NOTE: End date changed to 8/31/2021 per U. Israelsson/JPL (Ed., 5/12/2020)

NOTE: End date changed to 4/30/2020 per PI (Ed., 5/1/19)

Microgravity offers an increased set of technical possibilities for how ultracold atoms can be manipulated. Accordingly, our team has performed extensive numerical studies to exploit new ways of preparing the atoms in the internal states needed for the proposed few-body experiments. Such state preparation steps need to be carefully designed so that unwanted heating of the ultracold sample is avoided. To easily implement new procedures, we have also developed a Python-based table builder to better automate the task of writing programs with which the NASA Cold Atom Lab (CAL) apparatus can be controlled.

After the installation of SM3B on the International Space Station (ISS), an anomaly was detected during the commissioning phase when surprisingly short lifetimes of the atomic clouds were measured. An intense sequence of studies conducted by the JPL team concluded that the root cause was an issue with CAL’s ultrahigh vacuum. Fixing this problem requires the exchange of SM3B for an already built and tested science module, SM1. SM1 has successfully been used in ground-based studies at JPL since the original launch of CAL SM2 in 2018; however, this module has a slightly different magnetic field configuration than SM3B (due to the layout of the current-carrying tracks on the atom chip). We are therefore currently in the process of adapting our magnetic field models and experimental procedures to be able to quickly start potassium experiments after the installation of SM1 to the ISS.

In another line of work, we have provided input to NASA for the development of an updated version of the Physical Sciences Informatics (PSI) database. PSI is the central hub for accessing the experimental images taken with CAL. While our team has developed an efficient code for handling data downloads and locally organizing our data, it was clear that PSI had a number of shortcomings. In 2023, NASA decided to undertake an overhaul of the PSI database, leading to PSI 2.0. To support this development, we worked together with the NASA/JPL team to assemble a list of suggested improvements that will enhance the user experience of PSI 2.0. Now that these changes and upgrades are installed, we are retooling our local data handling software to provide us with the most efficient data evaluation. This is done using a custom software suite programmed in Python.

Theoretical research conducted by our group has been spearheaded by Jose D’Incao. This research focused on comparing the behavior of potassium-39, as used in CAL, with lithium-7, a species that is used in Earth-based studies. This comparison led to important insights, pointing at directions in which our theoretical models can be further improved to interpret forthcoming results from CAL. Such improvements have been and will continue to be one of our major tasks for our theory work during the next grant period.

During this grant period, a number of undergraduate and graduate students have worked on this project. At Washington State University, graduate student, Colby Schimelfenig, has worked with co-Principal Investigators (co-PIs) Engels and Mossman to analyze data from PSI and to continue to model the experimental system. At University of San Diego, Mossman engages with a number of undergraduate researchers to plan experiments and learn how to perform experiments remotely. One of these students, Kathryn Anawalt (now at Boeing), developed a new Python-based programming tool to make building programs for CAL experiments more familiar for the PIs across the collaborations. In doing this, she worked closely with Mossman and Jason Williams (JPL) to make sure limitations of the apparatus were incorporated to reduce mistakes in the writing of experimental control sequences. During Summer 2023, Kathryn visited JPL, taking a tour of the facilities and measuring the magnetic field strength for the “fast Feshbach coils” at the ground testbed. These tests verified that the magnetic field strength of the coils matched our models, an important benchmark for our studies.

A microgravity environment offers fascinating new perspectives for the investigation of intricate quantum mechanical few-body physics. The study of new phases of matter as well as applications to interferometric measurements are two examples for highly promising paths forward with direct relevance for topics suggested by the recent Decadal Survey. Within the frame of CAL, our team, as well as the team of Jason Williams and Ethan Elliott (JPL), are working in these directions. We are actively collaborating with Drs. Williams and Elliott to further promote few-body physics in microgravity through various channels. We have submitted white papers providing input for the recent Decadal Survey, have presented talks at a joint US-German workshop on future cooperation, and have presented a combined talk of our teams at the FunPAG Virtual Science Workshop in January 2024 to formulate input to NASA’s Fundamental Physics Program.

