A precision measurement of the gravitational redshift by the interference of matter waves

Single-Photon Interference over 8.4 km Urban Atmosphere: Toward Testing Quantum Effects in Curved Spacetime with Photons

The emergence of quantum mechanics and general relativity has transformed our understanding of the natural world significantly. However, integrating these two theories presents immense challenges, and their interplay remains untested. Recent theoretical studies suggest that the single-photon interference covering huge space can effectively probe the interface between quantum mechanics and general relativity. We developed an alternative design using unbalanced Michelson interferometers to address this and validated its feasibility over an 8.4 km free-space channel. Using a high-brightness single-photon source based on quantum dots, we demonstrated single-photon interference along this long-distance baseline. We achieved a phase measurement precision of 16.2 mrad, which satisfied the measurement requirements for a gravitational redshift at the geosynchronous orbit by 5 times the standard deviation. Our results confirm the feasibility of the single-photon version of the Colella-Overhauser-Werner experiment for testing the quantum effects in curved spacetime.

Quantum reference frames for an indefinite metric

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition. Comparison with other models shows that semi-classical gravity and gravitational collapse models do not obey the covariance of dynamical laws under quantum coordinate transformations.

Highly sensitive gyroscope based on a levitated nanodiamond

A gyroscope is one of the core components of an inertial navigation system. Both the high sensitivity and miniaturization are important for the applications of the gyroscope. We consider a nitrogen-vacancy (NV) center in a nanodiamond, which is levitated either by an optical tweezer or an ion trap. Based on the Sagnac effect, we propose a scheme to measure the angular velocity with ultra-high sensitivity through the matter-wave interferometry of the nanodiamond. Both the decay of the motion of the center of mass of the nanodiamond and the dephasing of the NV centers are included when we estimate the sensitivity of the proposed gyroscope. We also calculate the visibility of the Ramsey fringes, which can be used for estimating the limitation of gyroscope sensitivity. It is found that the sensitivity ∼6.86×10^-7 r a d/s/H z can be achieved in an ion trap. As the working area of the gyroscope is extremely small (∼0.01~μm²), it could be made on-chip in the future.

All acousto-optic modulator laser system for a 12 m fountain-type dual-species atom interferometer

We design and implement a laser system for ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometers based on acousto-optic frequency shift and tapered amplifier laser technologies. We use eight-pass acousto-optic modulators to generate repumping lasers for ⁸⁵Rb and ⁸⁷Rb atoms. The maximum frequency shift of the laser is 2.8 GHz, and the diffraction efficiency is higher than 20%. We use high-frequency acousto-optic modulators to generate the Raman lasers. This laser system uses only two seed lasers to provide the various frequencies required by ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometers, which greatly improves laser usage. The laser system is applied in the equivalence principle test experiment using an ⁸⁵Rb and ⁸⁷Rb dual-species atom interferometer. The signal of atoms launched to 12 meters is successfully observed, and the resolution of gravity differential measurement is improved from 8×10^-9 g to 1×10^-10g.

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.

Laboratory Courses on Laser Spectroscopy and Atom Trapping

We present an overview of experiments covered in two semester-length laboratory courses dedicated to laser spectroscopy and atom trapping. These courses constitute a powerful approach for teaching experimental physics in a manner that is both contemporary and capable of providing the background and skills relevant to a variety of research laboratories. The courses are designed to be accessible for all undergraduate streams in physics and applied physics as well as incoming graduate students. In the introductory course, students carry out several experiments in atomic and laser physics. In a follow up course, students trap atoms in a magneto-optical trap and carry out preliminary investigations of the properties of laser cooled atoms based on the expertise acquired in the first course. We discuss details of experiments, impact, possible course formats, budgetary requirements, and challenges related to long-term maintenance.

A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits

Modern navigation systems integrate the global positioning system (GPS) with an inertial navigation system (INS), which complement each other for correct attitude and velocity determination. The core of the INS integrates accelerometers and gyroscopes used to measure forces and angular rate in the vehicular inertial reference frame. With the help of gyroscopes and by integrating the acceleration to compute velocity and distance, precision and compact accelerometers with sufficient accuracy can provide small-error location determination. Solid-state implementations, through coherent readout, can provide a platform for high performance acceleration detection. In contrast to prior accelerometers using piezoelectric or capacitive readout techniques, optical readout provides narrow-linewidth high-sensitivity laser detection along with low-noise resonant optomechanical transduction near the thermodynamical limits. Here an optomechanical inertial sensor with an 8.2 μg Hz-1/2 velocity random walk (VRW) at an acquisition rate of 100 Hz and 50.9 μg bias instability is demonstrated, suitable for applications, such as, inertial navigation, inclination sensing, platform stabilization, and/or wearable device motion detection. Driven into optomechanical sustained-oscillation, the slot photonic crystal cavity provides radio-frequency readout of the optically-driven transduction with an enhanced 625 μg Hz-1 sensitivity. Measuring the optomechanically-stiffened oscillation shift, instead of the optical transmission shift, provides a 220× VRW enhancement over pre-oscillation mode detection.

