Atom interferometers in optical cavities benefit from strong laser intensities and high-quality wavefronts. The laser frequency pairs that are needed for driving Raman transitions (often generated by phase modulating a monochromatic beam) form multiple standing waves in the cavity, resulting in a periodic spatial variation of the properties of the atom-light interaction along the cavity axis. Here, we model this spatial dependence and calculate two-photon Rabi frequencies and ac Stark shifts. We compare the model to measurements performed with varying cavity and pulse parameters such as cavity offset from the carrier frequency and the longitudinal position of the atom cloud. We show how setting cavity parameters to optimal values can increase the Raman transition efficiency at all positions in the cavity and nearly double the contrast in a Mach-Zehnder cavity atom interferometer in comparison to the unoptimized case.
We investigate the effect of coherent population trapping (CPT) in an atom inter-ferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, of order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the k-reversal technique, which consists in averaging inertial measurements performed with two opposite orientations of the Raman wavevector k, provided that internal states at the input of the interferometer are kept identical for both configurations.
IIn this paper we demonstrate a new scheme for Raman transitions which realize a symmetric momentum-space splitting of $4 \hbar k$, deflecting the atomic wave-packets into the same internal state. Combining the advantages of Raman and Bragg diffraction, we achieve a three pulse state labelled interferometer, intrinsically insensitive to the main systematics and applicable to all kind of atomic sources. This splitting scheme can be extended to $4N \hbar k$ momentum transfer by a multipulse sequence and is implemented on a $8 \hbar k$ interferometer. We demonstrate the area enhancement by measur…
We investigated the Raman pulse duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser, which leads to an appreciable phase shift. When applied to an experiment measuring the Newtonian gravitational constant G, the effect contributes to a systematic offset as large as -49ppm in Nature 510, 518 (2014). Thus an underestimated value of G measured by atom interferometer…
We study the influence of off-resonant two photon transitions on high precision measurements with atom interferometers based on stimulated Raman transitions. These resonances induce a two photon light shift on the resonant Raman condition. The impact of this effect is investigated in two highly sensitive experiments: a gravimeter and a gyroscope-accelerometer. We show that it can lead to significant systematic phase shifts, which have to be taken into account in order to achieve best performances in term of accuracy and stability.
We present an observation of competition effect among multiple quantum paths in a Raman-type Mach-Zehnder atom interferometer. By measuring the contrast of interference fringes, the competition effect among multiple interference paths is experimentally investigated. Due to the phase competition, the contrast periodically oscillates when modulating either the phase or the interrogation time between Raman pulses. The multiple quantum paths form because of the imperfect population transfer efficiency in stimulated Raman transitions, and are verified by modulating the duration of Raman pulses. The…
The scattering length in a BEC confined in an amplitude - modulated optical lattice can be manipulated by the modulation strength. Two standing laser waves of main and sideband frequencies of an optical lattice induce a Raman transition; due to resonant Raman driving the effective scattering length depends on the modulation strength and the detuning from resonance and can be tuned to a given value.
We have developed a modified Michelson interferometer type Raman laser system to manipulate cold 87 Rb atoms to interfere. A frequency modulated continuous wave technique was introduced to determine the optical path difference, thus compensating it to zero to minimize the effects of common mode noise. The linewidth (full width at half maximum) of the beat signal at 6.834 GHz was measured to 1Hz limited by the resolution bandwidth of the spectral analyzer. The measured rms phase variance of the phase noise at 166 MHz was 0.015 rad2, mainly restricted by our poor performance radio frequency micr…
The use of Raman laser generated by modulation for light-pulse atom interferometer allows to have a laser system more compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase shift determination limits the accuracy of our compact gravimeter at 8.10^-8 m/s^2. We show that it is possible to reduce considerably this…
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…
We present a new scheme for measuring the differential phase in dual atom interferometers. The magnetic field is modulated in one interferometer, and the differential phase can be extracted without measuring the amplitude of the magnetic field by combining the ellipse and linear fitting methods. The gravity gradient measurements are discussed based on dual atom interferometers. Numerical simulation shows that the systematic error of the differential phase measurement is largely decreased when the duration of the magnetic field is symmetrically modulated. This combined fitting scheme has a high…