We have additionally made efforts to discuss the importance of few-body physics to the younger generation and to the general public. At the launch of SM3B from the NASA Wallops Flight Facility, co-PI Mossman took part in an outreach effort to bring CAL science to the public in an interview conducted by NASA Public Relations (PR) alongside JPL’s Jason Williams. In November 2023, Mossman presented a colloquium talk at California State University, Long Beach dedicated to performing ultracold atom experiments in microgravity, with a focus on few-body physics. This talk engaged primarily undergraduate and masters-level physics students.

Our team will continue to closely work together with the scientists and engineers at JPL to advance few-body research in microgravity and to promote CAL and microgravity research to the scientific community and general public.

NOTE: End date changed to 8/31/2021 per U. Israelsson/JPL (Ed., 5/12/2020)

NOTE: End date changed to 4/30/2020 per PI (Ed., 5/1/19)

The CAL instrument operates with two different atomic elements, rubidium and potassium. Due to the particular energy level structure of the atoms, only potassium allows one to manipulate the interatomic interaction strength within experimentally accessible regimes. Our experiments to create and measure exotic few-body bound states require the potassium atoms in the sample to be at temperatures very near absolute zero. While rubidium can be cooled using standard laser cooling and evaporative cooling techniques, these methods are inefficient for cooling potassium. To circumvent this difficulty, potassium is cooled by bringing it in thermal contact with ultracold rubidium, using the latter as a “refrigerant”. This requires simultaneous dual species operation of the CAL instrument, making the experiments more complex than single species experiments. However, the added complexity comes with a large payoff, as dual species operation and the ability to manipulate interatomic interactions are two essential ingredients for advanced current and future quantum gas experiments, including few-body measurements and differential atom interferometry, which strive to support the development of cutting-edge quantum devices.

CAL first demonstrated the sympathetic cooling of potassium in 2022. These early demonstration experiments successfully generated ultracold clouds, but also displayed a number of issues in need of optimization, including the achieved atom number, ultimate temperature, and the stability and reproducibility of the procedure. Furthermore, the atoms need to be prepared in a specific internal state to access the tunable interatomic interactions, requiring the precise application of radiofrequency and microwave pulses to excite atomic resonances. The frequency of these pulses depends strongly on the magnetic field environment in which the atoms are held, which in turn requires a precise experimental characterization using the flight instrument.

Our team, comprised of Principal Investigator (PI) Dr. Eric A. Cornell (JILA/University of Colorado), co-PI Dr. Peter Engels (Washington State University/WSU), co-I Dr. Maren Mossman (University of San Diego/USD) and Dr. Jose D’Incao (JILA/University of Colorado), has worked together with scientists and engineers at the NASA Jet Propulsion Lab (JPL) to conduct an extensive series of experimental runs characterizing the potassium performance and identifying the correct radiofrequency and microwave pulses. The investigations of radiofrequency resonances have provided our team with a precise calibration of the magnetic field environment, enabling us to devise a consistent theoretical model of the CAL apparatus. However, identifying the correct microwave resonances has been more difficult, despite our updated theoretical predictions. In an extensive series of investigations into this issue, we have concluded that the intensity of the applied microwave pulses delivered to the atoms is abnormally low. An unexpectedly low efficiency of the microwave transition was also detected in an independent measurement led by JPL. This triggered a major discussion with the CAL team at JPL to identify the root cause of this technical problem with the instrument, resulting in a change to the microwave setup and coil positioning for the upcoming replacement module SM3B. The ability to perform efficient microwave pulses is an important step for many applications and experimental procedures, so identifying this problem has been a critical step for the CAL project. To circumvent the problems with the current flight module, our team also developed an alternative scheme to prepare the atomic states that could work with significantly lower microwave powers.

To sum up the flight related portion of our work, the experimental studies conducted with the CAL instrument anboard the ISS have successfully characterized the radiofrequency transitions needed for state preparation but have also identified unexpected difficulties connected to the microwave setup. However, the lessons learned and the mitigating strategies developed to compensate these deficiencies will be highly valuable for future steps and experiments with this instrument. Our findings have informed changes to upcoming hardware replacements and will be important in designs for future space-based cold atom missions, as they have pinpointed areas of potential problems that will require careful engineering. With the upcoming installation of the new flight module SM3B, planned for the second half of 2023, we expect that a successful completion of these hardware exchanges will allow us to achieve the necessary state preparations and progress towards our research goals to measure few-body Efimov physics.