Spatial adiabatic passage of massive quantum particles in an optical Lieb lattice

Quantum interference lies at the heart of quantum mechanics. By utilizing destructive interference, it is possible to transfer a physical object between two states without populating an intermediate state which is necessary to connect the initial and final states. A famous application is a technique of stimulated Raman adiabatic passage, where atomic internal states can be transfered with high efficiency regardless of lossy intermediate states. One interesting situation is a case where the initial and final states are spatially well separated. Quantum mechanics allows a particle to move without practical possibility of being found at the intermediate area. Here we demonstrate this spatial adiabatic passage with ultracold atoms in an optical lattice. Key to this is the existence of dark eigenstates forming a flat energy band, with effective transfer between two sublattices being observed. This work sheds light on a study of coherent control of trapped cold atoms.

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.

Interference of clocks: A quantum twin paradox

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.

Many-Body Entanglement in Short-Range Interacting Fermi Gases for Metrology

We explore many-body entanglement in spinful Fermi gases with short-range interactions, for metrology purposes. We characterize the emerging quantum phases via density-matrix renormalization group simulations and quantify their entanglement content for metrological usability via quantum Fisher information (QFI). Our study establishes a method, promoting QFI to be an order parameter. Short-range interactions reveal to build up metrologically promising entanglement in the XY-ferromagnetic and cluster ordering, the cluster physics being unexplored so far.

Compact and robust diode laser system technology for dual-species ultracold atom experiments with rubidium and potassium in microgravity

We present a compact and robust distributed-feedback diode laser system architecture for ultracold atom experiments with K41 and Rb87 in a mobile setup operating at the ZARM drop tower in Bremen. Our system withstands DC accelerations of up to 43 g in operation with only minor adjustments over several drop campaigns. Micro-integrated master-oscillator-power-amplifier modules in conjunction with miniaturized, free-space opto-mechanics are integrated on a platform with a volume of 43 L. With compact control and driver electronics, this laser system features output power and spectral characteristics suitable for 2D⁺ and 3D magneto-optical trapping operation, atomic state preparation, Bragg-diffraction-based atom interferometry, and detection.

A Novel Monitoring Navigation Method for Cold Atom Interference Gyroscope

The implementation principle of a typical three-pulse cold atom interference gyroscope is introduced in this paper. Based on its configuration and current research status, the problems of cold atom interference gyro are pointed out. The data-rate is insufficient, and it is difficult to achieve high dynamic measurement. Then, based on these two limitations, a novel design of the monitoring navigation system of the cold atom interference gyroscope (CAIG) and an intermediate-grade inertial measurement unit (IMU) was proposed to obtain the long-term position result without GPS signals, such as the Inertial Navigation System (INS) in underwater vehicles. While the CAIG was used as the external gyro, the bias of IMU and the misalignment angle between the CAIG-frame and the IMU-frame are obtained through filtering technique. The simulation test and field test demonstrated the improvements of the long-term positioning accuracy of the INS.

High-precision gravimeter based on a nano-mechanical resonator hybrid with an electron spin

We show that the gravitational acceleration can be measured with the matter-wave Ramsey interferometry, by using a nitrogen-vacancy center coupled to a nano-mechanical resonator. We propose two experimental methods to realize the similar Hamiltonian, by using either a cantilever resonator or a trapped nanoparticle. The scheme is robust against the thermal noise, and could be realized at the temperature much higher than the quantum regime. The effects of decoherence on the interferometry fringe visibility is calculated, considering both the mechanical motional decay and dephasing of the nitrogen-vacancy center. In addition, we demonstrate that under the various sources of random and systematic noises, our gravimeter can be made on-chip and achieve a high measurement of precision. Under experimental feasible parameters, the proposed gravimeter could achieve 10^-10 relative precision.

Observation of Extra Photon Recoil in a Distorted Optical Field

Light carries momentum which induces on atoms a recoil for each photon absorbed. In vacuum, for a monochromatic beam of frequency ν, the global momentum per photon is bounded by general principles and is smaller than hν/c leading to a limit on the recoil. However, locally this limit can be broken. In this Letter, we give a general formula to calculate the recoil in vacuum. We show that in a laser beam with a distorted optical field, there are regions where the recoil can be higher than this limit. Using atoms placed in those regions we are able to measure directly the extra recoil.

