We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb and 87Rb was compared, yielding a difference Dg/g =(1.2 +-1.7)x10^{-7}. We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of Dg/g =(0.4 +-1.2)x10^{-7}.
Matter-wave interferometry with atoms and molecules has attracted a rapidly growing interest over the past two decades, both in demonstrations of fundamental quantum phenomena and in quantum-enhanced precision measurements. Such experiments exploit the non-classical superposition of two or more position and momentum states which are coherently split and rejoined to interfere. Here, we present the experimental realization of a universal near-field interferometer built from three short-pulse single-photon ionization gratings. We observe quantum interference of fast molecular clusters, with a com…
In 1995, Chapman et al. (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish under the presence of scattering events with photons, as required by the complementarity principle. In this work we provide an analytical study of this experiment, determining the evolution of the atom wave function along the three-grating Mach-Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representatio…
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 la…
We describe progress toward a precise measurement of the recoil energy of an atom measured using a perturbative grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, a perturbing sw pulse is used to shift the phase of excited momentum states---producing a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2ω_q$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temp…
The interaction of Na atoms with a surface was probed by inserting a nanofabricated material grating into one arm of an atom interferometer (IFM). This technique permits a direct measurement of the change in phase and coherence of matter waves as they pass within 25 nm of the grating bar surface. The practical concerns and challenges of making such a measurement are discussed here. Interference of spurious diffraction orders, IFM path overlap, and the partial obscuration of IFM beams are all important aspects of this experiment. The systematic effects that contribute to the measured phase shif…
We report an improved test of the weak equivalence principle by using a simultaneous $^{85}$Rb-$^{87}$Rb dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate its ability in suppressing common-mode phase noise of Raman lasers after their frequencies and intensity ratios are optimized. The statistical uncertainty of the experimental data for Eötvös parameter $η$ is $0.8\times10^{-8}$ at 3200 s. With various systematic errors corrected the final value is $η=(2.8\pm3.0)\times10^{-8}$. The major unc…
Atom-surface interactions can significantly modify the intensity and phase of atom de Broglie waves diffracted by a silicon nitride grating. This affects the operation of a material grating as a coherent beam splitter. The phase shift induced by diffraction is measured by comparing the relative phases of serveral interfering paths in a Mach-Zehnder Na atom interferometer formed by three material gratings. The values of the diffraction phases are consistent with a simple model which includes a van der Waals atom-surface interaction between the Na atoms and the silicon nitride grating bars.
The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle kn…
We theoretically investigate the application of the fringe-locking method (FLM) in the dual-species quantum test of the weak equivalence principle (WEP). With the FLM, the measurement is performed invariably at the midfringe, and the extraction of the phase shift for atom interferometers is linearized. For the simultaneous interferometers, this linearization enables a good common-mode rejection of vibration noise, which is usually the main limit for high precision WEP tests of dual-species kind. We note that this method also allows for an unbiased determination of the gravity accelerations dif…
Atomic three-grating Mach-Zehnder interferometry constitutes an important tool to probe fundamental aspects of the quantum theory. There is, however, a remarkable gap in the literature between the oversimplified models and robust numerical simulations considered to describe the corresponding experiments. Consequently, the former usually lead to paradoxical scenarios, such as the wave-particle dual behavior of atoms, while the latter make difficult the data analysis in simple terms. Here these issues are tackled by means of a simple grating working model consisting of evenly-spaced Gaussian sli…
Weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials. In this work we use Weyl functions to study the ``Talbot-Lau effect'' in a time-domain matter-wave interferometer. A ``displacement diagram'' is introduced to analyze and calculate the matter-wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo. Unlike previous treatments, this new approach allows the atomic ensemble to have an arbitrary initial phase-space distribution, and the…
We present here the performance of a simultaneous dual-species matter-wave accelerometer for measuring the differential acceleration between two different atomic species ($^{87}$Rb and $^{85}$Rb). We study the expression and the extraction of the differential phase from the interferometer output. The differential accelerometer reaches a short-term sensitivity of $1.23\times10^{-7}g/\sqrt{Hz}$ limited by the detection noise and a resolution of $2\times10^{-9}g$ after 11000 s, the highest reported thus far with a dual-species atom interferometer to our knowledge. Thanks to the simultaneous measu…
We review matter wave and clock comparison tests of the gravitational redshift. To elucidate their relationship to tests of the universality of free fall (UFF), we define scenarios wherein redshift violations are coupled to violations of UFF ("type II"), or independent of UFF violations ("type III"), respectively. Clock comparisons and atom interferometers are sensitive to similar effects in type II and precisely the same effects in type III scenarios, although type III violations remain poorly constrained. Finally, we describe the "Geodesic Explorer," a conceptual spaceborne atom interferomet…
