constant measurement using photon momentum transfer and Bloch oscillations.The result can be compared with an independent value derived from the electron’s anomalous magnetic moment.
4. Multi-axis measurements: Hundreds-of-meters-to-kilometers atom-accelerometer baselines are proposed for gravitational-wave detection using common laser beam splitters in a gradiometer configuration.The target signal has the same signature as gravity gradients.
4. Multi-axis measurements: Interferometer durations of tens of seconds in future space missions could boost Weak Equivalence Principle test sensitivity by 3 to 4 orders of magnitude.The proposed tests compare accelerations felt by different atomic species.

A. Large Momentum Transfer (LMT) atom optics

Large-momentum-transfer atom optics, colder sources, improved detection, and new atomic species are advancing scale factor, stability, and accuracy, while introducing demanding systematic and optical-control requirements.

A. Large Momentum Transfer (LMT) atom optics: Large-momentum-transfer techniques increase atomic wavepacket separation and thereby improve the sensors’ scale factor.Demonstrated methods include high-order Bragg diffraction, Bloch oscillations, and combined sequences.
A. Large Momentum Transfer (LMT) atom optics: 408 photon momenta of separation and subsequent recombination have been demonstrated with advanced beam splitters.Other methods can reach about a hundred photon momenta or more.
A. Large Momentum Transfer (LMT) atom optics: Diffraction phases and parasitic interferometers introduce phase systematics, phase noise, and contrast loss in multiport beam-splitting methods.Intensity fluctuations and spatial inhomogeneities contribute to these effects.
A. Large Momentum Transfer (LMT) atom optics: Optical cavities can provide laser-power enhancement greater than 100 for large-momentum-transfer beam splitters, but require millimeter-scale beam waists for homogeneous intensity.The cavity approach is motivated by the higher laser intensities required by LMT methods.
B. Ultracold atom sources: Ultracold sources reduce ballistic expansion and momentum spread, improving interrogation time, LMT efficiency, and sensitivity to beam-related systematics.Delta Kick collimation and optical-trap methods have produced temperatures below 100 pK.
B. Ultracold atom sources: Spatially resolving phase variations across the atomic source increases fringe visibility and sensor dynamical range.The improved detection methods operate at the interferometer output.
B. Ultracold atom sources: Alkaline-earth atoms offer reduced sensitivity to stray magnetic fields and narrow optical transitions suitable for single-photon beam splitters and quantum-metrology protocols.The relevant bosonic isotopes have zero ground-state spin.
VIII. CONCLUSION: Cold-atom sensors currently deliver their best performance with alkali sources and two-photon stimulated Raman transitions, while colder samples and richer atomic structure offer further improvement.The review expects substantial performance gains from these directions.

SUMMARY POINTS

Cold-atom interferometers combine quantum-state control with high stability and accuracy, supporting gravimetry, geoscience, metrology, and fundamental physics while engineering efforts target field deployment and navigation.

SUMMARY POINTS: Atom interferometers use quantum superpositions of different atomic momentum states.
SUMMARY POINTS: Two counter-propagating laser beams act as beam splitter and mirror for the atomic wave, efficiently creating these superposition states.
SUMMARY POINTS: The scale factor linking inertial effects to output phase is proportional to the interrogation lasers’ wavevector and the square of the interaction time.
SUMMARY POINTS: Cold-atom sources enable larger scale factors and high stability and accuracy through precise control of low-temperature atomic trajectories.
SUMMARY POINTS: Quantum projection noise is the fundamental sensitivity limit, but vibration noise often dominates instead.Typical output measurements involve ensembles of about 1 million atoms.
SUMMARY POINTS: Rubidium and cesium are the most commonly used atoms, while alkaline-earth sources such as strontium and ytterbium are attracting increasing interest.
SUMMARY POINTS: Cold-atom inertial sensors include a vacuum chamber, atom source, atom-optics systems, detectors, control electronics, and external instruments such as mechanical accelerometers.Typical instrument dimensions range from 10 cm to 10 m.
SUMMARY POINTS: Best atom gravimeters achieve inaccuracy better than 2×10^-8 m.s^-2 and stability of 5×10^-10 m.s^-2 in 10^5 s.Gravimeters were the first cold-atom sensors developed commercially.

Appendix A: List of groups working on cold-atom interferometers

The appendix surveys the main academic and industrial actors working on free-falling cold-atom inertial sensors across Europe, North America, Asia, and Oceania. A world map complements regional tables listing these groups and companies.

Tables I–III summarize the main actors in the cold-atom inertial-sensor field by geographic region.The tables cover Europe and EU-affiliated areas, North America, and Asia and Oceania.
The regional tables include research groups and companies active in inertial sensors based on free-falling cold atoms.Companies are identified typographically in the tables.
Figure 14 maps the different research groups and companies active in cold-atom inertial sensors worldwide.The map is based on the groups listed in Tables I–III.