Measurement of the gravity-field curvature by atom interferometry

Compact multi-channel radio frequency pulse-sequence generator with fast-switching capability for cold-atom interferometers

Cold-atom interferometers have matured into a powerful tool for fundamental physics research, and they are currently moving from realizations in the laboratory to applications in the field. A radio frequency (RF) generator is an indispensable component of these devices for controlling lasers and manipulating atoms. In this work, we developed a compact RF generator for fast switching and sweeping the frequencies and amplitudes of atomic-interference pulse sequences. In this generator, multi-channel RF signals are generated using a field-programmable gate array (FPGA) to control eight direct digital synthesizers (DDSs). We further propose and demonstrate a method for pre-loading the parameters of all the RF pulse sequences to the DDS registers before their execution, which eliminates the need for data transfer between the FPGA and DDSs to change RF signals. This sharply decreases the frequency-switching time when the pulse sequences are running. Performance characterization showed that the generated RF signals achieve a 100 ns frequency-switching time and a 40 dB harmonic-rejection ratio. The generated RF pulse sequences were applied to a cold-atom-interferometer gyroscope, and the contrast of atomic interference fringes was found to reach 38%. This compact multi-channel generator with fast frequency/amplitude switching and/or sweeping capability will be beneficial for applications in field-portable atom interferometers.

Review of Atom Chips for Absolute Gravity Sensors

As a powerful tool in scientific research and industrial technologies, the cold atom absolute gravity sensor (CAGS) based on cold atom interferometry has been proven to be the most promising new generation high-precision absolute gravity sensor. However, large size, heavy weight, and high-power consumption are still the main restriction factors of CAGS being applied for practical applications on mobile platforms. Combined with cold atom chips, it is possible to drastically reduce the complexity, weight, and size of CAGS. In this review, we started from the basic theory of atom chips to chart a clear development path to related technologies. Several related technologies including micro-magnetic traps, micro magneto-optical traps, material selection, fabrication, and packaging methods have been discussed. This review gives an overview of the current developments in a variety of cold atom chips, and some actual CAGS systems based on atom chips are also discussed. We summarize by listing some of the challenges and possible directions for further development in this area.

A Simplified Laser System for Atom Interferometry Based on a Free-Space EOM

In this paper, a compact laser system for 87Rb atom interferometry based on only one free-space electro-optic modulator (EOM) was realized, where repumping and Raman beams were generated with a free-space EOM. In addition, this laser system does not require a laser amplifier compared to fibered EOM since fibered EOM cannot transmit high-power lasers. However, due to the narrow modulation linewidth of free-space EOM, it is impossible to obtain the frequencies of repumping and Raman beams separately, which would lead to some complicated effects. Therefore, a theoretical analysis was carried out to solve this problem, and a new frequency scheme for AI is proposed. For the experiment, the laser system of AI was built up. Moreover, the atomic interference fringes were obtained with a contrast of 20.7% (T = 60 ms) and the fitted phase resolution is approximately 1.25 mrad. The presented laser system could provide a new solution for compact AI systems in the future.

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.

Magnetic Curvatures of a Uniformly Magnetized Tesseroid Using the Cartesian Kernels

In recent years, the gravitational curvatures, the third-order derivatives of the gravitational potential (GP), of a tesseroid have been introduced in the context of gravity field modeling. Analogous to the gravity field, magnetic field modeling can be expanded by magnetic curvatures (MC), the third-order derivatives of the magnetic potential (MP), which are the change rates of the magnetic gradient tensor (MGT). Exploiting Poisson's relations between ( n + 1 ) th-order derivatives of the GP and nth-order derivatives of the MP, this paper derives expressions for the MC of a uniformly magnetized tesseroid using the fourth-order derivatives of the GP of a uniform tesseroid expressed in terms of the Cartesian kernel functions. Based on the magnetic effects of a uniform spherical shell, all expressions for the MP, magnetic vector (MV), MGT and MC of tesseroids have been examined for numerical problems due to singularity of the respective integral kernels (i.e., near zone and polar singularity problems). For this, the closed analytical expressions for the MP, MV, MGT and MC of the uniform spherical shell have been provided and used to generate singularity-free reference values. Varying both height and latitude of the computation point, it is found numerically that the near zone problem also exists for all magnetic quantities (i.e., MP, MV, MGT and MC). The numerical tests also reveal that the polar singularity problems do not occur for the magnetic quantity as a result of the use of Cartesian as opposed to spherical integral kernels. This demonstrates that the magnetic quantity including the newly derived MC 'inherit' the same numerical properties as the corresponding gravitational functional. Possible future applications (e.g., geophysical information) of the MC formulas of a uniformly magnetized tesseroid could be improved modeling of the Earth's magnetic field by dedicated satellite missions.

