Quantum sensors based on atom interferometry are precise measurement devices whose ultimate performance can be reached using Bose–Einstein condensates (BECs) in extended free fall. This thesis summarizes the endeavour of the QUANTUS and MAIUS collaborations to enable BECs for precision interferometry in space. The presented results have set the foundation for future space missions aiming at geodesy applications or tests of fundamental physics.
Quantum sensors based on atom interferometry are precise measurement devices whose ultimate performance can be reached using Bose–Einstein condensates (BECs) in extended free fall. This thesis summarizes the endeavour of the QUANTUS and MAIUS collaborations to enable BECs for precision interferometry in space. The presented results have set the foundation for future space missions aiming at geodesy applications or tests of fundamental physics.
Inertial sensors based on matter-wave interferometry are currently approaching the precision and accuracy of state-of-the-art classical sensors. While these devices are often realised with ultracold but not Bose-condensed atoms as matter waves, employing Bose-Einstein Condensates (BEC) promises to overcome certain limitations, especially those related to the ensemble's expansion. The point-source like character of BECs also enables utilising spatial interference patterns to measure e.g. rotation rates in single-shot experiments. Matter wave-based inertial sensors are considered for experiments ranging from Gravitational Wave detection to tests of the Universality of Free Fall (UFF) to gain insight into the joint between Quantum Mechanics and General Relativity. In the scope of this thesis, matter-wave interferometry with BECs was demonstrated for the first time in a microgravity environment with the QUANTUS-1 apparatus. The same instrument was then employed as a quantum tiltmeter utilising a novel beam-splitting mechanism known as Bragg Double Diffraction. To this end, the QUANTUS-1 apparatus designed as a BEC instrument to be operated in the drop tower at ZARM at University of Bremen was equipped with optics and laser systems required for performing matter-wave interferometry based on Bragg Diffraction. The apparatus employs an atom chip to create BECs of around 10000 Rubidium 87 atoms within 15 s. With a Mach-Zehnder like interferometer scheme, spatial interference fringes were observed after a free evolution time in the interferometer of up to 677 ms. To achieve these long time scales, a method known as Delta-Kick Collimation (DKC) was adapted to slow the expansion of the BEC to a kinetic energy equivalent below 1 nK, and the atoms were transferred to a non-magnetic Zeeman state via an adiabatic rapid passage (ARP). A similar interferometer scheme with a newly developed beam-splitter mechanism known as Bragg Double Diffraction was used to measure the tilt of the instrument on ground with a precision of up to 4.4 AA rad. This thesis presents an overview of the apparatus including ground-based characterisations of all required experimental steps. Results from over 400 free fall experiments are evaluated for expansion studies of the BEC and matter-wave interferometry in microgravity. The time-evolution of first and second order Bragg Double Diffraction beam splitters is studied, and an interferometer sensitive to the tilt of the instrument is implemented. Based on this work, a gravimeter with a new launch mechanism comprising Bragg beam splitters and Bloch oscillations to enable atomic fountains in atom-chip based devices was developed. The microgravity experiments were adapted for the MAIUS-1 sounding-rocket instrument to create the first man-made BEC in outer space and study the feasibility of operating matter-wave interferometers on space-borne platforms. The results of this thesis lay the groundwork for future space-borne missions using matter-wave interferometry for precision measurements of inertial forces.