Low-phase-noise and pure-spectrum Raman light is vital for high-precision atom interferometry by two-photon Raman transition. A preferred and prevalent solution for Raman light generation is electro-optic phase modulation. However, phase modulation inherently brings in double sidebands, resulting in residual sideband effects of multiple laser pairs beside Raman light in atom interferometry. Based on a well-designed rectangular fiber Bragg grating and an electro-optic modulator, optical single-sideband modulation has been realized at 1560 nm with a stable suppression ratio better than -25 dB de…
It is shown that using beam splitters with non-equal wave vectors results in a new recoil diagram which is qualitatively different from the well-known diagram associated with the Mach-Zehnder atom interferometer. We predict a new asymmetric Mach-Zehnder atom interferometer (AMZAI) and study it when one uses a Raman beam splitter. The main feature is that the phase of AMZAI contains a quantum part proportional to the recoil frequency. A response sensitive only to the quantum phase was found. A new technique to measure the recoil frequency and fine structure constant is proposed and studied outs…
We propose and demonstrate a method for calibrating atomic trajectories in a large-area dual-atom-interferometer gyroscope. The atom trajectories are monitored by modulating and delaying the Raman transition, and they are precisely calibrated by controlling the laser orientation and the bias magnetic field. To improve the immunity to the gravity effect and the common phase noise, the symmetry and the overlapping of two large-area atomic interference loops are optimized by calibrating the atomic trajectories and by aligning the Raman-laser orientations. The dual-atom-interferometer gyroscope is…
Using the technique of point source atom interferometry, we characterize the sensitivity of a multi-axis gyroscope based on free-space Raman interrogation of a single source of cold atoms in a glass vacuum cell. The instrument simultaneously measures the acceleration in the direction of the Raman laser beams and the component of the rotation vector in the plane perpendicular to that direction. We characterize the sensitivities for the magnitude and direction of the rotation vector measurement, which are 0.033 $^{\circ}/\mathrm{s}$ and 0.27 $^{\circ}$ with one second averaging time, respectivel…
We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long-term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short term sensitivity of 3*10^(-9) g/Hz^(-1/2) to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows to reach a resolution of 5*10^(-11) g after 8000 s on…
We present an atom interferometry technique in which the beamsplitter 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 ($600 \, μ$m) interferometry beam, this procedure delivers an efficiency of $99\%$ per $\hbar k$ of momentum separation. Utilizing this efficiency, we first demonstrate interferometry with up to $16\hbar k$ momentum splitting and free-fall limited interrogation times. We then realize a single-sourc…
We realize a Mach-Zehnder-type dual-atom-interferometer gyroscope with an interrogation arm of 40 cm length and the interference area up to 1.2 cm$^2$. The precise angular alignment of the large-scale separated Raman lasers is demonstrated by seeking the phase intersection of Ramsey-Bord$\acute{e}$ interferometers after the gravity effect is compensated and by decoupling the velocity dependent crosstalk phase shifts, and applied to build the Mach-Zehnder atom interferometer. Then a compact inertial rotation sensor is realized based on dual large-area Mach-Zehnder atom interferometers by precis…
We have demonstrated stabilization of a fiber-optic Mach-Zehnder interferometer, with a centimeter-scale path difference, to the transmission minimum for the carrier wave of a frequency-modulated laser beam. A time-averaged extinction of 32 dB, limited by the bandwidth of the feedback, was maintained over several hours. The interferometer was used to remove the carrier wave from a 780 nm laser beam that had been phase modulated at 2.7 GHz.
We describe a collective state atomic interferometer (COSAIN) with the signal fringe as a function of phase-difference or rotation narrowed by $\sqrt{N}$ compared to a conventional interferometer - $N$ being the number of atoms - without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of ten nonillion Hz, or a de Broglie wavelength of ten attometer, for $N=10^6$ and $v = 300 m/s$. The population of the collective state of interest is detected by a null measurement scheme, in which an event correspond…
We describe the fabrication and characterization of a new surface-electrode Paul ion trap designed for experiments in scalable quantum information processing with Ca+. A notable feature is a symmetric electrode pattern which allows rotation of the normal modes of ion motion, yielding efficient Doppler cooling with a single beam parallel to the planar surface. We propose and implement a technique for micromotion compensation in all directions using an infrared repumper laser beam directed into the trap plane. Finally, we employ an alternate repumping scheme that increases ion fluorescence and s…
In atom interferometers based on two photon transitions, the delay induced by the difference of the laser beams paths makes the interferometer sensitive to the fluctuations of the frequency of the lasers. We first study, in the general case, how the laser frequency noise affects the performance of the interferometer measurement. Our calculations are compared with the measurements performed on our cold atom gravimeter based on stimulated Raman transitions. We finally extend this study to the case of cold atom gradiometers.
