Space-borne Bose-Einstein condensation for precision interferometry.

Owing to the low-gravity conditions in space, space-borne laboratories enable experiments with extended free-fall times. Because Bose-Einstein condensates have an extremely low expansion energy, space-borne atom interferometers based on Bose-Einstein condensation have the potential to have much greater sensitivity to inertial forces than do similar ground-based interferometers. On 23 January 2017, as part of the sounding-rocket mission MAIUS-1, we created Bose-Einstein condensates in space and conducted 110 experiments central to matter-wave interferometry, including laser cooling and trapping of atoms in the presence of the large accelerations experienced during launch. Here we report on experiments conducted during the six minutes of in-space flight in which we studied the phase transition from a thermal ensemble to a Bose-Einstein condensate and the collective dynamics of the resulting condensate. Our results provide insights into conducting cold-atom experiments in space, such as precision interferometry, and pave the way to miniaturizing cold-atom and photon-based quantum information concepts for satellite-based implementation. In addition, space-borne Bose-Einstein condensation opens up the possibility of quantum gas experiments in low-gravity conditions1,2.

Optical cavity reaching 10-16 frequency stability with compact optical circulator based in-coupling optics.

Future space missions will benefit from highly stable and compact optical frequency references. While many promising technologies are currently under investigation, optical cavities are a well-suited technique for applications in which relative references are required. To improve the frequency stability of optical cavities, a key step in combining high performance with compactness and robustness is the further development of in-coupling optics. Here, we present our work of using a fiber-coupled circulator based in-coupling for a high-finesse optical cavity. Implementing the new, to the best of our knowledge, in-coupling board to an extensively characterized crossed cavity set-up allows us to identify possible differences to the commonly used free-beam technique. With a frequency stability of 5.5×10-16 H z -1/2 at 1 Hz and with only a slight degradation in frequency stability below the mHz range, no circulator-caused instabilities were observed.

Optical pilot tone correction of phase errors in photodetection chains.

The phase delay introduced by photodetectors can be affected by intensity, reverse bias, and temperature through different effects. An optical pilot tone superimposed on the detected signal allows an independent measurement of such phase errors in the complete photodetection chain and provides an opportunity to correct them. This allows to further separate readout noise from the measurement, providing a more performant and intensity-invariant phase readout. We test the functional principle on a setup demonstrating an improved phase noise performance and a reduced phase walk below 10 mHz in particular. This benefits applications that require accurate timing or signal phase determination with photodiodes.

Interferometric sphere surface metrology with cylindrical reference for precision topography.

We demonstrate a method for measuring a surface map of a spherical body with interferometric optical point sensors while rotating the test subject. The setup takes advantage of the excellent performance of heterodyne interferometry at nanometer levels and suppression of common-mode errors, as a cylindrical mirror mounted adjacent to the sphere is used as a reference. Future space based missions for gravitational wave research demand an improved inertial reference sensor with reduced acceleration noise levels. Spherical test masses can enable increased performance by suspension-free operation, contrary to cuboid solutions suffering from cross-coupling of attitude control noise into test mass position. However, interferometric readout is affected by surface irregularities and test mass attitude. An accurate surface map for compensation of the center of gravity readout should be established, by characterization either a priori or in-flight, when optical path length changes due to the surface occur in the measurement bandwidth.

Simultaneous laser frequency stabilization to an optical cavity and an iodine frequency reference.

In this Letter, we demonstrate a method to combine a molecular iodine absolute frequency reference with a high-finesse optical cavity in a single laser to take advantage of the frequency stability properties of both systems at different time scales. The result is a laser exhibiting the long-term and short-term stability levels of the iodine frequency reference and optical cavity, respectively. The method uses frequency offset side-band locking and an acousto-optical modulator driven ac-coupled servo-loop to correct the iodine's short-term frequency fluctuations. Experimental results show cavity-limited stability at 1 Hz of 10-151/Hz and iodine stability below 10 mHz of 10-131/Hz. In terms of the Allan deviation, this corresponds to stability levels close to the 10-15 at 1 s and 10-14 for observation times >100s.

Long-term stable optical cavity for special relativity tests in space: erratum.

