All-optical matter-wave lens using time-averaged potentials
Henning Albers, Robin Corgier, Alexander Herbst, Ashwin Rajagopalan, Christian Schubert, Christian Vogt, Marian Woltmann, Cláus Lämmerzahl, Sven Herrmann, Éric Charron, Wolfgang A. Ertmer, Ernst Maria Rasel, Naceur Gaaloul, Dennis Schlippert
Abstract The stability of matter-wave sensors benefits from interrogating large-particle-number atomic ensembles at high cycle rates. The use of quantum-degenerate gases with their low effective temperatures allows constraining systematic errors towards highest accuracy, but their production by evaporative cooling is costly with regard to both atom number and cycle rate. In this work, we report on the creation of cold matter-waves using a crossed optical dipole trap and shaping it by means of an all-optical matter-wave lens. We demonstrate the trade off between residual kinetic energy and atom number by short-cutting evaporative cooling and estimate the corresponding performance gain in matter-wave sensors. Our method is implemented using time-averaged optical potentials and hence easily applicable in optical dipole trapping setups.
Abstract The stability of matter-wave sensors benefits from interrogating large-particle-number atomic ensembles at high cycle rates. The use of quantum-degenerate gases with their low effective temperatures allows constraining systematic errors towards highest accuracy, but their production by evaporative cooling is costly with regard to both atom number and cycle rate. In this work, we report on the creation of cold matter-waves using a crossed optical dipole trap and shaping it by means of an all-optical matter-wave lens. We demonstrate the trade off between residual kinetic energy and atom number by short-cutting evaporative cooling and estimate the corresponding performance gain in matter-wave sensors. Our method is implemented using time-averaged optical potentials and hence easily applicable in optical dipole trapping setups.
The precision of atom interferometers, targeted for example in the Hannover Very Long Baseline Atom Interferometer (VLBAI) facility, imposes stringent requirements in several respects. They concern the control of center-of-mass motion and expansion of the wave packets by the matter-wave source as well as the number of atoms. By reducing the expansion, systematic errors, appearing e.g. through wavefront aberrations, can be lowered. These requirements can be matched by employing ultracold quantum gases or even quantum degenerate gases. A promising method to create those ensembles is evaporative cooling in a spatially modulated optical dipole trap. Here, the utilization of time-averaged potentials enables the fast creation of ultracold atomic ensembles with large number of atoms. Both, the higher number of atoms and the increased repetition rate, enhance the performance of the interferometer due to a lower quantum projection noise, which scales with 1/sqrt(N), and a larger bandwidth of the sensor due to faster sampling. The shaping of the matter-waves by techniques such as matter-wave lensing or Delta-Kick collimation is also feasible due to the dynamic control of the trapping potential. In this thesis the implementation and application of dynamic time-averaged optical potentials created via center position modulation of dipole trap beams is demonstrated. By evaporative cooling in these potentials, 1.9(0.4) x 10^5 condensed atoms with an expansion temperature of 29.2(1.3) nK were achieved after 3 s of evaporation. Up to 4.2(0.1) x 10^5 condensed atoms could be observed with slower evaporation of 5 s. Subsequent matter-wave lensing is carried out yielding expansion rates as low as 553(49) μms^-1 resulting in an effective temperature of 3.2(0.6) nK in two dimensions. This lens can be applied at any stage of evaporative cooling, thus short-cutting the generation of ultracold effective temperatures. In this thesis the limitations of optical matter-wave lensing in the current setup are revealed and ways to improve the performance are discussed. The fast generation of ultracold atomic ensembles will enhance the performance of the dual-species atom interferometer, which represents the experiment apparatus for this thesis and strives for a test of the Universality of Free Fall with an uncertainty on the order of 10^-9. The results of this thesis were used to test numerical simulations which were utilized to show the perspective of generating up to 10^6 collimated condensed atoms within 1 s of cycle time in the rubidium source system of Hannover’s VLBAI.
