Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter

Laser frequency stabilization by modulation transfer spectroscopy and balanced detection of molecular iodine for laser cooling of 174Yb

We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (127I2), which is used as a new frequency reference for laser trapping and cooling of 174Yb on the 1S0 - 3P1 transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 ×10-13 at 0.17 s of averaging time.

Nonlinear Landau-Zener-Stückelberg-Majorana tunneling and interferometry of extended Bose-Hubbard flux ladders

The nonlinear Landau-Zener-Stückelberg-Majorana (LZSM) tunneling dynamics and interferometry of an extended Bose-Hubbard flux ladder are studied. Based on the mean-field theory, the dispersion relation of the system is given, and it is found that loop structures periodically appear in the band structure and the nonlinear LZSM interference occurs naturally without Floquet engineering, which can be effectively modulated by atomic interactions. The nonlinear energy bands and the unique chirality feature of the flux ladder system can be identified through the dynamics of nonlinear Landau-Zener tunneling. Remarkably, the critical position of the noise in the interference pattern can be employed to identify the loop structure in the energy band, establishing an effective link between the nonlinear loop structure and LZSM interferometry. The position, intensity, symmetry, and width of interference patterns strongly depend on the magnetic field, atomic interactions, rung-to-leg coupling ratio, and energy bias, which provides an effective way to measure these parameters using the nonlinear LZSM interferometry. This paper further expands the dynamics of flux ladder systems to complex interaction regions and has potential applications in the precise measurement of related nonlinear systems.

Micro-fabricated components for cold atom sensors

Laser cooled atoms have proven transformative for precision metrology, playing a pivotal role in state-of-the-art clocks and interferometers and having the potential to provide a step-change in our modern technological capabilities. To successfully explore their full potential, laser cooling platforms must be translated from the laboratory environment and into portable, compact quantum sensors for deployment in practical applications. This transition requires the amalgamation of a wide range of components and expertise if an unambiguously chip-scale cold atom sensor is to be realized. We present recent developments in cold-atom sensor miniaturization, focusing on key components that enable laser cooling on the chip-scale. The design, fabrication, and impact of the components on sensor scalability and performance will be discussed with an outlook to the next generation of chip-scale cold atom devices.

Influence of magnetic field on the seismometer in vibration correction for atom gravimeters

Vibration correction provides a simple and flexible method of suppressing ambient vibration noise in transportable atom gravimeters. However, in the seismometers used for vibration correction, a spurious output may be induced by the magnetic field of the magnetic-optical trap, introducing errors to the gravity measurements. This paper evaluates the influence of the magnetic field on the seismometer and the corresponding errors in the gravity measurements. It is found that an error level of order 10 μGal may be present if the seismometer is not configured carefully. The dependence of the influence on the orientation of the seismometer and the lasting time of the magnetic field are investigated. The effective suppression of the influence by shielding the seismometer is also demonstrated. Our results focus attention on the possible errors related to seismometers in high-precision gravity measurements by using atom gravimeters.

Planar diffractive grating for magneto-optical trap application: fabrication and testing

The design, fabrication, and demonstration of a planar two-dimensional-crossed reflective diffractive grating are proposed to construct a novel optical configuration, to the best of our knowledge, potentially applied for atom cooling and trapping in a magneto-optical trap. Based on the proposed single-beam single-exposure scheme by means of an orthogonal two-axis Lloyd's mirrors interferometer, we rapidly patterned a ∼1µm period grating capable of providing a uniform intensity of the diffracted beams. The key structural parameters of the grating including the array square hole's width and depth were determined, aiming at providing a high energy of the diffracted beams to perform the atom cooling and trapping. To guarantee the diffracted beams to be overlapped possibly, we adopted a polarized beam splitter to guide the optical path of the incident and zero-order diffracted beams. Therefore, one zero-order diffracted beam with a retroreflected mode and four first-order diffracted beams with appropriate optical path constructed a three-dimensional optical configuration of three orthogonal pairs of counterpropagating beams. Finally, three pairs of the counterpropagating cooling laser beams with 9 mm diameter and >10% diffraction efficiencies were achieved, and the circular polarization chirality, purity, and compensation of the desired diffracted beams are further evaluated, which preliminarily validated a high applicability for the magneto-optical trap system.

Gravitational Decoherence and the Possibility of Its Interferometric Detection

We present a general master equation describing the quantum dynamics of a scalar bosonic field interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence both in position and in energy momentum. We show how the master equation reproduces, thus generalizing, the previous results in the literature by taking appropriate limits. We estimate the effect of gravitational decoherence in atom interferometers, providing also a straightforward way to assess the magnitude of the effect.