We incorrectly cited a maximum acceleration sensitivity of the rigidly-mounted cavity of 2.5 × 10-10 1/(m s-2). The correct coupling factor is a factor of 100 smaller: 2.5 × 10-12 1/(m s-2).

Architecture and performance analysis of an optical metrology terminal for satellite-to-satellite laser ranging.

Interferometric laser ranging is an enabling technology for high-precision satellite-to-satellite tracking within the context of Earth observation, gravitational wave detection, or formation flying. In orbit, the measurement system is affected by environmental influences, particularly satellite attitude jitter and temperature fluctuations, imposing an instrument design with a high level of thermal stability and insensitivity to rotations around the spacecraft center of mass. The new design concept presented here combines different approaches for dynamic heterodyne laser ranging and features the inherent beam-tracking capabilities of a retroreflector in a mono-axial configuration. It allows for a continuously adjustable distance between the optical bench and the location of its fiducial point, facilitating future inter-satellite tracking with nanometer accuracy, e.g., the next-generation gravity mission.

Long-term stable optical cavity for special relativity tests in space.

BOOST (BOOst Symmetry Test) is a proposed space mission to search for Lorentz invariance violations and aims to improve the Kennedy-Thorndike parameter constraint by two orders of magnitude. The mission consists of comparing two optical frequency references of different nature, an optical cavity and a hyperfine transition in molecular iodine, in a low Earth orbit. Naturally, the stability of the frequency references at the orbit period of 5400 s (f=0.18 mHz) is essential for the mission success. Here we present our experimental efforts to achieve the required fractional frequency stability of 7.4×10-14 Hz -1/2 at 0.18 mHz (in units of the square root of the power spectral density), using a high-finesse optical cavity. We have demonstrated a frequency stability of (9±3)×10-14 Hz -1/2 at 0.18 mHz, which corresponds to an Allan deviation of 10-14 at 5400 s. A thorough noise source breakdown is presented, which allows us to identify the critical aspects to consider for a future space-qualified optical cavity for BOOST. The major noise contributor at sub-milli-Hertz frequency was related to intensity fluctuations, followed by thermal noise and beam pointing. Other noise sources had a negligible effect on the frequency stability, including temperature fluctuations, which were strongly attenuated by a five-layer thermal shield.

In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer.

The Laser Ranging Interferometer (LRI) instrument on the Gravity Recovery and Climate Experiment (GRACE) Follow-On mission has provided the first laser interferometric range measurements between remote spacecraft, separated by approximately 220 km. Autonomous controls that lock the laser frequency to a cavity reference and establish the 5 degrees of freedom two-way laser link between remote spacecraft succeeded on the first attempt. Active beam pointing based on differential wave front sensing compensates spacecraft attitude fluctuations. The LRI has operated continuously without breaks in phase tracking for more than 50 days, and has shown biased range measurements similar to the primary ranging instrument based on microwaves, but with much less noise at a level of 1 nm/sqrt[Hz] at Fourier frequencies above 100 mHz.

Line of sight calibration for the laser ranging interferometer on-board the GRACE Follow-On mission: on-ground experimental validation.

The laser ranging interferometer (LRI) on board of the GRACE follow-on spacecraft, launched in May 2018, is the first laser interferometer to perform an inter-satellite range measurement. It is designed for ranging noise levels of 80 nm Hz-1/2 for frequencies above 20 mHz, i.e., about a ten-fold improvement with respect to the GRACE follow-on main microwave ranging instrument. One of the most critical steps during the commissioning phase of the instrument is the so-called initial line of sight calibration procedure (or initial acquisition). This process is required to quantify large uncertainties with respect to laser beam pointing angles and laser frequency, which must be known to establish the interferometer link. It is a nine hour scan of five degrees of freedom, which all need to match simultaneously at least once. Here we report on laboratory tests to further validate the calibration procedure using a mock-up LRI and a set-up, the so-called laser link simulator, that creates conditions similar to those with ~220 km distance between the SC. The experiments presented here made use of LRI-like hardware and software and were carried out recreating critical conditions such as received laser powers on the pico-Watt level and their dependence on the SC misalignments, flat-top beams as receiving beams and Doppler frequency shifts. Several configurations were tested, including a full line of sight calibration with angular scans in both mock-up SC and frequency scan in one of the lasers. Results are well in agreement with the expectations and confirm, well before the LRI commissioning phase, the robustness of the procedure under realistic conditions, which had not yet been fully tested experimentally.

