Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function

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.

Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity

We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.

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.

Quantum reference frames for an indefinite metric

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition. Comparison with other models shows that semi-classical gravity and gravitational collapse models do not obey the covariance of dynamical laws under quantum coordinate transformations.

Large-Momentum-Transfer Atom Interferometers with μrad-Accuracy Using Bragg Diffraction

Large-momentum-transfer (LMT) atom interferometers using elastic Bragg scattering on light waves are among the most precise quantum sensors to date. To advance their accuracy from the mrad to the μrad regime, it is necessary to understand the rich phenomenology of the Bragg interferometer, which differs significantly from that of a standard two-mode interferometer. We develop an analytic model for the interferometer signal and demonstrate its accuracy using comprehensive numerical simulations. Our analytic treatment allows the determination of the atomic projection noise limit of a LMT Bragg interferometer and provides the means to saturate this limit. It affords accurate knowledge of the systematic phase errors as well as their suppression by 2 orders of magnitude down to a few μrad using appropriate light-pulse parameters.

Enhanced Readout from Spatial Interference Fringes in a Point-Source Cold Atom Inertial Sensor

When the initial size of an atom cloud in a cold atom interferometer is negligible compared to its size after free expansion, the interferometer is approximated to a point-source interferometer and is sensitive to rotational movements by introducing an additional phase shear in the interference sequence. This sensitivity on rotation enables a vertical atom-fountain interferometer to measure angular velocity in addition to gravitational acceleration, which it is conventionally used to measure. The accuracy and precision of the angular velocity measurement depends on proper extraction of frequency and phase from spatial interference patterns detected via the imaging of the atom cloud, which is usually affected by various systematic biases and noise. To improve the measurement, a pre-fitting process based on principal component analysis is applied to the recorded raw images. The contrast of interference patterns are enhanced by 7-12 dB when the processing is present, which leads to an enhancement in the precision of angular velocity measurements from 6.3 μrad/s to 3.3 μrad/s. This technique is applicable in various instruments that involve precise extraction of frequency and phase from a spatial interference pattern.

Macroscopic Quantum Test with Bulk Acoustic Wave Resonators

Recently, solid-state mechanical resonators have become a platform for demonstrating nonclassical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics by ruling out a classical description at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of μ=11.3 is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could test the quantum superposition principle at unprecedented scales and also place more stringent bounds on spontaneous collapse models.

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.

Generation of Entanglement from Mechanical Rotation

Many phenomena and fundamental predictions, ranging from Hawking radiation to the early evolution of the Universe rely on the interplay between quantum mechanics and gravity or more generally, quantum mechanics in curved spacetimes. However, our understanding is hindered by the lack of experiments that actually allow us to probe quantum mechanics in curved spacetime in a repeatable and accessible way. Here we propose an experimental scheme for a photon that is prepared in a path superposition state across two rotating Sagnac interferometers that have different diameters and thus represent a superposition of two different spacetimes. We predict the generation of genuine entanglement even at low rotation frequencies and show how these effects could be observed even due to the Earth's rotation. These predictions provide an accessible platform in which to study the role of the underlying spacetime in the generation of entanglement.

Measurement of the scalar curvature of high-power lasers

High-power lasers develop high energy per unit time, and as energy curves space, we expect atomic energy levels to change. The fluorescence spectrum is a good measurement of the matrix elements involved in the Rabi oscillation and consequently allows us to determine the scalar curvature. At high Z, electrons oppose ionization even for strong intensities. Because high-power lasers address relativistic atoms, the wave functions involved must be solutions of the Dirac equation in a curved space-time. The paper can be seen as a way to check whether the Einstein's gravitational theory is valid in the dimension of laboratory.

Trap frequency measurement with a pulsed atom laser

We describe a novel method of single-shot trap frequency measurement for a confined Bose-Einstein Condensate, which uses an atom laser to repeatedly sample the mean velocity of trap oscillations as a function of time. The method is able to determine the trap frequency to an accuracy of 39 ppm (16 mHz) in a single experimental realization, improving on the literature by a factor of three. Further, we show that by employing a reconstructive aliasing approach our method can be applied to trap frequencies more than a factor of 3 greater than the sampling frequency.