Noise-suppressing and lock-free optical interferometer for cold atom experiments

A novel noise-suppressing and lock-free interferometer is proposed and experimentally demonstrated in the study of the quantum non-destructive (QND) interaction of cold atoms. A QND measurement based on far-off resonant dispersive probing is usually carried out by a Mach-Zehnder type interferometer. It is an experimental challenge in its own right to reduce the classical noise, such as acoustic noise, phase noise and amplitude noise of lasers, and to lock the interferometer at the white-light position that corresponds to a nearly zero path-length difference. Here, we report an interferometer with an inserted acousto-optic modulator (AOM). It is noise immune and lock-free in principle. The experiments show that the new interferometer is able to measure cold atoms for more than 30 minutes and reduce the phase noise by about 30 dB.

Effect of an echo sequence to a trapped single-atom interferometer with photon momentum kicks

We investigate a single-atom interferometer (SAI) in an optical dipole trap (ODT) with photon momentum kicks. An echo sequence is used for the SAI. We find experimentally that interference visibilities of a counter-propagating Raman type SAI decay much faster than the co-propagating case. To understand the underlying mechanism, a wave-packet propagating simulation is developed for the ODT-guided SAI. We show that in state dependent dipole potentials, the coupling between external dynamics and internal states makes the atom evolve in different paths during the interfering process. The acquired momentum from counter-propagating Raman pulses forces the external motional wave packets of two paths be completely separated and the interferometer visibility decays quickly compared to that of the co-propagating Raman pulses process. Meanwhile, the echo interference visibility experiences revival or instantaneous collapse which depends on the π pulse adding time at approximate integer multiples or half integer multiples of the trap period.

Many-Body Quantum Dynamics of Initially Trapped Systems due to a Stark Potential: Thermalization versus Bloch Oscillations

We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both many-body-localized and thermalizing systems. We consider both fermions (t-V model) and bosons (Bose-Hubbard model). For the zero and infinite interaction limits, both systems are integrable: we provide analytic solutions in terms of the moments of the initial cloud shape and clarify how the recurrent dynamics (many-body Bloch oscillations) depends on the initial state. Away from the integrable points, we identify and explain the timescale at which Bloch oscillations decohere.

Low noise measurement method based on differential optical interferometer for cold atom experiments

We proposed and realized a low noise measurement method based on differential optical interferometer to measure trapped cold atoms in a magneto-optical trap (MOT). The configuration is based on a Mach-Zehnder type interferometer, which is composed of two beams of different frequencies. A long-term stability in phase monitor has been obtained by use of the vibration immune mechanism through subtraction of the interferograms imaged on the two photodetectors. With this new configuration, the noise caused by environmental perturbation is greatly reduced at low frequency while the signal of phase shift keeps a good long-term stability.

Probing gravity by holding atoms for 20 seconds

Atom interferometers are powerful tools for both measurements in fundamental physics and inertial sensing applications. Their performance, however, has been limited by the available interrogation time of freely falling atoms in a gravitational field. By suspending the spatially separated atomic wave packets in a lattice formed by the mode of an optical cavity, we realize an interrogation time of 20 seconds. Our approach allows gravitational potentials to be measured by holding, rather than dropping, atoms. After seconds of hold time, gravitational potential energy differences from as little as micrometers of vertical separation generate megaradians of interferometer phase. This trapped geometry suppresses the phase variance due to vibrations by three to four orders of magnitude, overcoming the dominant noise source in atom-interferometric gravimeters.

Extraction and identification of noise patterns for ultracold atoms in an optical lattice

To extract useful information about quantum effects in cold atom experiments, one central task is to identify the intrinsic fluctuations from extrinsic system noises of various kinds. As a data processing method, principal component analysis can decompose fluctuations in experimental data into eigenmodes, and give a chance to separate noises originated from different physical sources. In this paper, we demonstrate for Bose-Einstein condensates in one-dimensional optical lattices that the principal component analysis can be applied to time-of-flight images to successfully separate and identify noises from different origins of leading contribution, and can help to reduce or even eliminate noises via corresponding data processing procedures. The attribution of noise modes to their physical origins is also confirmed by numerical analysis within a mean-field theory. As the method does not rely on any a priori knowledge of the system properties, it is potentially applicable to the study of other quantum states and quantum critical regions.

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.