This project is a prime venue for the training of students. At WSU and USD, two graduate students, one post-bachelor student and one undergraduate student have contributed to the project. The students have been involved in all aspects of this project, including data handling and analysis, numerical modeling, discussing the results within our collaboration, and the presentation of the results at conferences. The results of our work have been presented at several conferences, including the 2023 NASA Fundamental Physics workshop in Santa Barbara and the 54th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (DAMOP). Work within the frame of this project has also been highlighted in several invited talks at academic institutions. Co-I Engels has co-authored a publication describing CAL in the journal Quantum Science and Technology which appeared in December 2022, together with the JPL team and other PIs of the CAL project. Drs. Mossman, D’Incao, and Engels are also co-authors on a joint publication with the JPL team and other PIs describing the commissioning of quantum gas mixtures and dual-species atom interferometry in space, available on the arXiv preprint server. The theoretical work conducted in the frame of this project has contributed to two publications co-authored by Dr. Jose D’Incao. [Ed. Note: For complete citations, see Bibliography.]

NOTE: End date changed to 8/31/2021 per U. Israelsson/JPL (Ed., 5/12/2020)

NOTE: End date changed to 4/30/2020 per PI (Ed., 5/1/19)

To generate Efimov states, the interaction strength between the atoms must be fine-tuned. In practice, this means the atoms need to be prepared in a specific environment with respect to the atoms’ internal state and the surrounding magnetic field. During the past year of this grant, our work has focused on the preparation of these required conditions. CAL operates with two atomic species – rubidium and potassium. While rubidium can efficiently be cooled using laser cooling and evaporative cooling, only potassium offers the ability to fine-tune the interaction strength with readily available magnetic fields. Potassium is more difficult to cool directly but can be cooled via thermal contact with cooled gaseous rubidium atoms. This “sympathetic cooling” requires magnetic fields and internal atomic states different from those required to achieve Efimov states. Therefore, after the cooling stage, we must take steps to prepare the state before we can perform experiments. These steps involve short pulses and frequency sweeps of microwave and radiofrequency radiation that we are currently optimizing.

After an initial phase of experimenting only with rubidium, CAL has progressed to dual species operation with rubidium and potassium in early 2022. The achievement of sympathetic cooling of potassium with rubidium by the NASA Jet Propulsion Laboratory (JPL) team has been a major success. Subsequently, we have identified the ideal microwave and radio frequencies needed for the state preparation of potassium. These resonances must be known precisely but vary depending on the local magnetic field. Therefore, they need to be found experimentally with the CAL apparatus. Our team has performed a successful series of such studies. These studies have also included commissioning a previously unused microwave generator for driving state transitions in potassium. Verifying the correct operation of this generator has been an important step not only for our experiments, but also for other investigations. Optimizing the correct state preparation for tuning interactions between atoms is now within reach and will be a major milestone towards new fundamental studies in Efimov physics. It will also be an important step for atom interferometry applications and inform the design of future experimental platforms.

Our work has been performed in a collaboration between JILA / University of Colorado (Professor Cornell / Dr. D’Incao), Washington State University (Professor Engels), and the University of San Diego (Professor Mossman). Cornell, Engels, and Mossman have worked together with the CAL team at JPL to design the flight experiments and analyze the resulting data. D’Incao has focused on the development of theoretical models to interpret the anticipated Efimov results and guide the experiments by identifying the necessary parameter regimes. The work has involved a postdoctoral researcher and three graduate students. Results have been presented at the 53rd Annual Meeting of the American Physical Society (APS) Division of Atomic, Molecular, and Optical Physics (DAMOP) in a presentation titled “Few-body Physics in Microgravity”, and in three invited talks at the Kavli Institute for Theoretical Physics (University of California, Santa Barbara), the Rochester Institute of Technology, and at the Congreso Nacional de Fisica de la Socieded Mexicana de Fisica (Tijuana, Mexico). All these presentations, as well as two manuscripts co-authored by D’Incao, acknowledge support by this grant.