Matter-wave interferometers utilizing different isotopes or chemical elements intrinsically have different sensitivities, and the analysis tools available until now are insufficient for accurately estimating the atomic phase difference under many experimental conditions. In this work, we describe and demonstrate two new methods for extracting the differential phase between dual-species atom interferometers for precise tests of the weak equivalence principle. The first method is a generalized Bayesian analysis, which uses knowledge of the system noise to estimate the differential phase based on…
We propose a scheme for testing the weak equivalence principle (Universality of Free Fall) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. A apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer fro…
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. 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. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a facto…
We propose an experiment to test the Weak Equivalence Principle (WEP) with a test mass consisting of two entangled atoms of different species. In the proposed experiment, a coherent measurement of the differential gravity acceleration between the two atomic species is considered, by entangling two atom interferometers operating on the two species. The entanglement between the two atoms is heralded at the initial beam splitter of the interferometers through the detection of a single photon emitted by either of the atoms, together with the impossibility of distinguishing which atom emitted the p…
Coriolis effect is an important error source in the weak equivalence principle (WEP) test using atom interferometer. In this paper, the problem of Coriolis error in WEP test is studied theoretically and experimentally. In theoretical simulation, Coriolis effect is analyzed by establishing an error model. The measurement errors of Eotvos coefficient (eta) in WEP test related to experimental parameters, such as horizontal-velocity difference and horizontal-position difference of atomic clouds, horizontal-position difference of detectors and rotation compensation of Raman laser's mirror are calcu…
We discuss techniques for probing the effects of a constant force acting on cold atoms using two configurations of a grating echo-type atom interferometer. Laser-cooled samples of $^{85}$Rb with temperatures as low as 2.4 $μ$K have been achieved in a new experimental apparatus with a well-controlled magnetic environment. We demonstrate interferometer signal lifetimes approaching the transit time limit in this system ($\sim 270$ ms), which is comparable to the timescale achieved by Raman interferometers. Using these long timescales, we experimentally investigate the influence of a homogeneous m…
Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i.) Contributions beyond linear order to …
Using a three-path contrast interferometer (CI) geometry and laser-pulse diffraction gratings, we create the first matter-wave interferometer with ytterbium (Yb) atoms. We present advances in contrast interferometry relevant to high-precision measurements. By comparing to a traditional atom interferometer, we demonstrate the immunity of the CI to vibrations for long interaction times (> 20 ms). We characterize and demonstrate control over the two largest systematic effects for a high-precision measurement of the fine structure constant via photon recoil with our interferometer: diffraction pha…
Do van der Waals interactions determine the smallest nanostructures that can be used for atom optics? This question is studied with regard to the problem of designing an atom interferometer with optimum sensitivity to de Broglie wave phase shifts. The optimum sensitivity to acceleration and rotation rates is also considered. For these applications we predict that nanostructures with a period smaller than 40 nm will cause atom interferometers to perform poorly because van der Waals interactions adversely affect how nanostructure gratings work as beam-splitters.
An atom interferometer based on a Stern-Gerlach beam splitter is proposed. Atom scattering from a combination of magnetic quadrupole and homogeneous magnetic fields is considered. Using Raman transitions, atoms are coherently excited into and de-excited from sublevels having nonzero magnetic quantum numbers. The spatial regions in which the atoms are in such sublevels are small and have magnetic fields designed to have constant gradients. Therefore, the atoms experience position-independent accelerations, and the aberration of the coherently separated and recombined atomic beams remains small.…
Does gravity influence local measurements? We use a dual-species atom interferometer with $2\,\text{s}$ 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 $η= [1.6\; \pm\; 1.8\; \text{(stat)}\; \pm \; 3.4 \; \text{(sys)}] \times 10^{-12}$, consistent with zero violation of the equivalence principle. With a resolution of up…
Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (C…
This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a no…
We describe the Quantum Test of the Equivalence principle and Space Time (QTEST), a concept for an atom interferometry mission on the International Space Station (ISS). The primary science objective of the mission is a test of Einstein's equivalence principle with two rubidium isotope gases at a precision of better than 10$^{-15}$. Distinct from the classical tests is the use of quantum wave packets and their expected large spatial separation in the QTEST experiment. This dual species atom interferometer experiment will also be sensitive to time-dependent equivalence principle violations that …
The past three decades have shown dramatic progress in the ability to manipulate and coherently control the motion of atoms. This exquisite control offers the prospect of a new generation of inertial sensors with unprecedented sensitivity and accuracy, which will be important for both fundamental and applied science. In this article, we review some of our recent results regarding the application of atom interferometry to inertial measurements using compact, mobile sensors. This includes some of the first interferometer measurements with cold $^{39}$K atoms, which is a major step toward achievi…
We report a hyperfine-states related weak equivalence principle (WEP) test which searches for possible WEP violation signal in single atom interferometer. With the ground hyperfine states $\left|F=1\right\rangle$ and $\left|F=2\right\rangle$ of $^{87}$Rb atoms simultaneously scanned over different paths in a Raman Mach-Zehnder interferometer (MZI), the difference of the free fall accelerations for the atom in the two hyperfine states is encoded into the phase shift of the MZI, contributing a WEP test signal. The test signal can be extracted out by reversing the direction of the effective wave …