Experimental Demonstration of Shaken-Lattice Interferometry

We experimentally demonstrate a shaken-lattice interferometer. Atoms are trapped in the ground Bloch state of a red-detuned optical lattice. Using a closed-loop optimization protocol based on the dcrab algorithm, we phase-modulate (shake) the lattice to transform the atom momentum state. In this way, we implement an atom beam splitter and build five interferometers of varying interrogation times T_{I}. The sensitivity of shaken-lattice interferometry is shown to scale as T_{I}^{2}, consistent with simulation (2C. A. Weidner, H. Yu, R. Kosloff, and D. Z. Anderson, Phys. Rev. A 95, 043624 (2017).PLRAAN2469-992610.1103/PhysRevA.95.043624). Finally, we show that we can measure the sign of an applied signal and optimize the interferometer in the presence of a bias signal.

Note: Effect of the parasitic forced vibration in an atom gravimeter

The vibration isolator usually plays an important role in atom interferometry gravimeters to improve their sensitivity. We show that the parasitic forced vibration of the Raman mirror, which is induced by external forces acting on the vibration isolator, can cause a bias in atom gravimeters. The mechanism of how this effect induces an additional phase shift in our interferometer is analyzed. Moreover, modulation experiments are performed to measure the dominant part of this effect, which is caused by the magnetic force between the passive vibration isolator and the coil of the magneto-optic trap. In our current apparatus, this forced vibration contributes a systematic error of -2.3(2) × 10^-7 m/s² when the vibration isolator works in the passive isolation mode. Even suppressed with an active vibration isolator, this effect can still contribute -6(1) × 10^-8 m/s²; thus, it should be carefully considered in precision atom gravimeters.

Squeezing on Momentum States for Atom Interferometry

We propose and analyze a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based strontium atom interferometer with large diffraction orders. This technique can be extended also to small diffraction orders and large atom numbers N by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling Δϕ∼N^{-3/4}. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the standard quantum limit. Our method is applicable to other atomic species where a narrow transition is available or can be synthesized.

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.

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.

Optimal control of complex atomic quantum systems

Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.

Fifteen years of cold matter on the atom chip: promise, realizations, and prospects

Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.

Test of the Universality of Free Fall with Atoms in Different Spin Orientations

We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6}  m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.

High-Resolution Atom Interferometers with Suppressed Diffraction Phases

We experimentally and theoretically study the diffraction phase of large-momentum transfer beam splitters in atom interferometers based on Bragg diffraction. We null the diffraction phase and increase the sensitivity of the interferometer by combining Bragg diffraction with Bloch oscillations. We demonstrate agreement between experiment and theory, and a 1500-fold reduction of the diffraction phase, limited by measurement noise. In addition to reduced systematic effects, our interferometer has high contrast with up to 4.4×10(6) radians of phase difference, and a resolution in the fine structure constant of δα/α=0.25  ppb in 25 h of integration time.

Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation

We investigate the mutiphoton process between different Bloch states in an amplitude modulated optical lattice. In the experiment, we perform the modulation with more than one frequency components, which includes a high degree of freedom and provides a flexible way to coherently control quantum states. Based on the study of single frequency modulation, we investigate the collaborative effect of different frequency components in two aspects. Through double frequency modulations, the spectrums of excitation rates for different lattice depths are measured. Moreover, interference between two separated excitation paths is shown, emphasizing the influence of modulation phases when two modulation frequencies are commensurate. Finally, we demonstrate the application of the double frequency modulation to design a large-momentum-transfer beam splitter. The beam splitter is easy in practice and would not introduce phase shift between two arms.

Measurement of the gravity-field curvature by atom interferometry

We present the first direct measurement of the gravity-field curvature based on three conjugated atom interferometers. Three atomic clouds launched in the vertical direction are simultaneously interrogated by the same atom interferometry sequence and used to probe the gravity field at three equally spaced positions. The vertical component of the gravity-field curvature generated by nearby source masses is measured from the difference between adjacent gravity gradient values. Curvature measurements are of interest in geodesy studies and for the validation of gravitational models of the surrounding environment. The possibility of using such a scheme for a new determination of the Newtonian constant of gravity is also discussed.

Test of Einstein equivalence principle for 0-spin and half-integer-spin atoms: search for spin-gravity coupling effects

We report on a conceptually new test of the equivalence principle performed by measuring the acceleration in Earth's gravity field of two isotopes of strontium atoms, namely, the bosonic (88)Sr isotope which has no spin versus the fermionic (87)Sr isotope which has a half-integer spin. The effect of gravity on the two atomic species has been probed by means of a precision differential measurement of the Bloch frequency for the two atomic matter waves in a vertical optical lattice. We obtain the values η=(0.2±1.6)×10(-7) for the Eötvös parameter and k=(0.5±1.1)×10(-7) for the coupling between nuclear spin and gravity. This is the first reported experimental test of the equivalence principle for bosonic and fermionic particles and opens a new way to the search for the predicted spin-gravity coupling effects.

