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Claus Lämmerzahl

Publications and source records attributed to Claus Lämmerzahl.

At least 37 records · Page 2Linked to original sources
arXiv2020

Twin-lattice atom interferometry

Inertial sensors based on cold atoms have great potential for navigation, geodesy, or fundamental physics. Similar to the Sagnac effect, their sensitivity increases with the space-time area enclosed by the interferometer. Here, we introduce twin-lattice atom interferometry exploiting Bose-Einstein condensates. Our method provides symmetric momentum transfer and large areas in palm-sized sensor heads with a performance similar to present meter-scale Sagnac devices.

quant-ph↗
arXiv2020

Detecting a logarithmic nonlinearity in the Schrödinger equation using Bose-Einstein condensates

We study the effect of a logarithmic nonlinearity in the Schrödinger equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate (BEC). The logarithmic nonlinearity was one of the first proposed nonlinear extensions to the SE which emphasized the conservation of important physical properties of the linear theory, e.g.: the separability of noninteracting states. Using this separability, we incorporate it into the description of a BEC obeying a logarithmic Gross-Pittaevskii equation. We investigate the dynamics of such BECs using variational and numerical methods and find that, using experimental techniques like delta kick collimation, experiments with extended free-fall times as available on microgravity platforms could be able to lower the bound on the strength of the logarithmic nonlinearity by at least one order of magnitude.

quant-ph↗
arXiv2020

The Relativistic Geoid: Gravity Potential and Relativistic Effects

The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of (post-)Newtonian notions. This potential exists in any stationary configuration with rigidly co-rotating observers, and it is the same as realized by local plumb lines. In a second step, we employ the gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limit, the framework allows to recover well-known (post-) Newtonian results. For a better illustration and proper interpretation of the general relativistic gravity potential and geoid, some particular examples are considered. Explicit results are derived for exact vacuum solutions to Einstein's field equation as well as a parametrized post-Newtonian model. Comparing the Earth's Newtonian geoid to its relativistic generalization is a very subtle problem, but of high interest. An isometric embedding into Euclidean three-dimensional space is an appropriate solution and allows a genuinely intrinsic comparison. With this method, the leading-order differences are determined, which are at the mm-level.

gr-qc↗
arXiv2019

The Bose-Einstein Condensate and Cold Atom Laboratory

Microgravity eases several constraints limiting experiments with ultracold and condensed atoms on ground. It enables extended times of flight without suspension and eliminates the gravitational sag for trapped atoms. These advantages motivated numerous initiatives to adapt and operate experimental setups on microgravity platforms. We describe the design of the payload, motivations for design choices, and capabilities of the Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL), a NASA-DLR collaboration. BECCAL builds on the heritage of previous devices operated in microgravity, features rubidium and potassium, multiple options for magnetic and optical trapping, different methods for coherent manipulation, and will offer new perspectives for experiments on quantum optics, atom optics, and atom interferometry in the unique microgravity environment on board the International Space Station.

physics.atom-ph↗
arXiv2019

A toy model of viscous relativistic geometrically thick disk in Schwarzschild geometry

In this earliest study of thick accretion disks with viscosity effects, we construct stationary solutions of a relativistic geometrically thick accretion disk in the Schwarzschild spacetime under the influence of shear viscosity and the curvature of the black hole by solving the general relativistic causal Navier-Stokes equation. Motivated by the causal prescription of relativistic hydrodynamics initially introduced in Müller-Israel-Stewart theories, our approach adopts a simplistic path and takes into account of only shear viscosity, discarding influences of bulk viscosity and heat flow. This work investigates possible impacts of both the shear viscosity tensor and black hole curvature on the shape of a thick disk characterized by constant specific angular momentum distribution. The existence of the integrability condition of the Navier-Stokes equation has been examined in our study which further supports the existence of stationary solutions in the given set-up.

gr-qc↗
arXiv2019

Space test of the Equivalence Principle: first results of the MICROSCOPE mission

The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of $10^{-15}$, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter $δ(Ti,Pt)=[-1\pm{}9{\rm (stat)}\pm{}9{\rm (syst)}] \times{}10^{-15}$ (both 1$σ$ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7\% of the current available data acquired during the whole mission. The quadratic combination of 1$σ$ uncertainties leads to a current limit on $δ$ of about $1.3\times{}10^{-14}$.

gr-qc↗
arXiv2019

The local dark sector. Probing gravitation's low-acceleration frontier and dark matter in the Solar System neighborhood

We speculate on the development and availability of new innovative propulsion techniques in the 2040s, that will allow us to fly a spacecraft outside the Solar System (at 150 AU and more) in a reasonable amount of time, in order to directly probe our (gravitational) Solar System neighborhood and answer pressing questions regarding the dark sector (dark energy and dark matter). We identify two closely related main science goals, as well as secondary objectives that could be fulfilled by a mission dedicated to probing the local dark sector: (i) begin the exploration of gravitation's low-acceleration regime with a man-made spacecraft and (ii) improve our knowledge of the local dark matter and baryon densities. Those questions can be answered by directly measuring the gravitational potential with an atomic clock on-board a spacecraft on an outbound Solar System orbit, and by comparing the spacecraft's trajectory with that predicted by General Relativity through the combination of ranging data and the in-situ measurement (and correction) of non-gravitational accelerations with an on-board accelerometer. Despite a wealth of new experiments getting online in the near future, that will bring new knowledge about the dark sector, it is very unlikely that those science questions will be closed in the next two decades. More importantly, it is likely that it will be even more urgent than currently to answer them. Tracking a spacecraft carrying a clock and an accelerometer as it leaves the Solar System may well be the easiest and fastest way to directly probe our dark environment.