The work of our team has been a prime venue for the training of students and postdoctoral researchers at the University of Colorado, Boulder, at Washington State University, and at the University of San Diego (USD). During this reporting period, one postdoc and three graduate students have been directly involved in this research. One PhD degree has been awarded. At the University of San Diego, Prof. Mossman is establishing a ground-based ultracold atomic, molecular, and optical physics (AMO) program, and the CAL project is creating a lot of excitement amongst her students. For example, at an event held at JPL this year to celebrate four years of CAL operation, the USD group has been represented by seven undergraduate students. Two students from the Mossman group also worked at JPL as summer interns, one working directly with the CAL project, and Prof. Mossman has advised and mentored a third JPL CAL intern on the simulation of magnetic fields.

NOTE: End date changed to 8/31/2021 per U. Israelsson/JPL (Ed., 5/12/2020)

NOTE: End date changed to 4/30/2020 per PI (Ed., 5/1/19)

Our experimental studies with the CAL apparatus have been accompanied by ground based studies conducted at both JILA and Washington State University (WSU). While JILA has continued its line of research into Efimov physics which provides highly relevant benchmark data for the planned CAL experiments, the WSU team has focused on studies into laser cooling and sympathetic cooling of potassium that provide insights into possible optimizations of the CAL procedures generating ultracold potassium clouds. JILA ground-based experiments have also expanded the focus to include a study of “implosions,” an effect where an ultra-cold atoms folds in upon itself after the interactions between the atoms are suddenly tuned to be attractive.

Our team has been in active discussions with the JPL team about the current CAL operation, about future extensions, and about the mitigation of anomalies that occurred with the instrument. Both graduate students and postdocs have been involved in this work in the frame of our collaboration. Furthermore, one of our team members, Maren Mossman, has contributed to the mentoring of a JPL “pre-doc,” working on code for the calculation of magnetic fields that was shared from our collaboration. Maren has also been interviewed and quoted in a Nature News article discussing CAL, and has been featured in a NASA JPL video for Women’s Equality Day in 2020. The research at JILA has resulted in an article published in Physical Review Letters, which is one of the highest ranked journals in this field of research.

During this reporting period, the theoretical component of our collaboration has focused on the implementation of several improvements that made the few-body numerical codes developed at JILA substantially accurate and efficient. These improvements have now been applied for various atomic species allowing for a more complete description of few-body processes with an emphasis on the importance of the spin structure in precisely determining the properties of Efimov states near Feshbach resonances. Other theoretical achievements include the development of numerical codes that determine elastic and inelastic atom-atom scattering properties for 39K and 87Rb atoms in an arbitrary spin state. These are necessary to determine the efficiency of the various experimental procedures to be further implemented at CAL and have been used frequently in our collaboration.

NOTE: End date changed to 4/30/2020 per PI (Ed., 5/1/19)

In 2019 CAL’s operations on board the ISS continued with Science Module 2 (SM2) until December 2019, when Science Module 3 (SM3) was launched to the ISS as an AI-enabled replacement of SM2. With SM2, we successfully used Rb-87 to test the traps needed to perform our planned few-body studies with potassium, confirming that our model replicated the trapping frequencies found for a trap with the necessary magnetic field characteristics. At the end of 2019, SM3 was launched to the ISS and installed at the start of 2020. The new science module has required a new numerical model and new calibrations. We have updated our calculations accordingly, both with basic Mathematica and with a new software package. We are currently developing strategies with the JPL team to calibrate the bias fields of SM3 to ensure accurate models. Along those lines, we have discovered a clear discrepancy with the manufacturer’s specification of one of the magnetic coil pairs (the Fast Feshbach coils), which we believe is due to an error in the manufacturer’s calibration routine. We plan to resolve this soon together with the JPL team. A deep understanding of CAL’s performance and magnetic field stability is key for the optimization of the planned few-body experiments.

During the operation of SM2 it became clear that a microwave generator used to effect state changes in Rb is malfunctioning. Pinpointing the exact cause of the malfunctioning was challenging due to the limited telemetry available. To help analyze this problem, members of our team, including Eric Cornell, Peter Engels, and Maren Mossman, traveled to JPL in October 2019 to serve as independent advisors. In discussions with JPL scientists and engineers, we were able to suggest a series of tests that in the end were able to pinpoint the most likely problem. Ground based tests performed by JPL have been able to duplicate this error and plans for correcting this problem are currently being discussed at JPL. Correcting this problem is an important step not only for facilitating experiments for potassium, but also for specific Rb experiments that require the flexibility of changing hyperfine states between different manifolds.