Equivalence principle and bound kinetic energy

We consider the role of the internal kinetic energy of bound systems of matter in tests of the Einstein equivalence principle. Using the gravitational sector of the standard model extension, we show that stringent limits on equivalence principle violations in antimatter can be indirectly obtained from tests using bound systems of normal matter. We estimate the bound kinetic energy of nucleons in a range of light atomic species using Green's function Monte Carlo calculations, and for heavier species using a Woods-Saxon model. We survey the sensitivities of existing and planned experimental tests of the equivalence principle, and report new constraints at the level of between a few parts in 10(6) and parts in 10(8) on violations of the equivalence principle for matter and antimatter.

A surface-patterned chip as a strong source of ultracold atoms for quantum technologies

Laser-cooled atoms are central to modern precision measurements. They are also increasingly important as an enabling technology for experimental cavity quantum electrodynamics, quantum information processing and matter-wave interferometry. Although significant progress has been made in miniaturizing atomic metrological devices, these are limited in accuracy by their use of hot atomic ensembles and buffer gases. Advances have also been made in producing portable apparatus that benefits from the advantages of atoms in the microkelvin regime. However, simplifying atomic cooling and loading using microfabrication technology has proved difficult. In this Letter we address this problem, realizing an atom chip that enables the integration of laser cooling and trapping into a compact apparatus. Our source delivers ten thousand times more atoms than previous magneto-optical traps with microfabricated optics and, for the first time, can reach sub-Doppler temperatures. Moreover, the same chip design offers a simple way to form stable optical lattices. These features, combined with simplicity of fabrication and ease of operation, make these new traps a key advance in the development of cold-atom technology for high-accuracy, portable measurement devices.

Observation of free-space single-atom matter wave interference

We observe matter wave interference of a single cesium atom in free fall. The interferometer is an absolute sensor of acceleration and we show that this technique is sensitive to forces at the level of 3.2×10(-27) N with a spatial resolution at the micron scale. We observe the build up of the interference pattern one atom at a time in a free-space interferometer where the mean path separation extends far beyond the coherence length of the atom. Using the coherence length of the atom wave packet as a metric, we directly probe the velocity distribution and measure the temperature of a single atom in free fall.

Photon-assisted tunneling in a biased strongly correlated Bose gas

We study the impact of coherently generated lattice photons on an atomic Mott insulator subjected to a uniform force. Analogous to an array of tunnel-coupled and biased quantum dots, we observe sharp, interaction-shifted photon-assisted tunneling resonances corresponding to tunneling one and two lattice sites either with or against the force and resolve multiorbital shifts of these resonances. By driving a Landau-Zener sweep across such a resonance, we realize a quantum phase transition between a paramagnet and an antiferromagnet and observe quench dynamics when the system is tuned to the critical point. Direct extensions will produce gauge fields and site-resolved spin flips, for topological physics and quantum computing.

Measurement of optical Feshbach resonances in an ideal gas

Using a narrow intercombination line in alkaline earth atoms to mitigate large inelastic losses, we explore the optical Feshbach resonance effect in an ultracold gas of bosonic (88)Sr. A systematic measurement of three resonances allows precise determinations of the optical Feshbach resonance strength and scaling law, in agreement with coupled-channel theory. Resonant enhancement of the complex scattering length leads to thermalization mediated by elastic and inelastic collisions in an otherwise ideal gas. Optical Feshbach resonance could be used to control atomic interactions with high spatial and temporal resolution.

Laser controlled tunneling in a vertical optical lattice

Raman laser pulses are used to induce coherent tunneling between neighboring sites of a vertical 1D optical lattice. Such tunneling occurs when the detuning of a probe laser from the atomic transition frequency matches multiples of the Bloch frequency, allowing for a spectroscopic control of the coupling between Wannier-Stark (WS) states. In particular, we prepare coherent superpositions of WS states of adjacent sites, and investigate the coherence time of these superpositions by realizing a spatial interferometer. This scheme provides a powerful tool for coherent manipulation of external degrees of freedom of cold atoms, which is a key issue for quantum information processing.

Equivalence principle and gravitational redshift

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter-wave, microwave, optical, and Mössbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the 10(-6) level.