Atom interferometry with picokelvin ensembles in microgravity

Atom interferometry enables precision measurements with outstanding sensitivities in a broad field of applications, ranging from fundamental physics to applications in geodesy or navigation. The development of robust and mobile devices paves the way for future satellite missions, e.g. striving for improved spaceborne gravimetry or a precision test of the universality of free fall.
The sensitivity of an atom interferometer scales quadratically with the interrogation time. Consequentially, exceptional sensitivities can be reached for interferometry with free evolving ensembles on time scales of several seconds, achievable by operating on a microgravity platform.
Such long interrogation times necessarily require ensembles with ultra-low expansion rates, making collimated Bose-Einstein condensates (BEC) the ideal input states. Therefore a method called magnetic lensing is used to narrow the momentum distribution. Together with the very good coherence properties of BECs, this reduces uncertainties in the interferometric measurement and enables high-fidelity beam splitter processes like Bragg diffraction.

Within the scope of this thesis, a novel matter-wave lens system is presented to lower the internal kinetic energy of a BEC to the picokelvin regime, which is then used to perform interferometric measurements in microgravity. This is achieved with the QUANTUS-2 apparatus, a high-flux rubidium BEC machine based on atom chip technology, which operates at the drop tower in Bremen.
Exploiting the excitation of a quadrupole mode in combination with a magnetic lens attains three-dimensional collimation of the BEC. With this technique, an unprecedented residual kinetic energy of $\sfrac{3}{2}k_B\cdot38\,$pK is achieved, where the ensemble is observed after an interrogation time of 2$\,$s with a high signal-to-noise ratio.

Upgrading the experiment to realize single and double Bragg diffraction enables the first demonstration of a double Bragg-based interferometer in microgravity with a retro-reflection setup. The symmetric splitting achieved with the double Bragg process doubles the enclosed interferometer area and reduces systematic effects compared to single diffraction techniques. A complete characterization is performed to optimize the beam splitting process and verify the feasibility of atom chip setups for interferometric measurements.

The potential of magnetically lensed BECs for interferometric measurements is investigated by probing the spatial coherence. To this end, a novel application of shear interferometry is developed to investigate the divergence of the magnetically lensed ensemble in analogy to an optical shear plate. Based on the interferometry pattern, the imperfections of the magnetic lens potential are studied, and the lens strength is optimized.
Shear interferometry even enables the spatially resolved determination of the BEC's velocity field based on the interferometry pattern. Consequentially, the internal kinetic energy can be deduced from a single absorption image. Especially compact, ground-based atom interferometers can profit from this characterization method since extended times of flight are not required. This shear interferometry represents a versatile tool to study BEC dynamics independently of the application in matter-wave optics.

The first demonstration of interferometry with picokelvin atomic ensembles and the tools developed in this work provide the basis to realize atom interferometry on extended time scales of several seconds. This will ultimately enable future space missions to employ cold atom interferometry at unrivalled levels of precision.