NOTE: End date changed to 9/27/2024 per U. Israelsson/JPL (Ed., 10/20/21)

NOTE: End date changed to 9/30/2023 per U. Israelsson/JPL (Ed., 4/16/21)

NOTE: End date changed to 5/3/2021 per PI information (Ed., 5/6/19)

In this year of performance, we have focused on maintaining operations throughout CAL's fourth year on the ISS and the commissioning of an upgraded frequency reference capable of sympathetic cooling of potassium in flight. Notable achievements include: 1) The first demonstration of dual-species Bose Einstein condensates in space 2) Achieved simultaneous dual-species atom interferometry in orbit.

Our ongoing work over the next year will concentrate on preparing rubidium-87 and potassium-41 dual-species ultracold gases for our planned flight projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the CAL testbeds (Ground Test Bed/GTB and Engineering Testbed/EMTB), has and will be enabling to mature our studies and to optimize our utilization of CAL. We will further prepare for the upcoming installation, commissioning, and continuation of science using a new Science Module (SM3B) to be installed in CAL in 2023.

NOTE: End date changed to 9/27/2024 per U. Israelsson/JPL (Ed., 10/20/21)

NOTE: End date changed to 9/30/2023 per U. Israelsson/JPL (Ed., 4/16/21)

NOTE: End date changed to 5/3/2021 per PI information (Ed., 5/6/19)

In this sixth and seventh year of performance, we have focused on maintaining operations throughout CAL's second year on the ISS and the development, launch, and commissioning of the new AI capable science module that enabled atom interferometry in the flight system in 2020. Notable achievements include 1) The first demonstration of atom interferometry in orbit, 2) Imaging of ultracold atoms in 3 dimensions in CAL, and 3) Adiabatic Rapid passage of >80% of Rb atoms to the magnetically insensitive state in space.

Our ongoing work on this project will concentrate on working with the CAL Ground Test Bed (GTB), Engineering Testbed (EMTB), and CAL Flight Systems towards a) validating the flight hardware and b) proving all of the functionality of CAL for proof of principle and characterization studies to support our dual-species flight science projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the GTB has and will be enabling to mature our studies and to optimize our utilization of CAL.

NOTE: End date changed to 5/3/2021 per PI information (Ed., 5/6/19)

In this fifth year of performance, we have focused on the studies of molecular association using magnetic field ramps; this analysis has been finalized. This represents an alternative method to the one we have previously proposed (within this program) using RF fields and a manuscript covering such methodology is in preparation. We ultimately want to determine which of the methods for association and dissociation is more efficient in the microgravity environment. Our main finding is that a simple ramp scheme might not be sufficient to create a substantial number of molecules in the CAL's microgravity environment. We, however, further propose a scheme to fix this deficiency and verify that a much better molecular association efficiency can be expected.

Although the theoretical studies are nearly complete, experimental efforts have been hampered during this year due to required efforts by key group members to assist the CAL project in the Engineering Testbed (EMTB), Ground Test Bed (GTB), and Flight System throughout the first year of CAL's operation onboard the ISS. Significant milestones of the team that will help enable our flight project include: Leading the efforts that demonstrated CAL's minimum mission success criteria during the three-month commissioning phase after flight, demonstrated laser-cooling of 39-K using flight-hardware in the flight system and loading of potassium onto the atom-chip using flight-like hardware in the EMTB, and development of a new AI capable science module that will enable dual-species atom interferometry in the flight system in 2020.

During the sixth year, our ongoing work on this project will concentrate on working with the CAL Ground Test Bed (GTB), Engineering Testbed (EMTB), and CAL Flight Systems towards a) validating the flight hardware and b) proving all of the functionality of CAL for proof of principle and characterization studies to support our flight science projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the GTB has and will be enabling to mature our studies and to optimize our utilization of CAL.

The flight experiments, supported by theoretical investigations and measurements using the ground test bed facilities at JPL, will concentrate on the physics of pairwise interactions and low-energy s-wave Feshbach molecules in ultracold quantum gases as a means to overcome uncontrolled AI shifts associated with the differential center of mass of two atomic species influenced by gravity gradients and rotations. We will further utilize the dual-species AI, expected to be integrated into CAL, for proof-of-principle demonstrations of unprecedented atom-photon coherence times, phase-readout techniques, and characterizations of the rotational noise on the ISS for use in the next-generation of precision metrology experiments based on AIs in microgravity. Our proposed experiments require the effective position invariance, long free fall times, and extremely low temperature samples uniquely available with the CAL apparatus. It is anticipated that these studies can lead to the unprecedented level of control and accuracy necessary for future space missions, based on precision AIs, to test some of the most fundamental questions of modern physics.