A point source atom 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. Unlike a conventional light pulse atom interferometer, the PSI can produce a signal that corresponds to multi-axis rotation only, independent of acceleration. In addition, it can be used to measure acceleration along one direction, independent of rotation. Here, we describe a modified PSI that can be used to measure multi-axis rotation and multi-axis acceleration. Specifi…
In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all c…
We perform the experimental demonstration of the method proposed in [Phys. Rev. A 91, 063615 (2015)] to extract the differential phase in dual atom interferometers. From a single magneto-optical trap, we generate two atomic sources, vertically separated and free-falling synchronously, with the help of an accelerated lattice. We drive simultaneous Raman interferometers onto the two sources, and use the correlation with the vibration signal measured by a seismometer to extract the phase of each interferometer. We demonstrate an optimal sensitivity of the extracted differential phase between the …
Monitoring and stabilizing the power ratio of laser pairs is significant to high-precision atom interferometers, especially as the compact electro-optic modulated all-fiber laser system prevails. In this Letter, we demonstrate a novel method to in-situ probe the relative power of laser pairs and to stabilize the power ratio of two Raman lasers using a high-dispersion virtually imaged phased array (VIPA) etalon. Sub-microsecond resolution on probing laser power transformation during atom interferometer sequence is achieved and the power ratio of two Raman lasers (PRTR) is tightly locked with hi…
Fine-structure Raman interferometry with metastable barium for magnetically resilient inertial sensing
Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Institute of Integrated Research, Institute of Science Tokyo（东京科学大学综合研究学院）；Product Development Center, Japan Aviation Electronics Industry, Ltd.（日本航空电子工业有限公司产品开发中心）
Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the regime ( ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the Gravimetric Atom Interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step size dependent magnetic field measurement uncertainty, present vector light shift (VLS) and tensor light shift (TLS) induced magnetic field mea…
A new approach to the theory of atoms' interaction with chirped Raman pulses is developed. When the pulses have sufficiently close effective wave lengths, which are smaller than the atomic cloud size, equations for the family of the matrix elements of the atomic density matrix in the Wigner representation are derived. The solution, involving linear (in the pulse duration) phase corrections, is obtained for the rectangular pulse. The interferometric part of the atoms' excitation is calculated.
We present a compact and transportable inertial sensor for precision sensing of rotations and accelerations. The sensor consists of a dual Mach-Zehnder-type atom interferometer operated with laser-cooled $^{87}$Rb. Raman processes are employed to coherently manipulate the matter waves. We describe and characterize the experimental apparatus. A method for passing from a compact geometry to an extended interferometer with three independent atom-light interaction zones is proposed and investigated. The extended geometry will enhance the sensitivity by more than two orders of magnitude which is ne…
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 report simultaneous conjugate Ramsey-Bordé interferometers with a sample of low-mass (lithium-7) atoms at 50 times the recoil temperature. We optically pump the atoms to a magnetically insensitive state using the $2S_{1/2} - 2P_{1/2}$ line. Fast stimulated Raman beam splitters address a broad velocity class and unavoidably drive two conjugate interferometers that overlap spatially. We show that detecting the summed interference signals of both interferometers, using state labeling, allows recoil measurements and suppression of phase noise from vibrations. The use of "warm" atoms allows for …
Atom Optics for Multidimensional Raman Interferometry
A-Knows Lab, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University（清华大学精密仪器系精密测量技术与仪器全国重点实验室A-Knows实验室）；The Key Laboratory of Quantum Precision Measurement of Zhejiang Province, School of Physcis and Optical Engineering, Zhejiang University of Technology（浙江工业大学物理与光学工程学院浙江省量子精密测量重点实验室）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
We present an observation of zero to $π$ phase flips induced by Rabi oscillation in an unbalanced Ramsey atom interferometer. The phase shift and visibility are experimentally investigated by modulating either the polarization or duration of Raman lasers, and they are well explained by a theoretical model. In an atom interferometer, the $π$-phase flips are caused not only by the sign of Rabi frequency but also by the Rabi oscillation. Considering the $π$-phase flips, we propose the composite-light-pulse sequences for realizing the large-momentum-transfer beam splitter and mirror, which have th…
We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $μ$Gal ($1~μ$Gal~=~$10^{-8}$~m/s$^2$). We also show that this effect is not compensated when averaging over the two directions…