Inertial navigation systems are vital for modern society, be it on airplanes or in the context of autonomous mobility. On the other hand atom interferometers are exquisite measurement devices for inertia in fundamental physics and field applications, but are mostly limited to measuring one inertial observable. By utilizing time averaged optical potentials, the ultra-cold atomic ensemble input to the interferometer can be prepared in nearly arbitrary fashion. This results in a boost of preparation speed and number of atoms in the interferometer by increasing the size of the trap to match the size of the pre-cooled ensemble for optimal loading. Successive fast reduction of the extend of the trap leads to optimal evaporation efficiency and leads to increased sensitivity of the device, due to reduced cycle time of the experiment and increased atom number. Beyond this, the technique allows for new sensor geometries via the creation of multiple single wells, allowing for differential atom interferometry with numerous simultaneous interferometers. In this thesis, the first matter-wave analogue of a classical accelerometer array is implemented via the creation of a 3 × 3 array of Bose-Einstein condensates, consisting of 3 × 105 atoms and spanning a total area of 1.6 mm2 . Successive manipulation of the matter-waves with atom optics, coherently addressing the momentum states of the ensembles, allows for splitting, redirecting and readout pulses, realizing Mach-Zehnder type atom interferometers. Correlation of the nine 1D-acceleration measurements output by the interferometers yields measurements of linear acceleration, Euler- and centrifugal acceleration. The estimated sensitivity limits per shot are 6 × 10−5m s−2 for linear acceleration, 0.19 rad s − 2 for rotational acceleration and 203 mrad s−1 for rotation rate and are mainly limited due to the short free fall time of the ensembles, constrained by the atom optics light field. The correlation also allowed to determine the rotation center, being close to the retro reflection mirror of the atom optics light field. Crucial for the realization of this measurement was the implementation of time averaged potentials as stated above, facilitated through two 2D acousto-optical deflectors and a software defined radio, allowing for generating the required RF-signals. The techniques to simultaneously load and evaporate multiple ensembles into distinct traps from a single cloud of cold atoms and subsequently enlarge the spacing between the ensembles with adiabatic transport ramps are of highest interest for e.g. the Very Long Baseline Atom Interferometer facility in Hannover. Due to the correlated outputs systematic errors, such as wave front abberations, can be nullified. Furthermore the scheme can be extended to 3D matter-wave arrays, fulfilling all requirements necessary for an autonomous inertial measurement unit.
Using a matter wave lens and a long time of flight, we cool an ensemble of ^{87}Rb atoms in two dimensions to an effective temperature of less than 50_{-30}^{+50} pK. A short pulse of red-detuned light generates an optical dipole force that collimates the ensemble. We also report a three-dimensional magnetic lens that substantially reduces the chemical potential of evaporatively cooled ensembles with a high atom number. By observing such low temperatures, we set limits on proposed modifications to quantum mechanics in the macroscopic regime. These cooling techniques yield bright, collimated sources for precision atom interferometry.
Most cold atoms experiments in microgravity platforms or in Space are achieved using atom chips, leading to limitations in terms of optical access and inhomogeneous magnetic fields. Optical dipole traps do not have these drawbacks but have difficulties producing atomic samples with a large number of atoms at ultra low temperature in the absence of gravity. Here, we report on an efficient evaporative cooling in two-crossed laser beams during parabolic flights. Time-averaged potentials combine the advantages of large capture volume and trap compression, increasing the initial phase space density and collision rate to favor the evaporative process. With this technique we demonstrate the production of an ultra cold gas of 2.5×104 rubidium atoms at a temperature below 100 nK in less than 4 seconds. Our experiment paves the way for the development of quantum sensors applied to fundamental physics and geodesy as well as the study of ultracold atomic physics in Space.