Superconductors and Gravity

We review and discuss some recent developments on the unconventional interaction between superconducting systems and the local gravitational field. While it is known that gravitational perturbations (such as gravitational waves) can affect supercondensates and supercurrents dynamics, we want to focus here on the more subtle superfluid back-reaction acting on the surrounding gravitational field, analysing some specific favourable situations. To this end, we will consider suitable quantum macrosystems in a coherent state, immersed in the static weak Earth’s gravitational field, investigating possible slight local alterations of the latter not explained in terms of classical physics.

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 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.

Interferometry in an Atomic Fountain with Ytterbium Bose–Einstein Condensates

We present enabling experimental tools and atom interferometer implementations in a vertical “fountain” geometry with ytterbium Bose–Einstein condensates. To meet the unique challenge of the heavy, non-magnetic atom, we apply a shaped optical potential to balance against gravity following evaporative cooling and demonstrate a double Mach–Zehnder interferometer suitable for applications such as gravity gradient measurements. Furthermore, we also investigate the use of a pulsed optical potential to act as a matter wave lens in the vertical direction during expansion of the Bose–Einstein condensate. This method is shown to be even more effective than the aforementioned shaped optical potential. The application of this method results in a reduction of velocity spread (or equivalently an increase in source brightness) of more than a factor of five, which we demonstrate using a two-pulse momentum-space Ramsey interferometer. The vertical geometry implementation of our diffraction beams ensures that the atomic center of mass maintains overlap with the pulsed atom optical elements, thus allowing extension of atom interferometer times beyond what is possible in a horizontal geometry. Our results thus provide useful tools for enhancing the precision of atom interferometry with ultracold ytterbium atoms.

High Sensitivity Multi-Axes Rotation Sensing Using Large Momentum Transfer Point Source Atom Interferometry

A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from the rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possible to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. We analyze how factors such as Doppler detuning, spontaneous emission, and the finite initial size of the atomic cloud compromise the advantage of LMT and how to find the optimal momentum transfer under these limitations, with both the semi-classical model and a model under which the motion of the center of mass of each atom is described quantum mechanically. We identify a set of realistic parameters for which LMT can improve the PSI by a factor of nearly 40.

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.

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.

40 W, 780 nm laser system with compensated dual beam splitters for atom interferometry

We demonstrate a narrow-linewidth 780 nm laser system with up to 40W power and a frequency modulation bandwidth of 230 MHz. Efficient overlap on nonlinear optical elements combines two pairs of phase-locked frequency components into a single beam. Serrodyne modulation with a high-quality sawtooth waveform is used to perform frequency shifts with >96.5% efficiency over tens of megahertz. This system enables next-generation atom interferometry by delivering simultaneous, Stark-shift-compensated dual beam splitters while minimizing spontaneous emission.

Atom-Interferometric Test of the Equivalence Principle at the 10^{-12} Level

We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between ^{85}Rb and ^{87}Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an Eötvös parameter of η=[1.6±1.8(stat)±3.4(syst)]×10^{-12}, consistent with zero violation of the equivalence principle. With a resolution of up to 1.4×10^{-11}  g per shot, we demonstrate a sensitivity to η of 5.4×10^{-11}/sqrt[Hz].

High-Precision Quantum-Enhanced Gravimetry with a Bose-Einstein Condensate

We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between 10^{4} and 10^{6} in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.

Effects of wave-front tilt and air density fluctuations in a sensitive atom interferometry gyroscope

We present a matter wave gyroscope with a Sagnac area of 5.92 cm², achieving a short-term sensitivity of 167 nrad/s/Hz^1/2. The atom interferometry gyroscope is driven by a π/2 - π - π - π/2 Raman pulse sequence based on an atom fountain with a parabolic trajectory. The phase-locked laser beams for Raman transitions partly propagate outside of the vacuum chamber and expose to the air when passing through the two arms of the vacuum chamber. This configuration leads to the tilt of the laser's wave-front and suffers the fluctuation of air density. The impacts on both the fringe contrast and long-term stability are experimentally investigated in detail, and effective schemes are developed to improve the performance of our atom gyroscope. The method presented here could be useful for developing large atom interferometry facilities with separated vacuum chambers.