Furthermore, our collaboration has continued to perform extensive accompanying studies on the ground in the Cornell lab at JILA and the Engels lab at WSU. While JILA has focused on experiments with 39K, the Engels lab at WSU has continued to work towards the formation of a quantum degenerate 41K gas. The variety of experimental approaches used in the ground-based studies at JILA and WSU allows us to validate a broad variety of aspect relevant for CAL. These studies not only serve to optimize the experimental procedures of our few-body experiments with CAL but have also produced a surprising science result. At JILA, our team has performed precision measurements with 39K that have resulted in an unprecedented calibration of the Feshbach resonance and knowledge of the exact scattering length at which the first Efimov trimer crosses the free-atom threshold. The experiments have been accompanied by theoretical investigations performed by Jose D’Incao. Compared to the previously known results, the new results are more precise by two orders of magnitude. This has enabled us to perform a precision measurement of the first Efimov resonance, leading to the surprising finding that a previously assumed “van-der-Waals universality” in the system is unambiguously broken. A theoretical analysis by Jose D’Incao has confirmed this surprising result. Furthermore, we have explored the temperature and density limits that constrain the observation of the first Efimov state in ground-based experiments. This work was published in Physical Review Letters in 2019 https://doi.org/10.1103/PhysRevLett.123.233402 . These studies have direct consequences for the planned measurement of the second, next higher Efimov state with CAL -- that can only been done with the flight module onboard the ISS -- by informing us about the required parameter regimes and optimal procedures.

Results of our research activities were presented at several conferences. In April 2019, we presented a poster at the NASA Fundamental Physics Workshop held in Washington DC. In December 2019, members of our team, Peter Engels and Maren Mossman, attended the BECCAL meeting in Ulm, Germany where we presented our planned Efimov studies with CAL and proposed future studies creating quantum droplets in microgravity. In addition to this, Peter Engels presented two talks on our work with CAL: one during the Physics Slam event at WSU’s Conference for Undergraduate Women in Physics (CUWiP) and the other at the WSU-hosted Northwest Quantum Nexus workshop for Quantum Computing, Sensing and Simulation with Cold Atoms.

Professor Jason Ho and his team at Ohio State University have been looking forward, both towards future more elaborate Cold-Atom work, and towards applications of related concepts to important topics like materials design and quantum information. Recent work focused in particular on how quantum simulation can be used to solve computationally difficult problems such as how to find find the ground state and the excitations of a doped antiferromagnet. Other results explained the properties of one of the most exotic new material currently under exploration, twisted bilayer graphene. This system has recently been shown to be a superconductor and could have interesting technological applications.

In summary, our continued experiments at JILA and at WSU are providing important benchmarks for the CAL apparatus, while our work with the CAL flight module onboard the ISS is contributing to a full characterization of the instrument in preparation for the planned Efimov measurements. As SM3 continues to be calibrated, we will optimize our model and procedures accordingly. Regarding the technical aspects of the CAL instrument, we will continue to work with JPL researchers on the microwave slice development before a potential launch of a new microwave module later this year.

In 2018 CAL’s operation on board the ISS has begun. We have been in constant discussions with the Jet Propulsion Laboratory (JPL) team to assist with and keep track of the calibration procedures that are being performed to evaluate the CAL instrument onboard the ISS. While science data runs with potassium are currently awaiting the optimization of potassium evaporation routines by the JPL team, the current calibrations performed using Rb in the CAL flight module already inform us about essential performance figures of CAL such as the vacuum limited lifetime, atom number stability, imaging capabilities, etc. A deep understanding of CAL’s performance is key for the optimization of the planned Efimov experiments.