Development of a compact optical absolute frequency reference for space with 10-15 instability.

We report on a compact and ruggedized setup for laser frequency stabilization employing Doppler-free spectroscopy of molecular iodine near 532 nm. Using a 30 cm long iodine cell in a triple-pass configuration in combination with noise-canceling detection and residual amplitude modulation control, a frequency instability of 6×10-15 at 1 s integration time and a Flicker noise floor below 3×10-15 for integration times between 100 and 1000 s was found. A specific assembly-integration technology was applied for the realization of the spectroscopy setup, ensuring high beam pointing stability and high thermal and mechanical rigidity. The setup was developed with respect to future applications in space, including high-sensitivity interspacecraft interferometry, tests of fundamental physics, and navigation and ranging.

Interferometric surface mapping of a spherical proof mass for ultra precise inertial reference sensors.

In the context of our investigations on novel inertial reference sensors for space applications, we have explored a design utilizing an optical readout of a spherical proof mass. This concept enables full drag-free operations, hence reducing proof mass residual acceleration noise to a minimum. The main limitations of this sensor are errors in position determination of the center of mass of the proof mass due to the surface topography and the involved path length changes upon rotation. One solution is to apply a surface map for correction of the measurement data, thus improving the precision of position determination. This article presents the results of our one-dimensional interferometric surface topography measurements of a sphere, achieving uncertainties of ≈10 nm, as a first step to realize a complete surface map. The measurement setup consists of two heterodyne interferometers positioned in an opposing configuration, which measure the surface topography while the sphere is continuously rotated by a rotation stage.

Mathematical model of thermal shields for long-term stability optical resonators.

Modern experiments aiming at tests of fundamental physics, like measuring gravitational waves or testing Lorentz Invariance with unprecedented accuracy, require thermal environments that are highly stable over long times. To achieve such a stability, the experiment including typically an optical resonator is nested in a thermal enclosure, which passively attenuates external temperature fluctuations to acceptable levels. These thermal shields are usually designed using tedious numerical simulations or with simple analytical models. In this paper, we propose an accurate analytical method to estimate the performance of passive thermal shields in the frequency domain, which allows for fast evaluation and optimization. The model analysis has also unveiled interesting properties of the shields, such as dips in the transfer function for some frequencies under certain combinations of materials and geometries. We validate the results by comparing them to numerical simulations performed with commercial software based on finite element methods.

Interspacecraft link simulator for the laser ranging interferometer onboard GRACE Follow-On.

Link acquisition strategies are key aspects for interspacecraft laser interferometers. We present an optical fiber-based setup able to simulate the interspacecraft link for the laser ranging interferometer (LRI) on gravity recovery and climate experiment Follow-On. It allows one to accurately recreate the far-field intensity profile depending on the mispointing between the spacecraft, Doppler shifts, and spacecraft attitude jitter. Furthermore, it can be used in late integration stages of the mission, since no physical contact with the spacecraft is required. The setup can also be easily adapted to other similar missions and different acquisition algorithms.

Interferometric characterization and modeling of pathlength errors resulting from beamwalk across mirror surfaces in LISA.

An alternative payload concept with in-field pointing for the laser interferometer space antenna utilizes an actuated mirror in the telescope for beam tracking to the distant satellite. This actuation generates optical pathlength variations due to the resulting beamwalk over the surface of subsequent optical components, which could possibly have a detrimental influence on the accuracy of the measurement instrument. We have experimentally characterized such pathlength errors caused by a λ/10 mirror surface and used the results to validate a theoretical model. This model is then applied to predict the impact of this effect for the current optical design of the LISA off-axis wide-field telescope.

Choice of the Miniature Inertial Optomechanical Sensor Geometric Parameters with the Help of Their Mechanical Characteristics Modelling.

