Comparison of the sensitivities for atom interferometers in two different operation methods

We investigated the sensitivities of atom interferometers in the usual fringe-scanning method （FSM） versus the fringe- locking method （FLM）. The theoretical analysis shows that for typical noises in atom interferometers, the FSM will degrade the sensitivity while the FLM does not. The sensitivity-improvement factor of the FLM over the FSM depends on the type of noises, which is validated by numerical simulations. The detailed quantitative analysis on this fundamental issue is presented, and our analysis is readily extendable to other kinds of noises as well as other fringe shapes in addition to a cosine one.

Wave–particle duality in a Raman atom interferometer

We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ- π- π /2 type of atom interferometer, we find that the visibility(V) and predictability(P) still satisfy the duality relation, P2+ V2≤ 1.

Systematic error suppression scheme of the weak equivalence principle test by dual atom interferometers in space based on spectral correlation

Systematic error suppression and test data processing are very important in improving the accuracy and sensitivity of the atom interferometer(AI)-based weak-equivalence-principle(WEP) test in space. Here we present a spectrum correlation method to investigate the test data of the AI-based WEP test in space by analyzing the characteristics of systematic errors and noises. The power spectrum of the Eotvos coefficient η, systematic errors, and noises in AI-based WEP test in space are analyzed and calculated in detail. By using the method, the WEP violation signal is modulated from direct current(DC) frequency band to alternating current(AC) frequency band. We find that the signal can be effectively extracted and the influence of systematic errors can be greatly suppressed by analyzing the power spectrum of the test data when the spacecraft is in an inertial pointing mode. Furthermore, the relation between the Eotvos coefficient η and the number of measurements is obtained under certain simulated parameters. This method will be useful for both isotopic and nonisotopic AI-based WEP tests in space.

Common-mode noise rejection using fringe-locking method in WEP test by simultaneous dual-species atom interferometers

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 the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.

Interference properties of a trapped atom interferometer in two asymmetric optical dipole traps

We investigate interference properties of a trapped atom interferometer where two symmetric optical dipole traps(ODTs)act as the atomic wave-packets splitter and combiner with internal state labelling.After the preparation of initial superposition states,the atomic wave-packet is adiabatically split and moves into two spatially separate asymmetric ODTs.The atomic wave-packets in two ODTs are then adiabatically recombined after a duration of free evolving in traps,completing the interference cycle of this atom interferometer.We show that the interferogram exhibits a series of periodic revivals in interference visibility.Furthermore,the revival period decreases as the asymmetry of two dipole potentials increases.By introducing an echo sequence to the interferometer,we show that while the echo effect is not influenced by the asymmetry of the two ODTs,the onset of periodic revivals changes by the echo sequence.Our study provides an effective method to cancel or compensate the phase shift caused by position and time correlated force.

Rapid extraction of the phase shift of the cold-atom interferometer via phase demodulation

Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.

Suppression of Coriolis error in weak equivalence principle test using ^85Rb-^87Rb dual-species atom interferometer

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,the Coriolis effect is analyzed by establishing an error model.The measurement errors of Eotvos coefficient(η)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 calculated.In experimental investigation,the position difference between^85Rb and^87Rb atomic clouds is reduced to 0.1 mm by optimizing the experimental parameters,an alternating detection method is used to suppress the error caused by detection position difference,thus the Coriolis error related to the atomic clouds and detectors is reduced to 1.1 × 10^-9.This Coriolis error is further corrected by com pensating the rotation of Raman laser's mirror,and the total uncertainty o f rj measurement related to the Coriolis effect is reduced as δη=4.4 × 10^-11.