In the fourth year of the project, we have finished our theoretical studies relevant for molecular delta-kick cooling, a possible cooling technique that can allow us to obtain much colder molecular samples for our interferometry studies as well as enable optimized collimation for two, initially co-trapped, atomic species. The differential ballistic expansion for two species is a limitation for achieving ultra-low temperatures for these dual-species gas studies in microgravity. In applying delta-kick cooling for molecules we found that the molecular internal degree of freedom can generate torques during the cooling process depending on the strength and duration of the delta-kick pulse. Such effects, although interesting from the fundamental point of view, are detrimental to our precision interferometry studies. Our analysis, therefore, focuses in determining the parameter regime in which such effects can be mitigated. We have developed a novel theoretical approach that accounts for the effects of the center-of-mass and relative motion of the molecules and additional studies are currently been performed in order to determine the final cooling efficiency. We are currently on the stage of developing other numerical tools to extract all the information necessary for qualitatively describing the delta-kick cooling technique for heteronuclear molecules in the microgravity environment.

We have also pursued during this year preliminary theoretical studies relevant for molecular association using magnetic field ramps. This represents an alternative method to the one we have previously proposed (within this program) using RF fields. We ultimately want to determine which of the methods for association and dissociation is more efficient in the microgravity environment. In order to qualitatively explore this problem, we developed a theoretical model in which a few atoms are subjected to an artificial trapping potential whose trap frequency is adjusted to reproduce the average interatomic distance in the ultracold gas. This model has been successfully used to analyze previous experiments in molecular formation and we will extend such an approach to include various quantitative aspects related to the few-body physics in the problem. In particular, processes that can lead to molecular losses during the magnetic field ramp and the possible formation of Efimov states. At this point, our studies were focused on a system with only two atoms. As a running test, this has all the ingredients relevant for our future experiments with dual species atomic gases (87Rb and 41K), a study to be performed in the next step of our program.

Although the theoretical studies are nearly complete, experimental efforts have been hampered during this year due to required efforts by key group members to build and test the CAL flight system. These efforts lead to the successful launch of CAL to the ISS on May 21, 2018. Therefore, during the fourth year, our ongoing work on this project has concentrated on working with the CAL Ground Test Bed (GTB) and CAL flight systems towards a) validating the flight hardware and b) providing all of the functionality of CAL for proof of principle and characterization studies to support the flight science projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the GTB has and will be enabling to mature our studies and to optimize our utilization of CAL.

The flight experiments, supported by theoretical investigations and measurements using the ground test bed facilities at JPL, will concentrate on the physics of pairwise interactions and low-energy s-wave Feshbach molecules in ultracold quantum gases as a means to overcome uncontrolled AI shifts associated with the differential center of mass of two atomic species influenced by gravity gradients and rotations. We will further utilize the dual-species AI, expected to be integrated into CAL, for proof-of-principle demonstrations of unprecedented atom-photon coherence times, phase-readout techniques, and characterizations of the rotational noise on the ISS for use in the next-generation of precision metrology experiments based on AIs in microgravity. Our proposed experiments require the effective position invariance, long free fall times, and extremely low temperature samples uniquely available with the CAL apparatus. It is anticipated that these studies can lead to the unprecedented level of control and accuracy necessary for future space missions, based on precision AIs, to test some of the most fundamental questions of modern physics.

In the third year of this project, we have finished the analysis of the conditions for efficient molecular association and dissociation, crucial for our goal of producing a dual specie ultracold quantum gas that mitigates systematic errors in differential AI related to the center-of-mass displacement of the two clouds. These studies were accepted for publication in Physical Review A. Our findings indicate that the microgravity environment of CAL provides an ideal scenario for such studies.

We also initiated a theoretical study relevant for molecular delta-kick cooling, a possible cooling technique that can allow us to obtain much colder molecular samples for our interferometry studies as well as enable optimized collimation for two, initially co-trapped, atomic species. The differential ballistic expansion for two species is a limitation for achieving ultra-low temperatures for these dual-species gas studies in microgravity. In applying delta-kick cooling for molecules we found that the molecular internal degree of freedom can generate torques during the cooling process, depending on the strength and duration of the delta-kick pulse. Such effects, although interesting from the fundamental point of view, are detrimental to our precision interferometry studies. Our analyses, therefore, focus on determining the parameter regime in which such effects can be mitigated. We have developed a novel theoretical approach that accounts for the effects of the center-of-mass and relative motion of the molecules and additional studies are currently being performed in order to determine the final cooling efficiency.