In this paper, the mechanical characteristics of a miniature optomechanical accelerometer, similar to those proposed for a wide range of applications, have been investigated. With the help of numerical modelling, characteristics such as eigenfrequencies, quality factor, displacement magnitude, normalized translations, normalized rotations versus eigenfrequencies, as well as spatial distributions of the azimuthal and axial displacements and stored energy density in a wide frequency range starting from the stationary case have been obtained. Dependencies of the main mechanical characteristics versus the minimal and maximal system dimensions have been plotted. Geometries of the optomechanical accelerometers with micron size parts providing the low and the high first eigenfrequencies are presented. It is shown that via the choice of the geometrical parameters, the minimal measured acceleration level can be raised substantially.

Ultracold atom interferometry in space.

Bose-Einstein condensates (BECs) in free fall constitute a promising source for space-borne interferometry. Indeed, BECs enjoy a slowly expanding wave function, display a large spatial coherence and can be engineered and probed by optical techniques. Here we explore matter-wave fringes of multiple spinor components of a BEC released in free fall employing light-pulses to drive Bragg processes and induce phase imprinting on a sounding rocket. The prevailing microgravity played a crucial role in the observation of these interferences which not only reveal the spatial coherence of the condensates but also allow us to measure differential forces. Our work marks the beginning of matter-wave interferometry in space with future applications in fundamental physics, navigation and earth observation.

Ultrastable assembly and integration technology for ground- and space-based optical systems.

Optical metrology systems crucially rely on the dimensional stability of the optical path between their individual optical components. We present in this paper a novel adhesive bonding technology for setup of quasi-monolithic systems and compare selected characteristics to the well-established state-of-the-art technique of hydroxide-catalysis bonding. It is demonstrated that within the measurement resolution of our ultraprecise custom heterodyne interferometer, both techniques achieve an equivalent passive path length and tilt stability for time scales between 0.1 mHz and 1 Hz. Furthermore, the robustness of the adhesive bonds against mechanical and thermal inputs has been tested, making this new bonding technique in particular a potential option for interferometric applications in future space missions. The integration process itself is eased by long time scales for alignment, as well as short curing times.

A three-layer magnetic shielding for the MAIUS-1 mission on a sounding rocket.

Bose-Einstein-Condensates (BECs) can be used as a very sensitive tool for experiments on fundamental questions in physics like testing the equivalence principle using matter wave interferometry. Since the sensitivity of these experiments in ground-based environments is limited by the available free fall time, the QUANTUS project started to perform BEC interferometry experiments in micro-gravity. After successful campaigns in the drop tower, the next step is a space-borne experiment. The MAIUS-mission will be an atom-optical experiment that will show the feasibility of experiments with ultra-cold quantum gases in microgravity in a sounding rocket. The experiment will create a BEC of 10(5) (87)Rb-atoms in less than 5 s and will demonstrate application of basic atom interferometer techniques over a flight time of 6 min. The hardware is specifically designed to match the requirements of a sounding rocket mission. Special attention is thereby spent on the appropriate magnetic shielding from varying magnetic fields during the rocket flight, since the experiment procedures are very sensitive to external magnetic fields. A three-layer magnetic shielding provides a high shielding effectiveness factor of at least 1000 for an undisturbed operation of the experiment. The design of this magnetic shielding, the magnetic properties, simulations, and tests of its suitability for a sounding rocket flight are presented in this article.

Dilatometer setup for low coefficient of thermal expansion materials measurements in the 140 K-250 K temperature range.

Space applications demand light weight materials with excellent dimensional stability for telescopes, optical benches, optical resonators, etc. Glass-ceramics and composite materials can be tuned to reach very low coefficient of thermal expansion (CTE) at different temperatures. In order to determine such CTEs, very accurate setups are needed. Here we present a dilatometer that is able to measure the CTE of a large variety of materials in the temperature range of 140 K to 250 K. The dilatometer is based on a heterodyne interferometer with nanometer noise levels to measure the expansion of a sample when applying small amplitude controlled temperature signals. In this article, the CTE of a carbon fiber reinforced polymer sample has been determined with an accuracy in the 10-8 K-1 range.