Improve the performance of interferometer with ultra-cold atoms

Ultra-cold atoms provide ideal platforms for interferometry.The macroscopic matter-wave property of ultra-cold atoms leads to large coherent length and long coherent time,which enable high accuracy and sensitivity to measurement.Here,we review our efforts to improve the performance of the interferometer.We demonstrate a shortcut method for manipulating ultra-cold atoms in an optical lattice.Compared with traditional ones,this shortcut method can reduce the manipulation time by up to three orders of magnitude.We construct a matter-wave Ramsey interferometer for trapped motional quantum states and significantly increase its coherence time by one order of magnitude with an echo technique based on this method.Efforts have also been made to enhance the resolution by multimode scheme.Application of a noise-resilient multi-component interferometer shows that increasing the number of paths could sharpen the peaks in the time-domain interference fringes,which leads to a resolution nearly twice compared with that of a conventional double-path two-mode interferometer.With the shortcut method mentioned above,improvement of the momentum resolution could also be fulfilled,which leads to atomic momentum patterns less than 0.6hkL. To identify and remove systematic noises,we introduce the methods based on the principal component analysis (PCA) that reduce the noise in detection close to the 1/√2 of the photon-shot noise and separate and identify or even eliminate noises.Furthermore,we give a proposal to measure precisely the local gravity acceleration within a few centimeters based on our study of ultracold atoms in precision measurements.

Micro-Gal level gravity measurements with cold atom interferometry

Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolution and accuracy for gravity measurements. This kind of quantum sensor has excited world-wide interest for both practical applications and fundamental research.

Elementary analysis of interferometers for wave particle duality test and the prospect of going beyond the complementarity principle

A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young＇s two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern （wave nature） and the which-way information （particle nature） of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.

Movable precision gravimeters based on cold atom interferometry

High precision atom interferometers have shown attractive prospects in laboratory for testing fundamental physics and inertial sensing.Efforts on applying this innovative technology to field applications are also being made intensively.As the manipulation of cold atoms and related matching technologies mature,inertial sensors based on atom interferometry can be adapted to various indoor or mobile platforms.A series of experiments have been conducted and high performance has been achieved.In this paper,we will introduce the principles,the key technologies,and the applications of atom interferometers,and mainly review the recent progress of movable atom gravimeters.

Measuring gravitational effect of superintense laser by spin-squeezed Bose-Einstein condensates interferometer

We consider an extremely intense laser,enclosed by an atom interferometer.The gravitational potential generated from the high-intensity laser is solved from the Einstein field equation under the Newtonian limit.We compute the strength of the gravitational force and study the feasibility of measuring the force by the atom interferometer.The intense laser field from the laser pulse can induce a phase change in the interferometer with Bose-Einstein condensates.We push up the sensitivity limit of the interferometer with Bose-Einstein condensates by spin-squeezing effect and determine the sensitivity gap for measuring the gravitational effect from intense laser by atom interferometer.

Dynamic splitting and merging of an atom cloud on an atom chip

Chip-based atom interferometers bring together the advantages of atom chips and Bose-Einstein condensates. Their central prerequisite is that a condensate can be coherently split into two halves with a determined relative phase. This paper demonstrates the dynamical splitting and merging of an atom cloud with two U-wires on an atom chip. Symmetrical and asymmetrical splittings are realized by applying a bias field with different directions and magnitudes. The trajectories of the splitting are consistent with theoretical calculations. The atom chip is a good candidate for constructing an atom interferometer.

Precision measurements with cold atoms and trapped ions

Recent progresses on quantum control of cold atoms and trapped ions in both the scientific and technological aspects greatly advance the applications in precision measurement. Thanks to the exceptional controllability and versatility of these massive quantum systems, unprecedented sensitivity has been achieved in clocks, magnetometers, and interferometers based on cold atoms and ions. Besides, these systems also feature many characteristics that can be employed to facilitate the applications in different scenarios. In this review, we briefly introduce the principles of optical clocks, cold atom magnetometers, and atom interferometers used for precision measurement of time, magnetic field, and inertial forces. The main content is then devoted to summarize some recent experimental and theoretical progresses in these three applications, with special attention being paid to the new designs and possibilities towards better performance. The purpose of this review is by no means to give a complete overview of all important works in this fast developing field, but to draw a rough sketch about the frontiers and show the fascinating future lying ahead.