Matter-wave interference of a native polypeptide

The de Broglie wave nature of matter is a paradigmatic example of quantum physics and it has been exploited in precision measurements of forces and fundamental constants. However, matter-wave interferometry has remained an outstanding challenge for natural polypeptides, building blocks of life, which are fragile and difficult to handle. Here, we demonstrate the wave nature of gramicidin, a natural antibiotic composed of 15 amino acids. Its center of mass is delocalized over more than 20 times the molecular size in our time-domain Talbot-Lau interferometer. We compare the observed interference fringes with a model that includes both a rigorous treatment of the peptide’s quantum wave nature as well as a quantum chemical assessment of its optical properties to distinguish our result from classical predictions. The realization of quantum optics with this prototypical biomolecule paves the way for quantum-assisted measurements on a large class of biologically relevant molecules.

Matter-wave interferometry of complex molecules is challenging due to difficulties in preparing and detecting molecular beams. Here the authors demonstrate quantum behavior of a polypeptide using matter-wave interference in an all-optical time-domain Talbot-Lau interferometer.

A fibered laser system for the MIGA large scale atom interferometer

We describe the realization and characterization of a compact, autonomous fiber laser system that produces the optical frequencies required for laser cooling, trapping, manipulation, and detection of 87Rb atoms - a typical atomic species for emerging quantum technologies. This device, a customized laser system from the Muquans company, is designed for use in the challenging operating environment of the Laboratoire Souterrain à Bas Bruit (LSBB) in France, where a new large scale atom interferometer is being constructed underground - the MIGA antenna. The mobile bench comprises four frequency-agile C-band Telecom diode lasers that are frequency doubled to 780 nm after passing through high-power fiber amplifiers. The first laser is frequency stabilized on a saturated absorption signal via lock-in amplification, which serves as an optical frequency reference for the other three lasers via optical phase-locked loops. Power and polarization stability are maintained through a series of custom, flexible micro-optic splitter/combiners that contain polarization optics, acousto-optic modulators, and shutters. Here, we show how the laser system is designed, showcasing qualities such as reliability, stability, remote control, and flexibility, while maintaining the qualities of laboratory equipment. We characterize the laser system by measuring the power, polarization, and frequency stability. We conclude with a demonstration using a cold atom source from the MIGA project and show that this laser system fulfills all requirements for the realization of the antenna.

T^{3} Stern-Gerlach Matter-Wave Interferometer

We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers that make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.

Multidimensional Atom Optics and Interferometry

We propose new multidimensional atom optics that can create coherent superpositions of atomic wave packets along three spatial directions. These tools can be used to generate light-pulse atom interferometers that are simultaneously sensitive to the three components of acceleration and rotation, and we discuss how to isolate these inertial components in a single experimental shot. We also present a new type of atomic gyroscope that is insensitive to parasitic accelerations and initial velocities. The ability to measure the full acceleration and rotation vectors with a compact, high-precision, low-bias inertial sensor could strongly impact the fields of inertial navigation, gravity gradiometry, and gyroscopy.

Interleaved atom interferometry for high-sensitivity inertial measurements

Cold-atom inertial sensors target several applications in navigation, geoscience, and tests of fundamental physics. Achieving high sampling rates and high inertial sensitivities, obtained with long interrogation times, represents a challenge for these applications. We report on the interleaved operation of a cold-atom gyroscope, where three atomic clouds are interrogated simultaneously in an atom interferometer featuring a sampling rate of 3.75 Hz and an interrogation time of 801 ms. Interleaving improves the inertial sensitivity by efficiently averaging vibration noise and allows us to perform dynamic rotation measurements in a so far unexplored range. We demonstrate a stability of 3 × 10^-10 rad s^-1 , which competes with the best stability levels obtained with fiber-optic gyroscopes. Our work validates interleaving as a key concept for future atom-interferometry sensors probing time-varying signals, as in on-board navigation and gravity gradiometry, searches for dark matter, or gravitational wave detection.

Three-Path Atom Interferometry with Large Momentum Separation

We demonstrate the scale up of a symmetric three-path contrast interferometer to large momentum separation. The observed phase stability at separation of 112 photon recoil momenta exceeds the performance of earlier free-space interferometers. In addition to the symmetric interferometer geometry and Bose-Einstein condensate source, the robust scalability of our approach relies on the suppression of undesired diffraction phases through a careful choice of atom optics parameters. The interferometer phase evolution is quadratic with number of recoils, reaching a rate as high as 7×10^{7}  rad/s. We discuss the applicability of our method towards a new measurement of the fine-structure constant and a test of QED.

