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Theoretical study of quantum gas experiments in an Earth-orbiting research laboratory

Annie Pichery

Published Apr 1, 2024• 0 citations
Publisher

Abstract

One of the major goals of fundamental physics is to unify general relativity, which describes macroscopic phenomena driven by the influence of gravity, with quantum mechanics, which focuses on effects at microscopic scales. Ensembles of cold atoms, as massive quantum objects, lie at the crossroads of both theories and appear as a test object of choice. They can be used to test theories that postulate a violation of Einstein's Equivalence Principles, in particular a violation of the Universality of Free Fall (UFF). Recent proposals suggest using mixtures of Bose-Einstein condensates (BEC) as sources for precision atom interferometry to perform UFF. These have the potential to match the precision of the best tests with classical test masses performed during the MICROSCOPE mission, and may even provide better results in the long term. The realization of experiments in microgravity, where atoms can float for long periods of time, allows longer interrogation times, thus increasing the performance of matter-wave sensors. To optimize the implementation of UFF tests, one needs exquisite control of the atoms due to stringent requirements on the error budget. In this work, we focus on the design of the input state with control over the position and velocity of the atom clouds, as well as their size evolution. The experiments studied here are designed with atom chip setups that manipulate atoms with magnetic traps. Most of the applications presented are experiments performed in the NASA Cold Atom Laboratory (CAL) aboard the International Space Station as part of the Consortium for Ultracold Atoms in Space (CUAS). This multi-user BEC machine allows the manipulation of single species BEC at its installation as well as dual species mixtures after upgrades. Following this chronology, we first study the dynamics of single species BEC and then extend the work to the manipulation of an interacting mixture of two BECs. The first step after calibrating the chip model is to design a fast and robust transport protocol to move the atoms away from the atom chip. We present and use a Shortcut-To-Adiabaticity (STA) protocol, based on reverse engineering, to transport the BEC and meet the requirements of position control at the sub-\textmu m level and velocity control at the hundreds of \textmu m/s level. The free expansion of the atom cloud with its inherent atomic density drop makes signal detection difficult. By analogy with light, it is possible to collimate the atom cloud with atomic lenses using the Delta-Kick Collimation (DKC) technique. Application to CAL resulted in expansion energies in the tens of pK level. To simulate the imaging process and to support the data analysis, theoretical models are presented that take into account the resolution effects of the camera and the frame transformations associated with the orientation of the camera or the orientation of the trapping potential with respect to the atom chip. Space allows the operation of Bose-Einstein condensate mixtures under miscibility conditions not possible on the ground. The colocation of the trap center for the different species in microgravity can lead to different topologies of the trap ground state. Moreover, the interaction energy between the species, which is almost negligible in the ground state, plays a significant role in the dynamics of the mixture during its transport. However, the simulation of the dynamics of interacting dual-species BEC mixtures is computationally challenging, particularly due to the long expansion times. In this work, scaling techniques to overcome these limitations are presented and illustrated in the case of space experiments in CAL and aboard sounding rockets. Such scaled-grid approaches make it possible to simulate long transports with free expansion times on the order of seconds, which would not be feasible with a fixed-grid approach on reasonable time scales, not to mention the problems of memory usage.