Determining the tilt of the Raman laser beam using an optical method for atom gravimeters

The tilt of a Raman laser beam is a major systematic error in precision gravity measurement using atom interferometry.The conventional approach to evaluating this tilt error involves modulating the direction of the Raman laser beam and conducting time-consuming gravity measurements to identify the error minimum.In this work,we demonstrate a method to expediently determine the tilt of the Raman laser beam by transforming the tilt angle measurement into characterization of parallelism,which integrates the optical method of aligning the laser direction,commonly used in freely falling corner-cube gravimeters,into an atom gravimeter.A position-sensing detector(PSD)is utilized to quantitatively characterize the parallelism between the test beam and the reference beam,thus measuring the tilt precisely and rapidly.After carefully positioning the PSD and calibrating the relationship between the distance measured by the PSD and the tilt angle measured by the tiltmeter,we achieved a statistical uncertainty of less than 30μrad in the tilt measurement.Furthermore,we compared the results obtained through this optical method with those from the conventional tilt modulation method for gravity measurement.The comparison validates that our optical method can achieve tilt determination with an accuracy level of better than 200μrad,corresponding to a systematic error of 20μGal in g measurement.This work has practical implications for real-world applications of atom gravimeters.

Cavity-enhanced metrology in an atomic spin-1 Bose−Einstein condensate

Atom interferometer has been proven to be a powerful tool for precision metrology. Here we propose a cavity-aided nonlinear atom interferometer, based on the quasi-periodic spin mixing dynamics of an atomic spin-1 Bose−Einstein condensate trapped in an optical cavity. We unravel that the phase sensitivity can be greatly enhanced with the cavity-mediated nonlinear interaction. The influence of encoding phase, splitting time and recombining time on phase sensitivity are carefully studied. In addition, we demonstrate a dynamical phase transition in the system. Around the criticality, a small cavity light field variation can arouse a strong response of the atomic condensate, which can serve as a new resource for enhanced sensing. This work provides a robust protocol for cavity-enhanced metrology.

Atomic Interferometric Gravitational-Wave Space Observatory(AIGSO)

We propose a space-borne gravitational-wave detection scheme,called atom interferometric gravitationalwave space observatory(AIGSO).It is motivated by the progress in the atomic matter-wave interferometry,which solely utilizes the standing light waves to split,deflect and recombine the atomic beam.Our scheme consists of three drag-free satellites orbiting the Earth.The phase shift of AIGSO is dominated by the Sagnac effect of gravitational-waves,which is proportional to the area enclosed by the a√tom interferometer,the frequency and amplitude of gravitational-waves.The scheme has a strain sensitivity<10^(-20)/Hz^(1/2)in the 100 mHz–10 Hz frequency range,which fills in the detection gap between space-based and ground-based laser interferometric detectors.Thus,our proposed AIGSO can be a good complementary detection scheme to the space-borne laser interferometric schemes,such as LISA.Considering the current status of relevant technology readiness,we expect our AIGSO to be a promising candidate for the future space-based gravitational-wave detection plan.

Magnetic-field-sensitive multi-wave interference

We report an experimental study of magnetic-field-sensitive multi-wave interference,realized in a three-wave RF-atom system.In the F=1 hyperfine level of the ^(87)Rb 5^(2)S_(1/2) ground state,Ramsey fringes were observed via the spin-selective Raman detection.A decrease in the fringe contrast was observed with increasing free evolution time.The maximum evolution time for observable fringe contrasts was investigated at different atom temperatures,under free-falling and trapped conditions.As the main interest of the Ramsey method,the improvement in magnetic field resolution is observed with an increase of evolution time T up to 3 ms and with the measurement resolution reaching 0.85 nT.This study paves the way for precision magnetic field measurements based on cold atoms.