Ultra-cold atoms have become indispensable in quantum sensing, quantum computing, and quantum communication applications, as well as in fundamental sciences. In quantum sensing, they enable precision measurements with outstanding sensitivities that can be of great benefit in navigation, geodesy, and fundamental physics applications. The sensitivity of the atom interferometers used herefore typically scales with the square of the interrogation time. Therefore, in atom interferometric measurements, one seeks ensembles that feature a particularly low internal kinetic energy and can thus be detected after a long time-of-flight. The lowest values are achieved using Bose-Einstein condensates in conjunction with delta-kick collimation, a technique for the collimation of the atomic wave function. Bose-Einstein condensation can be achieved using a multi-stage laser cooling scheme, followed by evaporative cooling, which finally brings the temperature down to the critical temperature, typically in the nanokelvin regime. In addition to the low thermal spread, microgravity enables particularly long observation times, as it avoids limitations of the interrogation time due to vacuum chamber constraints, which are present when falling freely under the influence of gravity. Additionally, microgravity enables measurements that are not possible under normal gravity conditions, such as buoyancy-free miscibility studies, truly uniform potentials, and advanced cold atom quantum memories, which are projected to feature unprecedented time-bandwidth products. For the preparation of a Bose-Einstein condensate, two techniques are widely used in science, namely magnetic traps and optical dipole traps. For microgravity missions, magnetic traps on atom chips have been used in nearly all setups so far due to their particularly low SWAP budget and high cold atom flux. In contrast, ground-based experiments often prefer optical traps due to their higher versatility, full optical access, and the absence of surfaces in proximity to the atoms, which is fundamental for precision measurements. Additionally, optical traps enable the manipulation of intra- and inter-species scattering lengths using Feshbach resonances. Compared to atom chip traps, they also feature an intrinsically better symmetry of the trapping potential, in theory leading to fewer aberrations in matter-wave optics. The latter could enable the generation of ensembles in the yet unreached femtokelvin regime using delta-kick collimation with fewer perturbations. This thesis is about the realization of a 1064nm optical dipole trap set up for the microgravity environment of the Bremen Drop Tower. It aims to highlight the advantages of optical traps in conjunction with microgravity and prepare optical trapping technology for use in future microgravity and space missions. The thesis describes the experimental setup, the direct loading process, the characterization of the optical potential, and the optimization and investigation of the evaporative cooling in the optical dipole trap. For the evaporation process, the influence of gravity is comprehensively investigated through analytical calculations and microgravity tests. Bose-Einstein condensation is demonstrated, proving the achievement of condensation through absorption imaging of the spatial distribution, tests on the free evolution of the ensemble, and investigation of the phase-space densities achieved. Up to (74 ± 4)% condensation of an ensemble featuring (30 000 ± 13 000) atoms at a kinetic temperature of (37 ± 3) nK is demonstrated. The evaporation shows high efficiency down to a 3 s evaporation time, while a critical phase-space density can be achieved within (1.29 ± 0.07) s using an even faster evaporation ramp. This opens the door to fundamental physics experiments on Bose-Einstein condensates in microgravity, as well as applications pursuing atomic ensembles with exceptionally low expansion velocities.
We present experiments with cold atoms in optical dipole potentials which are directed towards developing an integrated coherent atom optics with micro-optical systems. We describe an experiment on evaporative cooling in a far-detuned optical dipole trap for ⁸⁷Rb. The dipole trap is created by a solid state laser at a wavelength of 1030 nm. To achieve high initial phase space densities allowing for efficient evaporative cooling, we have optimised the loading process from a magneto-optical trap into the dipole trap. Starting with an initial phase space density of 2 × 10⁻⁴ the trap depth was ramped down and temperatures below 200 nK and phase space densities of about 0.2 could be reached. These investigations aim at the creation of an ’all-optical’ BEC based on a simple experimental scheme. As an example for an integrated atom optical system, we present the transport of atoms in a ring-shaped guiding structure, i.e. optical storage ring, for cold atoms which is produced by a micro-fabricated ring lens.