Exploring gravity with the MIGA large scale atom interferometer

We present the MIGA experiment, an underground long baseline atom interferometer to study gravity at large scale. The hybrid atom-laser antenna will use several atom interferometers simultaneously interrogated by the resonant mode of an optical cavity. The instrument will be a demonstrator for gravitational wave detection in a frequency band (100 mHz–1 Hz) not explored by classical ground and space-based observatories, and interesting for potential astrophysical sources. In the initial instrument configuration, standard atom interferometry techniques will be adopted, which will bring to a peak strain sensitivity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{2}}\cdot {\bf{1}}{{\bf{0}}}^{-{\bf{13}}}/\sqrt{{\bf{H}}{\bf{z}}}$$\end{document}2⋅10−13/Hz at 2 Hz. This demonstrator will enable to study the techniques to push further the sensitivity for the future development of gravitational wave detectors based on large scale atom interferometers. The experiment will be realized at the underground facility of the Laboratoire Souterrain à Bas Bruit (LSBB) in Rustrel–France, an exceptional site located away from major anthropogenic disturbances and showing very low background noise. In the following, we present the measurement principle of an in-cavity atom interferometer, derive the method for Gravitational Wave signal extraction from the antenna and determine the expected strain sensitivity. We then detail the functioning of the different systems of the antenna and describe the properties of the installation site.

Gravimetry through non-linear optomechanics

Precision gravimetry is key to a number of scientific and industrial applications, including climate change research, space exploration, geological surveys and fundamental investigations into the nature of gravity.  A variety of quantum systems, such as atom interferometry and on-chip-Bose–Einstein condensates have thus far been investigated to this aim. Here, we propose a new method which involves using a quantum optomechanical system for measurements of gravitational acceleration. As a proof-of-concept, we investigate the fundamental sensitivity for gravitational accelerometry of a cavity optomechanical system with a trilinear radiation pressure light-matter interaction. The phase of the optical output encodes the gravitational acceleration g and is the only component which needs to be measured. We prove analytically that homodyne detection is the optimal readout method and we predict an ideal fundamental sensitivity of Δg = 10⁻¹⁵ ms⁻² for state-of-the-art parameters of optomechanical systems, showing that they could, in principle, surpass the best atomic interferometers even for low optical intensities. Further, we show that the scheme is strikingly robust to the initial thermal state of the oscillator.

Precise gravimetric measurements are an important but challenging task. Here, Qvarfort et al. theoretically show that, in an optomechanical cavity, only the phase of the optical output needs to be measured to obtain a precise value for the gravitational acceleration with high sensitivity.

Observation of Extra Photon Recoil in a Distorted Optical Field

Light carries momentum which induces on atoms a recoil for each photon absorbed. In vacuum, for a monochromatic beam of frequency ν, the global momentum per photon is bounded by general principles and is smaller than hν/c leading to a limit on the recoil. However, locally this limit can be broken. In this Letter, we give a general formula to calculate the recoil in vacuum. We show that in a laser beam with a distorted optical field, there are regions where the recoil can be higher than this limit. Using atoms placed in those regions we are able to measure directly the extra recoil.

Time base evaluation for atom gravimeters

Time is an inevitable quantity involved in absolute gravity measurements, and 10 MHz frequency standards are usually utilized as time base. Here we investigate the influence of time base bias on atom-interferometry-based gravity measurements and present an onsite calibration of the time base bias relying on an atom gravimeter itself. With a microwave source referenced to the time base, the time base bias leads to a magnified frequency shift of the microwave source output. The shift is then detected by Ramsey spectroscopy with the clock transition of ⁸⁷Rb atoms as a frequency discriminator. Taking advantage of available free-fall cold atoms and developed techniques of measuring the atom energy level shift in atom gravimeters, the calibration achieves an accuracy of 0.6 mHz for the time base. And the corresponding error for gravity measurements is constrained to 0.1 μGal, meeting the requirement of state-of-the-art gravimeters. The presented evaluation is important for the applications of atom gravimeters.