The gravitational acceleration of antimatter, gbar, has yet to be directly measured; an unexpected outcome of its measurement could change our understanding of gravity, the universe, and the possibility of a fifth force. Three avenues are apparent for such a measurement: antihydrogen, positronium, and muonium, the last requiring a precision atom interferometer and novel muonium beam under development. The interferometer and its few-picometer alignment and calibration systems appear feasible. With 100 nm grating pitch, measurements of gbar to 10%, 1%, or better can be envisioned. These could co…
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 superpos…
Atom density profile arising in the atomic beam after passing through the one or two microfabricated structures (MS) is considered. Two limiting cases the beam with large and small angular divergence are considered. An equivalence of the considerations based on the Fresnel-Kirchhoff theory of diffraction and on the atomic recoil-effect is established. Higher order gratings' profiles produced in the collinear beam owing to the atomic Talbot effect are calculated. For an atomic beam with large angular divergence, two regimes of atoms' scattering off the MS, classical and quantum, are analyzed. F…
We propose a very long baseline atom interferometer test of Einstein's equivalence principle (EEP) with ytterbium and rubidium extending over 10m of free fall. In view of existing parametrizations of EEP violations, this choice of test masses significantly broadens the scope of atom interferometric EEP tests with respect to other performed or proposed tests by comparing two elements with high atomic numbers. In a first step, our experimental scheme will allow reaching an accuracy in the Eötvös ratio of $7\times 10^{-13}$. This achievement will constrain violation scenarios beyond our present k…
Time domain deBroglie wave interferometry [Cahn et al, Phys. Rev. Lett. 79, 784] is applied to Rb87 atoms in a magnetic guide. A standing wave light field is carefully aligned along the guiding direction of the magnetic trapping potential from a soft-ferromagnetic 4-foil structure. A sequence of two standing wave pulses is applied to the magnetically trapped atoms. The backscattered light at the atomic density grating revival time is collected and detected via a heterodyning technique. In addition to the observed recoil oscillations that fit the interferometer theory for atoms in free space, w…
We study the environmental dependence of ultralight scalar dark matter (DM) with linear interactions to the standard model particles. The solution to the DM field turns out to be a sum of the cosmic harmonic oscillation term and the local exponential fluctuation term. The amplitude of the first term depends on the local DM density and the mass of the DM field. The second term is induced by the local distribution of matter, such as the Earth. And it depends not only on the mass of the Earth, but also the density of the Earth. Then, we compute the phase shift induced by the DM field in atom inte…
Four atom optics experiments that each serve to measure atom-surface interactions near nanofabricated gratings are presented here. In these experiments atoms in a beam travel within 25 nm of a material grating bar, and the analysis incorporates phase shifts for the atomic de Broglie waves due to interactions betwen Na atoms and silicon nitride surfaces. One atom diffraction experiment determines the van der Waals coefficient $C_3=2.7\pm$0.8 meVnm$^3$, and one atom interferometer experiment determines $C_3=4\pm$1 meVnm$^3$. The results of all four experiments are consistent with the Lifshitz pr…
Evaluation of the systematic error induced by quadratic Zeeman effect using hyperfine ground state exchange method in a long-baseline dual-species atom interferometer
Atom interferometry is the most successful technique for precision metrology. However, current interferometers using ultracold atoms allows one to probe the interference pattern only momentarily and has finite duty cycle, resulting in an aliasing effect and a low-bandwidth measurement -- also known as Dick effect. Interferometry with a continuous-wave atom laser shows promise in overcoming these limitations due a continuous monitoring of the interference pattern. In this work, we demonstrate a key step towards such an interferometry by demonstrating a diffraction of an `atom laser' in the Rama…
The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new type of underground laser-linked interferometer facility, and is currently under construction. It is in the 200-meter-on-average underground of a mountain named Zhaoshan which is about 80 km southeast to Wuhan. ZAIGA will be equipped with long-baseline atom interferometers, high-precision atom clocks, and large-scale gyros. ZAIGA facility will take an equilateral triangle configuration with two 1-km-apart atom interferometers in each arm, a 300-meter vertical tunnel with atom fountain and atom clocks mounted, a…
Atom interferometers are promising tools for precision measurement with applications ranging from geophysical exploration to tests of the equivalence principle of general relativity, or the detection of gravitational waves. Their optimal sensitivity is ultimately limited by their detection noise. We review resonant and near-resonant methods to detect the atom number of the interferometer outputs and we theoretically analyze the relative influence of various scheme dependent noise sources and the technical challenges affecting the detection. We show that for the typical conditions under which a…
We investigate an integrated optical chip immersed in atomic vapor providing several waveguide geometries for spectroscopy applications. The narrow-band transmission through a silicon nitride waveguide and interferometer is altered when the guided light is coupled to a vapor of rubidium atoms via the evanescent tail of the waveguide mode. We use grating couplers to couple between the waveguide mode and the radiating wave, which allow for addressing arbitrary coupling positions on the chip surface. The evanescent atom-light interaction can be numerically simulated and shows excellent agreement …