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.

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.

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.

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.

Realization of a compact one-seed laser system for atom interferometer-based gravimeters

A simple and compact design of the laser system is important for realization of compact atom interferometers (AIs). We design and realize a simple fiber bench-based 780-nm laser system used for ⁸⁵Rb AI-based gravimeters. The laser system contains only one 780 nm seed laser, and the traditional frequency-doubling-module is not used. The Raman beams are shared with one pair of the cooling beams by using a liquid crystal variable retarder based polarization control technique. This laser system is applied to a compact AI-based gravimeter, and a best gravity measurement sensitivity of 230 μGal/Hz^1/2 is achieved. The gravity measurements for more than one day are also performed, and the long-term stability of the gravimeter is 5.5 μGal.

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.

Invited Review Article: Measurements of the Newtonian constant of gravitation, G

By many accounts, the Newtonian constant of gravitation G is the fundamental constant that is most difficult to measure accurately. Over the past three decades, more than a dozen precision measurements of this constant have been performed. However, the scatter of the data points is much larger than the uncertainties assigned to each individual measurement, yielding a Birge ratio of about five. Today, G is known with a relative standard uncertainty of 4.7 × 10-5, which is several orders of magnitudes greater than the relative uncertainties of other fundamental constants. In this article, various methods to measure G are discussed. A large array of different instruments ranging from the simple torsion balance to the sophisticated atom interferometer can be used to determine G. Some instruments, such as the torsion balance can be used in several different ways. In this article, the advantages and disadvantages of different instruments as well as different methods are discussed. A narrative arc from the historical beginnings of the different methods to their modern implementation is given. Finally, the article ends with a brief overview of the current state of the art and an outlook.

Quantum test of the equivalence principle for atoms in coherent superposition of internal energy states

The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms: a Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eötvös ratio of atoms in two hyperfine levels with relative uncertainty in the low 10^-9, improving previous results by almost two orders of magnitude.

Bifurcation trees of Stark-Wannier ladders for accelerated Bose-Einstein condensates in an optical lattice

In this paper we show that in the semiclassical regime of periodic potential large enough, the Stark-Wannier ladders become a dense energy spectrum because of a cascade of bifurcations while increasing the ratio between the effective nonlinearity strength and the tilt of the external field; this fact is associated to a transition from regular to quantum chaotic dynamics. The sequence of bifurcation points is explicitly given.

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

Spacetime curvature induces tidal forces on the wave function of a single quantum system. Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces. The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold. Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

Circumventing Heisenberg's Uncertainty Principle in Atom Interferometry Tests of the Equivalence Principle

Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenberg's uncertainty principle. We present a promising scheme that overcomes these problems by compensating the effects of the gravity gradients and circumvents the fundamental limitations due to Heisenberg's uncertainty principle. Furthermore, it relaxes the experimental requirements on initial colocation by several orders of magnitude.

Continuous Cold-Atom Inertial Sensor with 1 nrad/sec Rotation Stability

We report the operation of a cold-atom inertial sensor which continuously captures the rotation signal. Using a joint interrogation scheme, where we simultaneously prepare a cold-atom source and operate an atom interferometer (AI), enables us to eliminate the dead times. We show that such continuous operation improves the short-term sensitivity of AIs, and demonstrate a rotation sensitivity of 100  nrad/sec/sqrt[Hz] in a cold-atom gyroscope of 11  cm^{2} Sagnac area. We also demonstrate a rotation stability of 1  nrad/sec at 10^{4}  sec of integration time, which represents the state of the art for atomic gyroscopes. The continuous operation of cold-atom inertial sensors will lead to large area AIs at their full sensitivity potential, determined by the quantum noise limit.