Spin-Orbit-Coupled Interferometry with Ring-Trapped Bose-Einstein Condensates

We propose a method of atom interferometry using a spinor Bose-Einstein condensate with a time-varying magnetic field acting as a coherent beam splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub-μG scale. We split a ring-trapped condensate, initially in the m_{f}=0 hyperfine state, into superpositions of internal m_{f}=±1 states and condensate superflow, which are spin-orbit coupled. After interrogation, the relative phase accumulation can be inferred from a population transfer to the m_{f}=±1 states. The counterflow generation protocol is adiabatically deterministic and does not rely on coupling to additional optical fields or mechanical stirring techniques. Our protocol can maximize the classical Fisher information for any rotation, magnetic field, or interrogation time and so has the maximum sensitivity available to uncorrelated particles. Precision can increase with the interrogation time and so is limited only by the lifetime of the condensate.

An atom interferometer inside a hollow-core photonic crystal fiber

Coherent interactions between electromagnetic and matter waves lie at the heart of quantum science and technology. However, the diffraction nature of light has limited the scalability of many atom-light-based quantum systems. We use the optical fields in a hollow-core photonic crystal fiber to spatially split, reflect, and recombine a coherent superposition state of free-falling ⁸⁵Rb atoms to realize an inertia-sensitive atom interferometer. The interferometer operates over a diffraction-free distance, and the contrasts and phase shifts at different distances agree within one standard error. The integration of phase coherent photonic and quantum systems here shows great promise to advance the capability of atom interferometers in the field of precision measurement and quantum sensing with miniature design of apparatus and high efficiency of laser power consumption.

Measurement and control of the sideband to carrier ratio of an electro-optic modulator used in atom interferometers

The sideband and carrier of an electro-optic modulator (EOM) are usually used as Raman lasers in atom interferometry. To eliminate AC-Stark shift in atom interferometry, the stability of sideband to carrier ratio (SCR) is of great significance. We present a beating method to accurately measure and control the SCR. The influence of imperfect frequency response of the beating system is avoided by chirping the reference laser with half chirping rate of the modulation frequency. Making use of this method, we performed a SCR locking by feedback to the modulation depth. The locked SCRs' variation is averaged to be less than 0.1% within 20 MHz chirping span, and the according error for gravity measurement with 180 ms free evolution time is 6.2×10^-11g. Thus both the SCR variation and the estimated gravity measurement error are reduced by about 2 orders. This work may provide hints to other EOM involving experiments.

Ramsey Interference with Single Photons

Interferometry using discrete energy levels of nuclear, atomic, or molecular systems is the foundation for a wide range of physical phenomena and enables powerful techniques such as nuclear magnetic resonance, electron spin resonance, Ramsey-based spectroscopy, and laser or maser technology. It also plays a unique role in quantum information processing as qubits may be implemented as energy superposition states of simple quantum systems. Here, we demonstrate quantum interference involving energy states of single quanta of light. In full analogy to the energy levels of atoms or nuclear spins, we implement a Ramsey interferometer with single photons. We experimentally generate energy superposition states of a single photon and manipulate them with unitary transformations to realize arbitrary projective measurements. Our approach opens the path for frequency-encoded photonic qubits in quantum information processing and quantum communication.

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.

Test of Equivalence Principle at 10(-8) Level by a Dual-Species Double-Diffraction Raman Atom Interferometer

We report an improved test of the weak equivalence principle by using a simultaneous 85Rb-87Rb 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 0.8×10(-8) at 3200 s. With various systematic errors corrected, the final value is η=(2.8±3.0)×10(-8). The major uncertainty is attributed to the Coriolis effect.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Mu and epsilon near zero metamaterials for perfect coherence and new antenna designs

Wave interference is a fundamental physical phenomenon. Traditionally, the coherent effect of two identical point sources only takes place when the optical path is an integer number of wavelengths. In this paper, we show that mu and epsilon near zero (MENZ) metamaterials can be used to realize a perfectly constructive and isotropic interference. No matter how many point sources are embedded in the MENZ region, the wavefronts overlap perfectly. This translates into a total relaxation of the conventional condition for coherence enabled by the apparent infinite wavelength of the fields within MENZ metamaterials. Furthermore, we investigate crucial parameters such as the shape and size of the MENZ region. We demonstrate that flat sided geometries give rise to constructive interference beams serving as a powerful design mean. We also reveal the importance of relying on deeply sub-wavelength MENZ volumes as larger sizes increase the impedance and therefore reduce the output power of the device. The proposed concepts bear significance for current trends in antenna design which are inspired by the recent developments of electromagnetic metamaterials. Moreover, the perfect coherence effect can be appealing for power combiners, especially in the terahertz where sources are dim, as the irradiation intensity scales with the square of the number of embedded sources.