Still during this period of performance, we have also developed other numerical techniques in which molecular association and dissociation can be studies, e.g., during magnetic field ramps. We are also moving towards the elaboration of novel numerical techniques in which we will be able to study, in more detail, the effects of atomic and molecular losses during the association and dissociation processes. These studies, therefore, partially define our goals for the next funding year.

Recent and ongoing work on this project has also concentrated on working with the CAL Ground Test Bed (GTB) and Science teams in maturing the GTB to a) validate the flight hardware and b) provide all of the functionality of CAL in a ground-based lab system for proof of principle and characterization studies to support the flight science projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the GTB has and will be enabling to mature our studies and to optimize our utilization of CAL. This work will progress through the remaining two months of this third-year effort.

The flight experiments, supported by theoretical investigations and measurements using the ground test bed facilities at JPL, will concentrate on the physics of pairwise interactions and low-energy s-wave Feshbach molecules in ultracold quantum gases as a means to overcome uncontrolled AI shifts associated with the differential center of mass of two atomic species influenced by gravity gradients and rotations. We will further utilize the dual-species AI, recently integrated into CAL, for proof-of-principle demonstrations of unprecedented atom-photon coherence times, phase-readout techniques, and characterizations of the rotational noise on the ISS for use in the next-generation of precision metrology experiments based on AIs in microgravity. Our proposed experiments require the effective position invariance, long free fall times, and extremely low temperature samples uniquely available with the CAL apparatus. It is anticipated that these studies can lead to the unprecedented level of control and accuracy necessary for future space missions, based on precision AIs, to test some of the most fundamental questions of modern physics.

In the second year of this project, we finalized the science concepts, requirements, and feasibility studies for both the originally proposed flight project, studying Feshbach molecules as a tool to enhance high-precision AI-based experiments in space, as well as for the flight experiments to use the CAL dual-species AI to further mature the technology of high-precision AI for enabling future space-based fundamental physics missions. For each proposed study, the approach, science management and data analysis plans, generalized experimental sequences, science requirements, and all other relevant experimental considerations were compiled into a Science Requirements Document that was submitted for review in October, 2015. At the same time, our group presented and conditionally passed the Science Concept Review to the CAL Science Review Board, allowing the project to continue in its flight status.

As part of the Feshbach molecule filtering study we 1) Developed the specific sets of experimental sequences required to associate and dissociate the heteronuclear molecules with minimal heating and loss. 2) Characterized the expected efficiency for removing unpaired atoms while minimally perturbing the Feshbach molecules. 3) Developed the dual-species imaging routine, error budgets, and analyses for optimally measuring the differential density distributions for the dissociated clouds and estimated the total averaging time required to achieve differential center-of-mass accuracy on the nanometer scale. 4) Identified the ground tests required to sufficiently characterize the atomic and molecular loss rates, heating rates, and all potential ground tests to optimally utilize the experimental time with the CAL apparatus on the ISS, and 5) Identified potential shortfalls and mitigations for this study.

For the dual-species AI studies, our tasks over the year included: 1) Calculated the expected contrast and systematic shifts based on the Bragg-beam design. 2) Developed the experimental sequences for demonstrating extended atom-photon coherence in a 3-pulse AI in free fall. 3) Developed the experimental sequences for observing rotational phase-fringes on the ISS. 4) Quantified the expected SNR and optimum sensitivity for the dual-species AI, leading to the required interrogation times and expected precision of each measurement. 5) Identified the possible AI-based ground tests to optimally utilize the experimental time with the CAL apparatus on the ISS, and 6) Identified potential shortfalls, mitigations, and applications of the CAL AI, including the feasibility of using the CAL AI during the anticipated down time as a high-precision sensor for local accelerations and rotations.

Recent work on this project has concentrated on assisting the CAL Ground Test Bed (GTB) and Science teams in maturing the GTB to a) validate the flight hardware and b) provide all of the functionality of CAL in a ground-based lab system for proof of principle and characterization studies to support the flight science projects. Due to the technical innovations required in our project and the sensitivity to numerous experimental/environmental parameters, access to the GTB will be enabling to mature our studies and to optimize our utilization of CAL. This work will progress through the remaining two months of this second-year effort.