Furthermore, our collaboration has performed extensive studies on the ground in the labs at JILA and Washington State University (WSU). These studies not only serve to optimize the experimental procedures of our Efimov experiments with CAL but have also produced a surprising science result. At JILA, we have performed precision measurements with 39K that have resulted in an unprecedented calibration of the Feshbach resonance and knowledge of the exact scattering length at which the first Efimov trimer crosses the free-atom threshold. The experiments have been accompanied by theoretical investigations performed by Jose D’Incao. Compared to the previously known results, the new results are more precise by two orders of magnitude. This has enabled us to perform a precision measurement of the first Efimov resonance, leading to the surprising finding that a previously assumed “van-der-Waals universality” in the system is unambiguously broken. A theoretical analysis by our collaborator Jose D’Incao has confirmed this surprising result. Furthermore, we have explored the temperature and density limits that constrain the observation of the first Efimov state in ground-based experiments. These studies have direct consequences for the planned measurement of the second, next higher Efimov state with CAL -- that can only been done with the flight module onboard the ISS -- by informing us about the required parameter regimes and optimal procedures.

While JILA has focused on experiments with 39K, efforts at WSU have been directed towards the formation of a quantum degenerate 41K cloud. This is the potassium isotope that will be used in later stages of CAL for extended Efimov studies and for atom interferometry experiments. The variety of experimental approaches used in the ground based studies at JILA and WSU allows us to validate a broad variety of aspect relevant for CAL. For example, laser cooling of the bosonic potassium isotopes poses particular difficulties related to the level structure of these atoms. We are developing optimized cooling strategies to address these difficulties and to provide an optimized starting point for the generation of quantum degenerate potassium clouds with CAL.

In summary, our ground based experiments at JILA and at WSU provide important benchmark results for the CAL apparatus. As more and more calibration and machine characterization is performed with the CAL flight module, we continue to update our proposed experimental procedures for the planned Efimov measurements. Our experiments have also delivered important science results, such as the characterization of a Feshbach resonance with a record precision (improving previous results by a factor of 100) as well as the unambiguous confirmation of breaking of a “van-der-Waals universality” that in the past had been an important paradigm.

In anticipation of the next-generation of CAL, we’ve been doing extensive theoretical work at Ohio State University, with a goal of understanding the exotic states of matter than can result when ultra-cold atoms rotate very rapidly. Generically known as “quantum Hall states,” the various excitations of these states are generally regarded as examples for hardware components for fault tolerant quantum computers.

Effort has been focused on (i) realizing quantum Hall states cold atoms in different platforms, (ii) the manipulation of the quasi-particles of the quantum Hall states, and (iii) quantum dynamics of multi-component quantum Hall states.

For Project (i),we study the feasibility of realizing quantum Hall states in rotating potentials generated by Digital Mirror Devices, while K.H. Chen studies the creation of quantum Hall states using photons, motivated by the recent experiments of Jon Simon’s group at University of Chicago to create quantum Hall states with photons in cavities. The latter work has led to the discovery of a “super-degenerate” quantum Hall regime in photonic systems, where all the higher Landau levels (such as those in Simon’s experiment) are made degenerate with the lowest one by simply adjusting the configurations of the laser beam. The degeneracy of “super-degenerate” manifold is considerably larger than those of the usual quantum Hall states, and is an exciting regime to study quantum many-body physics.

For Project (ii), we worked on the protocols to engineer singlet and triplet spin states of quasi-particles in a fully filled Landau levels with both spin up and spin down fermions. The creation and manipulation of these spin states with precision is crucial for the study of non-abelian exchanges processes in these systems, a process of key importance in quantum information processing.

For Project (iii), we have been studying the quantum evolution of ferromagnetic quantum Hall states in a quadrupolar field. The ferromagnetic quantum Hall state will emerge in a two-component fermions each in a half-filled lowest Landau level. The particular kind of quantum evolution we study will generate Skyrmion excitations in this ferromagnet. This work is in progress.

Our initial work has focused on the study of exotic three-body states. In 1970, theoretical physicist Vitaly Efimov predicted that, under certain conditions, three atoms can form a bound state even if the attractions between just two atoms are too weak to cause binding. CAL will provide a unique new environment for testing few-body systems in previously inaccessible regimes that are prerequisite for the next generation of Efimov experiments. We have worked diligently to prepare an experimental plan for research both at the ground test bed and with the CAL apparatus on board the ISS.