Antimatter interferometry for gravity measurements

We describe a light-pulse atom interferometer that is suitable for any species of atom and even for electrons and protons as well as their antiparticles, in particular, for testing the Einstein equivalence principle with antihydrogen. The design obviates the need for resonant lasers through far-off resonant Bragg beam splitters and makes efficient use of scarce atoms by magnetic confinement and atom recycling. We expect to reach an initial accuracy of better than 1% for the acceleration of the free fall of antihydrogen, which can be improved to the part-per million level.

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 1014 nm linearly polarized low noise narrow-linewidth single-frequency fiber laser

We present the demonstration of a compact linearly polarized low noise narrow-linewidth single-frequency fiber laser at 1014 nm. The compact fiber laser is based on a 5-mm-long homemade Yb(3+)-doped phosphate fiber. Over 164 mW stable continuous-wave single transverse and longitudinal mode lasing at 1014 nm has been achieved. The measured relative intensity noise is less than -135 dB/Hz at frequencies of over 2.5 MHz. The signal-to-noise ratio of the laser is larger than 70 dB, and the linewidth is less than 7 kHz, while the obtained linear polarization extinction ratio is higher than 30 dB.

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.

A Clock Directly Linking Time to a Particle's Mass

Historically, time measurements have been based on oscillation frequencies in systems of particles, from the motion of celestial bodies to atomic transitions. Relativity and quantum mechanics show that even a single particle of mass m determines a Compton frequency ω0 = mc2/ℏ, where c is the speed of light and ℏ is Planck's constant h divided by 2π. A clock referenced to ω0 would enable high-precision mass measurements and a fundamental definition of the second. We demonstrate such a clock using an optical frequency comb to self-reference a Ramsey-Bordé atom interferometer and synchronize an oscillator at a subharmonic of ω0. This directly demonstrates the connection between time and mass. It allows measurement of microscopic masses with 4 × 10−9 accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms.

Redshift controversy in atom interferometry: representation dependence of the origin of phase shift

Motivated by the recent debate on whether the Kasevich-Chu atom interferometer can measure the gravitational redshift, we show that in different representations of quantum mechanics chosen for the calculation, the observed phase shift appears as though it originates from different physical phenomena. In particular, we demonstrate that the decomposition of the total phase shift into three dynamical phases, which emerges in a semiclassical approach and is at the very heart of the redshift controversy, does not appear in an exact treatment based on a representation-free analysis. Here only two phenomena determine the phase shift: the difference of the laser phases and the acceleration of the atom. Hence, the Kasevich-Chu interferometer is an accelerometer or gravimeter.

Force-free gravitational redshift: proposed gravitational Aharonov-Bohm experiment

We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.

Influence of the Coriolis force in atom interferometry

In a light-pulse atom interferometer, we use a tip-tilt mirror to remove the influence of the Coriolis force from Earth's rotation and to characterize configuration space wave packets. For interferometers with a large momentum transfer and large pulse separation time, we improve the contrast by up to 350% and suppress systematic effects. We also reach what is to our knowledge the largest space-time area enclosed in any atom interferometer to date. We discuss implications for future high-performance instruments.

Quantum interferometric visibility as a witness of general relativistic proper time

Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'-a particle with evolving internal degrees of freedom-that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space-time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.

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.

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

We report on a precision measurement of gravitational acceleration using ultracold strontium atoms confined in an amplitude-modulated vertical optical lattice. An uncertainty Δg/g ≈ 10(-7) is reached by measuring at the 5th harmonic of the Bloch frequency. The value obtained with this microscopic quantum system is consistent with the one measured with a classical gravimeter. Using lattice modulation to prepare the atomic sample, we also achieve high visibility of Bloch oscillations for ∼ 20 s. These results can be of relevance for testing gravitational redshift and Newtonian law at micrometer scale.

Atom gravimeters and gravitational redshift

In ref. 1 the authors present a re-interpretation of atom interferometry experiments published a decade ago. They now consider the atom interferometry experiments as a measurement of the gravitational redshift on the quantum clock operating at the Compton frequency omega(C) = mc(2)/ approximately 2pi x 3.0 x 10(25) Hz, where m is the caesium (Cs) atom rest mass. They then argue that this redshift measurement compares favourably with existing as well as projected clock tests. Here we show that this interpretation is incorrect.

A Drop of Quantum Matter

Studies of a quantum object—a Bose-Einstein condensate—in free-fall conditions may provide high-precision tests of general relativity.