astro-ph.IM↗
arXiv2019

Evaporative cooling from an optical dipole trap in microgravity

In recent years, cold atoms could prove their scientific impact not only on ground but in microgravity environments such as the drop tower in Bremen, sounding rockets and parabolic flights. We investigate the preparation of cold atoms in an optical dipole trap, with an emphasis on evaporative cooling under microgravity. Up to $ 1\times10^{6} $ rubidium-87 atoms were optically trapped from a temporarily dark magneto optical trap during free fall in the droptower in Bremen. The efficiency of evaporation is determined to be equal with and without the effect of gravity. This is confirmed using numerical simulations that prove the dimension of evaporation to be three-dimensional in both cases due to the anharmonicity of optical potentials. These findings pave the way towards various experiments on ultra-cold atoms under microgravity and support other existing experiments based on atom chips but with plans for additional optical dipole traps such as the upcoming follow-up missions to current and past spaceborne experiments.

physics.atom-ph↗
arXiv2019

Modeling approaches for precise relativistic orbits: Analytical, Lie-series, and pN approximation

Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth's albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions.

gr-qc↗
arXiv2019

Physical dimensions/units and universal constants: their invariance in special and general relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, we are naturally led, besides the dimensions of length and time, to the fundamental units of action $\mathfrak h$, electric charge $q$, and magnetic flux $ϕ$. We have $q\times ϕ=\text{action}$ and $q/ϕ=1/\text{resistance}$. These results of \emph{classical physics} suggests to look into the corresponding quantum aspects of $q$ and $ϕ$ (and also of $\mathfrak h$): The electric charge occurs exclusively in elementary charges $e$, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, $ϕ$ appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum $h$. Thus, we are directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity, that is, if gravity is thought to be switched off versus the case in the gravitational field.

gr-qc↗
arXiv2018

Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.

gr-qc↗
arXiv2018

Effects of non-linear vacuum electrodynamics on the polarization plane of light

We consider the Pleba{ń}ski class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a theory, on an unspecified general-relativistic spacetime and with an unspecified electromagnetic background field. To that end we start out from an approximate-plane-harmonic-wave ansatz that takes the generation of higher harmonics into account. By this ansatz, the electromagnetic field is written as an asymptotic series with respect to a parameter $α$, where the limit $α\to 0$ corresponds to sending the frequency to infinity. We demonstrate that by solving the generalized Maxwell equations to zeroth and first order with respect to $α$ one gets a unique transport law for the polarization plane along each light ray. We exemplify the general results with the Born-Infeld theory.

gr-qc↗
arXiv2018

On slowly rotating black holes and nonlinear electrodynamics

We discuss the solution to Einstein's equations for a Lense-Thirring inspired metric describing a slowly rotating black hole coupled to nonlinear electrodynamics. We show that different schemes of rotation for the black hole exist; they depend on a parameter $γ$ defining the dependence of the metric on the polar angle. The fulfilment of the complete set of gravitational field equations and conservation laws implies constraints on this parameter and the metric functions. The vanishing of $γ$ provides the Lense-Thirring line element associated to any non-linear electrodynamics; the Kerr-Newman metric for slow rotation arises when $γ$ is not vanishing, a feature that emphasises the unique role played by Maxwell's electrodynamics.

gr-qc↗
arXiv2018

Gravitational clock compass in General Relativity

We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass. Particular attention is paid to the construction of the underlying reference frame. Conceptual differences between the clock compass and the standard gravitational compass, which is based on the measurement of the mutual accelerations between the constituents of a swarm of test bodies, are highlighted. Our results are of direct operational relevance for the setup of networks of clocks, for example in the context of relativistic geodesy.

gr-qc↗
arXiv2018

Space-borne Bose-Einstein condensation for precision interferometry

Space offers virtually unlimited free-fall in gravity. Bose-Einstein condensation (BEC) enables ineffable low kinetic energies corresponding to pico- or even femtokelvins. The combination of both features makes atom interferometers with unprecedented sensitivity for inertial forces possible and opens a new era for quantum gas experiments. On January 23, 2017, we created Bose-Einstein condensates in space on the sounding rocket mission MAIUS-1 and conducted 110 experiments central to matter-wave interferometry. In particular, we have explored laser cooling and trapping in the presence of large accelerations as experienced during launch, and have studied the evolution, manipulation and interferometry employing Bragg scattering of BECs during the six-minute space flight. In this letter, we focus on the phase transition and the collective dynamics of BECs, whose impact is magnified by the extended free-fall time. Our experiments demonstrate a high reproducibility of the manipulation of BECs on the atom chip reflecting the exquisite control features and the robustness of our experiment. These properties are crucial to novel protocols for creating quantum matter with designed collective excitations at the lowest kinetic energy scales close to femtokelvins.

physics.atom-ph↗
arXiv2018

Charged fluid structures around a rotating compact object with a magnetic dipole field

We study stationary, electrically charged fluid structures encircling a rotating compact object with a dipole magnetic field oriented along the rotation axis. This situation is described in an idealized way by the Kerr metric and a magnetic dipole "test" field, that does not affect the spacetime. The self-gravitational and self-electromagnetic field of the fluid are neglected and the fluid is assumed to be non conductive and in rigid motion. Our work generalizes a previous study by Kovář et al.(2016) by taking into account the rotation of the central object. Therefore, we focus on the influence of the rotation onto the existence and position of bound fluid structures. Frame dragging effects allow the existence of polar clouds, which could not be found in non-rotating case. Furthermore counter-rotating equatorial tori become more preferred the faster the central object is spinning.

astro-ph.HE↗
arXiv2018

Finsler geometry as a model for relativistic gravity

We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian versions of Maxwell's equations, of the Klein-Gordon equation and of the Dirac equation, and several experimental tests of Finsler gravity.

gr-qc↗