Over the past year, we have also extended the scope of our work to investigate quantum droplets using the CAL apparatus. Quantum droplets are an intriguing state of quantum matter that can be created out of a dilute-gas BEC. Quantum droplets are fluids, rather than gases, which means that they are characterized by a constant density and exhibit pronounced surface effects. They have a sparse excitation spectrum, making them essentially zero-temperature objects. Furthermore, they are self-bound, implying that they are stable, non-dispersing objects even in the absence of a trap. Their self-bound nature makes them ideal candidates for studies in microgravity: only in microgravity is it possible to investigate these droplets in the absence of any confinement, and thus in their purest form. Our goal is to measure basic properties of these systems, including their excitation spectrum, surface effects, and lifetime in microgravity, using the existing technology of CAL.

In the meantime, we have been working on some ground-based measurements that are complementary to our planned CAL-based measurements. We have made very precise studies of how ultracold gases (in particular, Potassium-39) collide as one changes the ambient magnetic field. In particular, we have determined the value of magnetic field at which an Efimov resonance occurs. We are in the midst of extensive calculations that predict the difference in magnetic field between this Efimov and the next highest up. That next resonance can not be accurately studied in a ground-based experiment, because temperatures on Earth, although very cold, are not cold enough. In the much colder temperature accessible on CAL, below one nanokelvin, we anticipate making the second, critical half of the comparison. These combined measurements will yield the most precise ever study of resonant three-body quantum mechanics.

In addition to our experimental work on Efimov physics, we have been doing some more purely theoretical investigations into rapidly rotating ultracold gases. Our hope is that these studies will provide the ground work for a more advanced set of ISS-based cold-atom experiments early in the next decade. These future experiments, combined with the Efimov studies planned for next year, will yield insight and understanding into the nature of the quantum mechanics of interacting particles. Quantum mechanics is the science of the very, very small, and if the trends of technology tell us anything, it is that the future of technology lies in the direction of the very small.

One component our project is to study methods to realize quantum Hall states in cold atoms systems. Quantum Hall states are remarkable quantum states with fractionally charge quasi-particles and fractional statistics. They can also be divided into two classes, those with the so-called “Abelian” statistics, and those with “non-Abelian” statistics. All of them are useful for quantum information storage, and the “non-Abelian” ones are found theoretically to be a robust hardware component for quantum computation – the so-called “fault’ tolerant qubits. The reason that these quasi-particles are so robust in holding quantum information is because of the strongly correlated nature of the quantum Hall state that prevents their decay, unlike the excitations in all other quantum systems. This correlated nature originates from the unique correlated mechanism of particles that rotate relative to one-another with fixed angular momentum, hence giving rise to usual exchange properties of the quasi-particle excitations.

In our proposal, we plan to realize quantum Hall states with bosonic and fermionic atoms using rotating quantum gases. The realization of these states is not to reproduce that known states in condensed matter, but to (i) find ways to locate and manipulate quasi-particles that are necessary for quantum information processing but have so far elude all solid-state experiments, (ii) to realize quantum Hall states (such as those of high spin particles) that are inaccessible to solid-state systems, (iii) to resolve long standing problems in quantum Hall effect such as whether the nu=1/2 and 5/2 fractional quantum Hall state is indeed the Pfaffian state that hosts non-Abelian excitations.

Recently, it is also realized that quantum Hall states can also be realized in a number of other cold atom systems, such as 2D optical lattices and optical ladders with artificial magnetic fluxes. Moreover, recent experiments at the National Institute of Standards and Technology (NIST) by Spielman’s group on the so-called Yang Monopole also suggest the possibility of realizing 4D quantum Hall systems. The fact that experiments in low dimensional space can access the physics in higher dimensional ones is an exciting possibility, and may even be a new avenue for quantum information processing.

In this cycle of NASA-funded research, we have looked into a number other topological matters that are closely related to quantum Hall systems, new physics settings to realize quantum Hall states, as well as mechanisms and protocols to locate and manipulate quasi-particles. The first is to realize the Majorana edge modes in 1D chains with fermions near p-wave resonance. The Majorana edge modes in 1D chains obey non-Abelian statistics like those in the Pfaffian states in quantum Hall systems. The system we considered is a generalization of the Kitaev model with the “p-wave superconductivity” replaced by the fluctuating closed channel bosons. This scheme is much simpler than other schemes to realize Majorana edge modes currently proposed for cold atom systems. We have performed exact calculations to prove that the Majorana edge modes indeed exist in these systems.