DOI
10.15488/17008

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The capability to reach ultracold atomic temperatures in compact instruments has recently been extended into space. Ultracold temperatures amplify quantum effects, while free-fall allows further cooling and longer interactions time with gravity - the final force without a quantum description. On Earth, these devices have produced macroscopic quantum phenomena such as Bose-Einstein condensation (BECs), superfluidity, and strongly interacting quantum gases. Quantum sensors interfering the superposition of two ultracold atomic isotopes have tested the Universality of Free Fall (UFF), a core tenet of Einstein's classical gravitational theory, at the 10−1210^{-12}10−12 level. In space, cooling the elements needed to explore the rich physics of strong interactions and preparing the multiple species required for quantum tests of the UFF has remained elusive. Here, utilizing upgraded capabilities of the multi-user Cold Atom Lab (CAL) instrument within the International Space Station (ISS), we report the first simultaneous production of a dual species Bose-Einstein condensate in space (formed from 87^{87}87Rb and 41^{41}41K), observation of interspecies interactions, as well as the production of 39^{39}39K ultracold gases. We have further achieved the first space-borne demonstration of simultaneous atom interferometry with two atomic species (87^{87}87Rb and 41^{41}41K). These results are an important step towards quantum tests of UFF in space, and will allow scientists to investigate aspects of few-body physics, quantum chemistry, and fundamental physics in novel regimes without the perturbing asymmetry of gravity.
Extended free fall enables experiments with quantum gases unbiased by gravity. Apart from a 10m-fountain, we have access to various platforms comprising the Bremen drop- and gravi-tower, the Einstein Elevator, sounding rockets as well as NASA‘s cold atom laboratory (CAL) in orbit, all offering experiments with different durations and repetition rates. Atom chips turned out to successfully create Rubidium Bose-Einstein condensates on these platforms. Recently we have lowered the expansion energies of Bose-Einstein condensates to an unprecedented level corresponding to 38pK which makes them an excellent resource for interferometry. We exploit the latter to study delta-kick collimation as well to extend interferometry times in free fall. Atom chips also allow to investigate quantum mixtures in absence of bouyancy. For this purpose, we have been creating potassium 41 BECs by sympathetic cooling with rubidium. These experiments were continued to space by sounding rocket missions and the CAL. In future, the recently inaugurated Einstein elevator as well as gravitower will be important platforms to increase the experimental cycles to study quantum gas mixtures and high-precision interferometry as well as to test fundamental physics such as Einstein’s principle of equivalence and the nature of dark energy on ground in free fall.
Dual-species atomic sources in space promise to be the testbed for a multitude of searches in quantum gas physics such as a precise test of the Universality of Free Fall (UFF), few-body physics, cold molecules and quantum bubbles. These experiments demand exquisite control over the expansion energies of both condensed ensembles as well as over their differential center-of-mass dynamics. We propose a trap-quenched collimation technique featuring in-trap excitations of collective modes compatible with state-of-the-art atom-chip setups. Using NASA's Cold Atom Laboratory aboard the International Space Station, we demonstrate it on a single-species 87^{87}87Rb condensate. By controlling the center-of-mass release dynamics, we observe free expansion times up to 700 ms and measure a two-dimensional expansion energy of kB⋅78±9  pKk_B \cdot 78\pm 9 \;\mathrm{pK}kB​⋅78±9pK in the imaging plane. A detailed model of the magnetically-induced dynamics indicates that this corresponds to a two-dimensional expansion energy of about kB⋅15−5+12  pKk_B \cdot 15^{+12}_{-5}\; \mathrm{pK}kB​⋅15−5+12​pK along two of the condensate's eigenaxes. Finally, we theoretically study this trap-quenched collimation scheme for a 41^{41}41K-87^{87}87Rb mixture, predicting a simultaneous collimation that meets the expansion energy requirements for a state-of-the-art UFF test at the 10−1510^{-15}10−15 accuracy level.
Abstract We report the status of the Cold Atom Lab (CAL) instrument to be operated aboard the International Space Station (ISS). Utilizing a compact atom chip-based system to create ultracold mixtures and degenerate samples of 87 Rb, 39 K, and 41 K, CAL is a multi-user facility developed by NASA’s Jet Propulsion Laboratory to provide the first persistent quantum gas platform in the microgravity conditions of space. Within this unique environment, atom traps can be decompressed to arbitrarily weak confining potentials, producing a new regime of picokelvin temperatures and ultra-low densities. Further, the complete removal of these confining potential allows the free fall evolution of ultracold clouds to be observed on unprecedented timescales compared to earthbound instruments. This unique facility will enable novel ultracold atom research to be remotely performed by an international group of principle investigators with broad applications in fundamental physics and inertial sensing. Here, we describe the development and validation of critical CAL technologies, including demonstration of the first on-chip Bose–Einstein condensation (BEC) of 87 Rb with microwave-based evaporation and the generation of ultracold dual-species quantum gas mixtures of 39 K/ 87 Rb and 41 K/ 87 Rb in an atom chip trap via sympathetic cooling.
Abstract Ultracold quantum gases are ideal sources for high-precision space-borne sensing as proposed for Earth observation, relativistic geodesy and tests of fundamental physical laws as well as for studying new phenomena in many-body physics during extended free fall. Here we report on experiments with the Cold Atom Lab aboard the International Space Station, where we have achieved exquisite control over the quantum state of single 87Rb Bose-Einstein condensates paving the way for future high-precision measurements. In particular, we have applied fast transport protocols to shuttle the atomic cloud over a millimeter distance with sub-micrometer accuracy and subsequently drastically reduced the total expansion energy to below 100 pK with matter-wave lensing techniques.
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.