Tim van Zoest, Naceur Gaaloul, Yeshpal Singh, Henning Ahlers, Waldemar Herr, Stephan Seidel, Wolfgang A. Ertmer, Ernst Maria Rasel, M. Eckart, E. Kajari, Stefan Arnold, G. Nandi, Wolfgang P. Schleich, R. Walser, Anika Vogel, K. Sengstock, Kai Bongs, Wojciech Lewoczko-Adamczyk, Max Schiemangk, Thilo Schuldt, Achim Peters, Thorben Könemann, Hauke Müntinga, Cláus Lämmerzahl, H. Dittus, T. Steinmetz, Theodor W. Hänsch, Jakob Reichel
Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.
Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.
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.
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.
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.
Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.
Quantum sensors based on the interference of cold atoms have advanced to the forefront of precision measurements in geodesy, metrology and tests of fundamental physics. The ultimate potential of these devices is realized using quantum degenerate atoms in extended free fall. This can be achieved on microgravity platforms such as drop towers, parabolic flights, ballistic rockets, satellites and space stations. The transition to mobile and robust devices that can withstand the demands of these environments comes with many challenges. Quantum sensors need to be scaled down and integrated without compromising their performance. In fact, they need to significantly outpace conventional instruments, since microgravity time is an expensive resource and limited to a few seconds at a time on the most accessible platforms. This thesis describes the construction, qualification and operation of a miniaturized ultracold atom experiment that meets these challenges. The QUANTUS-2 apparatus features a payload weight of 147 kg and a payload volume of 0.3 m^3. It generates Bose-Einstein condensates of 4×10^5 ^87Rb atoms every 1.6 seconds, a flux of ultra-cold atoms that is on par with the best lab-sized devices. Ensembles of 1×10^5 atoms can be created at a 1 Hz rate. It is currently the fastest machine of its kind and achieves the highest atom number of any atom chip setup. The apparatus continuously withstands peak accelerations of up to 45 g during microgravity campaigns at the drop tower facility in Bremen, Germany. Here, the payload has accrued 208 drops and 9 catapult launches over 24 month. The setup is the first atom optics experiment to stand up to the technical demands of catapult operation. Four condensates can be created and observed consecutively during nine seconds of free fall in a single catapult launch. In total, the experiment has been suspended in microgravity for over 17 minutes. With the record source performance, the repetition rate for microgravity experiments with ultra-cold atoms was increased by a factor of four compared to previous devices. The total atom number was increased by a factor of 40, vastly improving the signal to noise ratio for absorption images of spatially extended clouds. The ensembles can be prepared consistently over many weeks of drop tower operation. The variance of the mean center of mass velocity in two observable directions is 7.3 μm/s and 6.9 μm/s. Magnetic lensing techniques were employed to manipulate the expansion of the ensembles. First results yield a residual expansion rate in three dimensions of σ_v = 116.9 ± 13.9 μm/s, which implies a three-dimensional effective temperature of T = 47.6 ± 11.3 pK at an average condensate atom number of N = 93000. These values constitute the best collimation of any atomic ensemble and the most promising source for atom interferometry reported to date. Optimizing the current lensing sequence will reduce the expansion rate further to effective temperatures in the femtokelvin regime. The level of control demonstrated over the condensates is highly relevant for the advancement of matter-wave optics and quantum sensors. Controlling the motion and size of atomic clouds is intrinsically tied to many systematic effects in high precision measurements. QUANTUS-2 will provide a platform to explore and mitigate these limitations on unprecedented time scales of up to seven seconds of free evolution.
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.