The effects of low-frequency ISS vibrations on the performance of CAL and on our experiments requiring high-stability dual-species imaging capabilities were a significant concern at the beginning of the task. To address these issues, we developed a general algorithm to collect and analyze the raw accelerometer data from the Principal Investigator Microgravity Services (PIMS) website for the 121F04 SAMS sensor located nearest the projected CAL location. A representative acceleration record for the entire day of January 01, 2015 was analyzed, from which we determined that the displacements between the ultracold atoms in free fall and the CAL apparatus, from ISS vibrations, are on the order of 10s of microns, negligible in comparison to the distance from the atoms to the surfaces of the Science Chamber and also as compared to the diameter of the AI Bragg beam. Further, we considered the effects of ISS vibrations on the ability to determine the overlap of two clouds that are sequentially imaged. Assuming that the images of the two clouds are taken within 100 microseconds of each other, and assuming that vibrations at all frequencies above 200 Hz is negligible, the displacement extrapolates to a root-mean-square displacement between the two images on the order of 10 nanometers along all directions, well-below the camera resolution. Vibrations from hardware on the CAL apparatus and the related effects still need to be characterized and similar analyses will be required when that data becomes available.

Our main project explores a unique energy regime for studying the dynamics and adiabaticity in associating/dissociating long-lived, heteronuclear Feshbach molecules from low-density, dual-species gases at 100s of pK. During this year, we completed many of the theoretical investigations that were required to understand the lifetime and heating rates/mechanisms in these ultra-low energy gas studies on CAL. It is well known that at large scattering lengths (a), three-body collisions can lead to the formation of deeply bound states with large enough kinetic energy to make them escape from typical traps. Therefore, three-body losses set an important time scale within which our experiments have to be performed, i.e., before losses start drastically affecting the atomic and molecular densities. We used our previously calculated semi-analytical results and those from K. Helfrich et al., Phys. Rev. A 81, 042715 (2010) in order to estimate the importance of three-body losses for the experimental scenario described in our proposal.

The free-atom lifetimes are found to be long for small values of a, and they reach a minimum value for a << 1/(2uT)^(1/2), where u is the three-body reduced mass. As the temperature decreases [implying the decrease of the atomic densities for a given phase-space density and interparticle interaction strength], the lifetime increases for all values of a. Temperatures of about 100pK and densities of the order of 10^8 /cm^3 are expected to be accessible at CAL, which would allow for lifetimes greater than 1s for values of a<10^5 a0, where a0 is the Bohr radius. For inelastic atom-molecule collisions, similar temperatures and densities correspond to lifetimes in excess of 100s of milliseconds. It should be stressed that the presence of three-body (Efimov) and atom-molecule resonances are expected in the range of scattering lengths accessible on CAL, in the close-vicinity of which, the lifetime can be reduced significantly. Ground studies are planned to map out the Efimov resonances in our system to optimize the flight studies and avoid anomalous loss due to these resonant loss channels. More detailed analyses of three-body, atom-molecule, and molecule-molecule losses will be performed as results from the ground studies become available.

One other collisional effect that can lead to systematic errors in preparing our initial state for interferometry (two perfectly overlapping clouds of Rb and K) are elastic atom-molecule collisions. In this case, elastic collision can introduce additional momentum to the molecules, which in turn can affect the molecular dissociation rates. Therefore, we also estimated the typical collision time in which elastic atom-molecule collisions are important. We found that the collision times are considerably shorter than the lifetime corresponding to inelastic atom-molecule for large values of a, by an order of magnitude or greater. This indicates that some attention will be required to understand the effects of elastic atom-molecule collisions in our system. We note, however, that since elastic rates can vanish for some specific values of the scattering lengths, it is possible to minimize the atom-molecule collisional effects. The actual position of such zeros, however, can only be determined from ground experiments or through full numerical simulations.

The CAL AI is developed as a technology demonstration to perform experiments related to atom interferometry in microgravity on a “best effort” basis. The great majority of the work developing the dual-species AI and incorporating it into the already-mature CAL system design was carried out before the start of this NRA. However, on April 28, 2014, the atom interferometer was peer-reviewed as a delta PDR (preliminary design review) for this subsystem. I supported this review by developing the AI performance budget and as a consultant for required hardware developments for the AI upgrade. I was also a reviewer at the PMR2/TIM of ColdQuanta's chip trap and atom interferometer designs on November 3, 2014. My findings and recommendations for the CAL AI system are summarized below.