Efficient Adiabatic Spin-Dependent Kicks in an Atom Interferometer

We present an atom interferometry technique in which the beam splitter is split into two separate operations. A microwave pulse first creates a spin-state superposition, before optical adiabatic passage spatially separates the arms of that superposition. Despite using a thermal atom sample in a small (600  μm) interferometry beam, this procedure delivers an efficiency of 99% per ℏk of momentum separation. Utilizing this efficiency, we first demonstrate interferometry with up to 16ℏk momentum splitting and free-fall limited interrogation times. We then realize a single-source gradiometer, in which two interferometers measuring a relative phase originate from the same atomic wave function. Finally, we demonstrate a resonant interferometer with over 100 adiabatic passages, and thus over 400ℏk total momentum transferred.

Effective Inertial Frame in an Atom Interferometric Test of the Equivalence Principle

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.

Measurement of the fine-structure constant as a test of the Standard Model

Measurements of the fine-structure constant α require methods from across subfields and are thus powerful tests of the consistency of theory and experiment in physics. Using the recoil frequency of cesium-133 atoms in a matter-wave interferometer, we recorded the most accurate measurement of the fine-structure constant to date: α = 1/137.035999046(27) at 2.0 × 10^-10 accuracy. Using multiphoton interactions (Bragg diffraction and Bloch oscillations), we demonstrate the largest phase (12 million radians) of any Ramsey-Bordé interferometer and control systematic effects at a level of 0.12 part per billion. Comparison with Penning trap measurements of the electron gyromagnetic anomaly g_e - 2 via the Standard Model of particle physics is now limited by the uncertainty in g_e - 2; a 2.5σ tension rejects dark photons as the reason for the unexplained part of the muon's magnetic moment at a 99% confidence level. Implications for dark-sector candidates and electron substructure may be a sign of physics beyond the Standard Model that warrants further investigation.

Atom Interferometry with the Sr Optical Clock Transition

We report on the realization of a matter-wave interferometer based on single-photon interaction on the ultranarrow optical clock transition of strontium atoms. We experimentally demonstrate its operation as a gravimeter and as a gravity gradiometer. No reduction of interferometric contrast was observed for a total interferometer time up to ∼10  ms, limited by geometric constraints of the apparatus. Single-photon interferometers represent a new class of high-precision sensors that could be used for the detection of gravitational waves in so far unexplored frequency ranges and to enlighten the boundary between quantum mechanics and general relativity.

Canceling the Gravity Gradient Phase Shift in Atom Interferometry

Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.

Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity

All existing quantum-gravity proposals are extremely hard to test in practice. Quantum effects in the gravitational field are exceptionally small, unlike those in the electromagnetic field. The fundamental reason is that the gravitational coupling constant is about 43 orders of magnitude smaller than the fine structure constant, which governs light-matter interactions. For example, detecting gravitons-the hypothetical quanta of the gravitational field predicted by certain quantum-gravity proposals-is deemed to be practically impossible. Here we adopt a radically different, quantum-information-theoretic approach to testing quantum gravity. We propose witnessing quantumlike features in the gravitational field, by probing it with two masses each in a superposition of two locations. First, we prove that any system (e.g., a field) mediating entanglement between two quantum systems must be quantum. This argument is general and does not rely on any specific dynamics. Then, we propose an experiment to detect the entanglement generated between two masses via gravitational interaction. By our argument, the degree of entanglement between the masses is a witness of the field quantization. This experiment does not require any quantum control over gravity. It is also closer to realization than detecting gravitons or detecting quantum gravitational vacuum fluctuations.

Multi-line fiber laser system for cesium and rubidium atom interferometry

We present an innovative multi-line fiber laser system for both cesium and rubidium manipulation. The architecture is based on frequency conversion of two lasers at 1560 nm and 1878 nm. By taking advantage of existing high performance fibered components at these wavelengths, we have demonstrated multi-line operation of an all fiber laser system delivering 350 mW at 780 nm for rubidium and 210 mW at 852 nm for cesium. This result highlights the promising nature of such laser system especially for Cs manipulation for which no fiber laser system has been reported. It offers new perspectives for the development of atomic instruments dedicated to onboard applications and opens the way to a new generation of atom interferometers involving three atomic species (⁸⁵Rb, ⁸⁷Rb and ¹³³Cs) for which we propose an original laser architecture.