We demonstrate an atom interferometer that uses a laser-cooled continuous beam of $^{87}$Rb atoms having velocities of 10--20 m/s. With spatially separated Raman beams to coherently manipulate the atomic wave packets, Mach--Zehnder interference fringes are observed at an interference distance of 2L = 19 mm. The apparatus operates within a small enclosed area of 0.07 mm$^2$ at a bandwidth of 190 Hz with a deduced sensitivity of $7.8\times10^{-5}$ rad/s/$\sqrt{Hz}$ for rotations. Using a low-velocity continuous atomic source in an atom interferometer enables high sampling rates and bandwidths wi…
Atom interferometry relies on the separation and recombination of atom wavepackets. When the two paths overlap perfectly at the end of the interferometer, the phase is insensitive to the atomic velocity distribution. Here, we show that, when the separation and recombination is performed using a Raman transition there is a displacement of the atomic wavepacket due to a phase shift during light pulses. Because of the variation of the laser intensity seen by the atoms, there is an imperfect cancellation of these displacements. The observation of a velocity-dependent phase shift on the interferome…
We present the realization of a compact micro-wave frequency synthesizer for an atom interferometer based on stimulated Raman transitions, applied to transportable inertial sensing. Our set-up is intended to address the hyperfine transitions of Rubidium 87 atoms at 6.8 GHz. The prototype is evaluated both in the time and the frequency domain by comparison with state-of-the-art frequency references developed at LNE-SYRTE. In free-running mode, it features a residual phase noise level of -65 dBrad$^2.Hz^{-1} at 10-Hz offset frequency and a white phase noise level in the order of -120 dBrad^2.Hz^…
We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of $^{85}$Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional $π$ pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the $π$ pulse fideli…
We demonstrate a proof-of-principle of direct Earth gravity gradient measurement with an atom interferometer-based gravity gradiomter using a single proof mass of cold 87 rubidium atoms. The atomic gradiometer is implemented in the so-called double-loop configuration, hence providing a direct gravity gradient dependent phase shift insensitive do DC acceleration and constant rotation rate. The atom interferometer (AI) can be either operated as a gravimeter or a gradiomter by simply adding an extra Raman $π$-pulse. We demonstrate gravity gradient measurements first using a vibration isolation pl…
We present a compact high-resolution gravity gradiometer based on dual Rb-85 atom interferometers using stimulated Raman transitions. A baseline L=44.5 cm and an interrogation time T=130 ms are realized in a sensor head with volume of less than 100 liters. Experimental parameters are optimized to improve the short-term sensitivity while a rejection algorithm relying on inversion of the Raman wave vector is implemented to improve the long-term stability. After an averaging time of 17000 s, a phase resolution of 104 μrad is achieved, which corresponds to a gravity gradient resolution of 0.86 E. …
We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift where the leading coefficient in the phase terms up to T^k dependences (k >= 0) in…
We present an elegant application of matterwave interferometry to the velocimetry of cold atoms whereby, in analogy to Fourier transform spectroscopy, the 1-D velocity distribution is manifest in the frequency domain of the interferometer output. By using stimulated Raman transitions between hyperfine ground states to perform a three-pulse interferometer sequence, we have measured the velocity distributions of clouds of freely-expanding $^{85}$Rb atoms with temperatures of 33 $μ$K and 17 $μ$K. Quadrature measurement of the interferometer output as a function of the temporal asymmetry yields ve…
We provide a comprehensive study of ultra-cold atom diffraction by an optical lattice. We focus on an intermediate regime between the Raman-Nath and the Bragg regimes, the so-called quasi-Bragg regime. The experimental results are in a good agreement with a full numerical integration of the Schrödinger equation. We investigate the long pulse regime limited by a strong velocity selection and the short pulse regime limited by non-adiabatic losses. For each of these regimes, we estimate the multi-port features of the Bragg interferometers. Finally, we discuss the best compromise between these two…
We demonstrate a dual-axis accelerometer and gyroscope atom interferometer, which forms the building blocks of a six-axis inertial measurement unit. By recapturing the atoms after the interferometer sequence, we maintain a large atom number at high data-rates of 50 to 100 measurements per second. Two cold ensembles are formed in trap zones located a few centimeters apart, and are launched toward one-another. During their ballistic trajectory, they are interrogated with a stimulated Raman sequence, detected, and recaptured in the opposing trap zone. We achieve sensitivities at $\mathrm{μ\mathit…
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…