Measuring effects of General Relativity and beyond in the gravitational field of the Earth is a main goal of current research and cutting-edge technology. These effects, predicted by Einstein’s theory, already play an important role in everyday life, for example in enabling for precise positioning and time keeping in global satellite navigation systems, such as GPS and GALILEO. The breakthrough experimental realisation of Bose-Einstein condensation in 1995, some 70 years after Einstein’s prediction, has since established matter-wave interferometers in laboratories worldwide, in which laser pulses are used to coherently split, reflect, and recombine a Bose-Einstein condensate. While already enabling highly accurate quantum sensors for technological applications as accelerometers, gyroscopes, and gravity gradiometers, matter-wave interferometers with their unprecedented potential sensitivity are highly anticipated to serve as formidable quantum probes of fundamental physics. For this reason, concentrated international efforts are currently under way to develop this promising technology into robust and sensitive instruments. The German QUANTUS collaboration is at the forefront of this development, having demonstrated the first Bose-Einstein condensates and matter-wave interferometers in free fall, and having recently achieved the very first BEC in space on the sounding-rocket mission MAIUS-1 in early 2017. As its long-time goal, QUANTUS is aiming at a quantum test of Einstein’s famous Equivalence Principle, which is at the heart of General Relativity as a geometric theory of gravity. In this context, it is relevant to develop a precise description of free fall in Earth’s gravity beyond the usual Newtonian approximation, and thus to take into account the full reality of curved space-time in terms Einstein’s theory of General Relativity. In this thesis, we take a grand tour of the relevant concepts of Special and General Relativity and eventually apply these to the modelling of free falling quantum gases. We base our description on the experimentally relevant local inertial and non-inertial frames which we can think of as moving along with experiments in free fall, for example in a drop tower, or in satellites orbiting the Earth, such as the International Space Station ISS. Our main tool are Fermi normal coordinates attached to these frames, which provide a local curvature expansion around flat space-time that exhibits local tidal effects, and can thus be seen as an expansion around the Equivalence Principle. Being fairly under-represented in the literature, we extensively discuss these Fermi coordinates, as well as the so-called Riemann normal coordinates on which they are built. In particular, we provide a new combinatorial interpretation for the complicated polynomials in the Riemann tensor and its derivatives, which arise in the expansion for the tetrads and the metric in these coordinates. We finally apply these methods to the mean-field description of free falling Bose-Einstein condensates in the gravitational field of the Earth. Modelling the space-time curvature around our planet in terms of the Schwarzschild metric, we explicitly calculate the metric in Fermi coordinates for local inertial frames in free fall along purely radial geodesics, which approximates the experimental situation in a drop tower, as well as along circular equatorial geodesics which can be used to model the situation on satellites, such as the ISS. We then use these metrics in the non-linear Klein-Gordon equation which can be seen to generalise the usual Gross-Pitaevskii equation to curved space-time. Performing the non-relativistic limit, we obtain the different local tidal-type Newtonian and relativistic corrections and discuss their orders of magnitude.
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.
On 23rd of January 2017 the first Bose-Einstein Condensate (BEC) in Space was created on-board the sounding rocket mission MAIUS-1. The successful launch marks a major advancement in the effort of performing matter wave interferometry with BECs on space vehicles. Its high BEC-flux enables more than 100 experiments during flight, characterizing the creation of BECs in space, their free evolution, state preparation, and the creation of cold atoms in highly dynamic environments. MAIUS-1 opens a new path towards space borne inertial sensing employing interferometers with high accuracy and sensitivity. Two follow-up missions will investigate dual-species interferometry. Recently several missions were proposed ranging from tests of the universality of free fall to gravimetry. Due to their small initial size and low expansion rates BECs are the ideal source for such an interferometric measurement. The findings of the mission will contribute to the NASA CAL project and BECCAL (NASA and DLR). This research is funded by DLR under grant 50WP1435.
On 23rd of January 2017 the first Bose-Einstein Condensate (BEC) in Space was created on-board the sounding rocket mission MAIUS-1. The successful launch marks a major advancement in the effort of performing matter wave interferometry with BECs on space vehicles. Its high BEC-flux enables more than 100 experiments during flight, characterizing the creation of BECs in space, their free evolution, state preparation, and the creation of cold atoms in highly dynamic environments. MAIUS-1 opens a new path towards space borne inertial sensing employing interferometers with high accuracy and sensitivity. Two follow-up missions will investigate dual-species interferometry. Recently several missions were proposed ranging from tests of the universality of free fall to gravimetry. Due to their small initial size and low expansion rates BECs are the ideal source for such an interferometric measurement. The findings of the mission will contribute to the NASA CAL project and BECCAL (NASA and DLR). This research is funded by DLR under grant 50WP1435.
On 23rd of January 2017 the first Bose-Einstein Condensate (BEC) in Space was created on-board the sounding rocket mission MAIUS-1. The successful launch marks a major advancement in the effort of performing matter wave interferometry with BECs on space vehicles. Its high BEC-flux enables more than 100 experiments during flight, characterizing the creation of BECs in space, their free evolution, state preparation, and the creation of cold atoms in highly dynamic environments. MAIUS-1 opens a new path towards space borne inertial sensing employing interferometers with high accuracy and sensitivity. Two follow-up missions will investigate dual-species interferometry. Recently several missions were proposed ranging from tests of the universality of free fall to gravimetry. Due to their small initial size and low expansion rates BECs are the ideal source for such an interferometric measurement. The findings of the mission will contribute to the NASA CAL project and BECCAL (NASA and DLR). This research is funded by DLR under grant 50WP1435.