The pointing of the Bragg beam must be constrained to (a) maintain the optical lattice-depth and (b) maintain overlap with the atomic clouds throughout the AI sequence. After delta-kick cooling, the 87Rb (39K) atoms have a Gaussian width on the order of 200 (400) microns, whereas the Bragg beam diameter is designed to be 1 mm. Lateral translations of the Bragg beam should be made as stable as possible to preserve contrast and to minimize wavefront-related systematic shifts for precision measurements; however, vibrations of the ISS, discussed previously, practically limit the overlap of the Bragg beam and the free-fall atoms to 10s of microns with no benefit for lateral pointing stability beyond this level. Further, if the atoms travel a maximum of two inches from the chip in the science cell, the mirror must be normal to the Bragg beam to within 2 mRad at all timescales! This level of pointing-accuracy is also required to assure that the atoms don't drift out of the Bragg beam during interferometry. This is a requirement on the overlap of the incident and reflected beams so absolute pointing accuracy is required.

The curvature of the coated chip surface and the mode of the beam out of the GRIN lens are also a concern, with different constraints for beam-overlap and for controlling systematic shifts for precision measurements. I proposed that the ColdQuanta team characterize the beam wavefront out of the GRIN lens and also after reflection from the entire AI beam path (including the coated chip during operation and through the vacuum cells). I recommend using a Shack-Hartmann wavefront sensor camera that will provide unambiguous pictures of the wavefronts for a quick measurement of the curvature.

The contrast of the CAL AI and the loss of atoms from the interferometer are calculated with a simple model that we developed, taking into account the temperature-dependent density profile of the atomic gases in freefall and the spatially dependent Rabi frequency for the two-photon Bragg pulses in a Mach-Zehnder AI. We find that there is a complicated tradeoff between the initial temperature, cloud size, and Bragg pulse-width for achieving the optimum contrast and population in the AI. These constraints arise due to the significant initial atom size in comparison to the Bragg beam waist for the coldest delta-kick-cooled samples (100 pK), the faster rate of ballistic expansion at higher (1 nK) temperatures, and the Doppler width of the transitions for the ultracold clouds. The model allows us to optimize the interferometer interrogation time, the time-dependent cloud density, and the temperature and pulse times depending on the sensitivity and temperature requirements of the AI experiments planned. Further, we calculated the noise requirements on the retro-reflecting mirror fluctuations and the Bragg laser noise to demonstrate that these effects will negligibly affect the performance of the CAL AI based on the known ISS vibration environment and the laser system performance already characterized for CAL.

In the final two months of our first-year effort, we will concentrate on preparing for the Science Concept Review (SCR) that is expected to be held sometime in May, 2015. It is expected that in March, a CAL performance package will be sent out to the NASA Research Announcement (NRA) PIs highlighting the expected CAL system performance and noise characteristics, and hopefully information about the imaging system, SNR, and software or PI interface. This information will then guide the following tasks that will be among the subjects reviewed at the SCR:

For the Feshbach molecule filtering study we anticipate to 1) Develop the specific sets of experimental sequences required to associate and dissociate the heteronuclear molecules with minimal heating and loss. 2) Characterize the expected efficiency for removing unpaired atoms while minimally perturbing the Feshbach molecules. 3) Develop the dual-species imaging routine and analyses for optimally measuring the differential density distributions for the dissociated clouds and estimate the total averaging time required to achieve ~nanometer level differential center-of-mass accuracy. 4) Identify the ground tests required to sufficiently characterize the atomic and molecular loss rates, heating rates, and all potential ground tests to optimally utilize the experimental time with the CAL apparatus on the ISS and 5) Identify potential shortfalls and mitigations for the study.

For the dual-species AI studies, our tasks over the next two months include: 1) Calculate the expected contrast and systematic shifts based on the measured Bragg-beam characteristics. 2) Develop the experimental sequences for demonstrating extended AI time by refocusing the 87Rb atomic clouds with a near-resonance dipole trap. 3) Develop the experimental sequences for observing rotational phase-fringes on the ISS. 4) Quantify the expected SNR and optimum sensitivity for the dual-species AI, leading to the required interrogation times and expected precision of each measurement. 5) Identify the possible AI-based ground tests to optimally utilize the experimental time with the CAL apparatus on the ISS. and 6) Identify potential shortfalls, mitigations, and applications of the CAL AI, including the feasibility of using the CAL AI during the anticipated down time as a high-precision sensor for local accelerations and rotations.