One recent and exciting venture in experiments with ultracold quantum gases is the three-body problem. In 1970, theoretical physicist Vitaly Efimov predicted that, under certain conditions, three atoms can form a bound state even if the attractions between just two atoms are too weak to cause binding. It was not until 2005 that this was first demonstrated in an experiment by a group at the University of Innsbruck. This initiated significant research efforts worldwide both in theoretical and in experimental research. Despite these efforts, further experimental input is needed to assist in theoretical predictions. CAL provides a unique new environment for testing few-body systems in previously inaccessible regimes that are prerequisite for the next generation of Efimov experiments. In preparation for CAL’s launch, our collaboration has modeled actual Efimov experiments to be conducted with CAL.

This past year, we have worked diligently to prepare for initial tests at the Ground Test Bed (GTB) and to prepare our cold atom apparatus at Washington State University (WSU) for corroborative tests with ultracold Potassium-39 clouds. To this goal, we have outlined an experimental plan for work at the GTB that will allow us to test and optimize our planned experimental strategies. This experimental plan will also provide benchmark results that will later be used to verify the proper operation of the CAL apparatus onboard the ISS. At the same time we have made great progress towards the generation of ultracold Potassium-39 clouds at WSU. The motivation behind these experimental efforts at WSU is twofold: First, we try to identify experimental steps that are specific to K-39 and that need to be optimized for the generation of ultracold Potassium-39 clouds with CAL. We have found a number of technical aspects that can affect the operation of a Potassium-39 experiment, and have discussed these aspects with members of the CAL team. A second motivation is the acquisition of control data that will later be needed to interpret the data taken with CAL.

Meanwhile, in the experimental effort at JILA, we have been performing ground-based few-body studies using ultracold atoms. These experiments are meant to compliment the results we anticipate harvesting from the ISS-based Cold Atom Lab in the next two years. We have explored the properties of a potassium/rubidium bose polaron, which is a tiny “snowball” of two or three ultacold atoms right at the conceptual boundary between few- and many-body physics. This work appeared in press in the elite physics journal, Physical Review Letters. We also completed and submitted for publication a ground-based experiment on efimov molecules in Rubidium-85. These efimov molecules were in the first excited state, quite analogous to the efimov molecules we will eventually examine in space, in Potassium-39. Because we were working in the influence of Earth’s gravity, we were unable to access the extreme low-temperature, low-density regime we will achieve in space, and thus we were not able to do the precise comparison we will do next year in space. Finally, we made progress towards completing a precision study on the ground-state efimov trimer in Potassium-39. This will be a control for a similar study done in space.

At the same time, our theoretical wing at Ohio State made progress on few- and many-body calculations of the properties of ultracold gases, with an emphasis on rotating gases, in anticipation of a possible second-generation Cold Atom Laboratory experiment. Our team focuses on “strongly Interacting Bose gas” and “Quantum Hall states of Bose gases.” Bosons are identical particles that tend to occupy the same quantum state. As a result, the ground state of a Bose gas will consist of atoms condensing in the same state, forming a “Bose-Einstein condensate,” thereby magnifying quantum phenomena to a macroscopic scale. It is highly unusual for a Bose system not to have a condensed ground state. Yet an uncondensed ground state can emerge under special circumstances. One example is the strongly interacting Bose gas in low dimensions, where bosons will effectively turn into spinless fermions to avoid interacting with each other. The other example is the fast rotating Bose gas, where the system has many single particle states of the same energy competing for condensation. As a result, the bosons fail to condense into a single state, but form a highly correlated wavefunction (called quantum Hall state) with many novel properties. Our NASA projects are to study the property of a three dimensional Bose gas in the strongly interacting limit, and to realize the quantum Hall state in the fast rotating limit. During last year, we have explored different ways to realize the bosonic quantum Hall states, and to identify their signatures. Achieving bosonic quantum Hall state turns out to be a very challenging task, as this state is strongly competed against by the usual condensed ground state. We noted that it is easier to the create a quantum Hall state of fermions, as their exchange properties (or “Fermi statistics”) favors formation of quantum Hall state. On the other hand, by varying the interactions between fermions, one can associate two fermions of opposite spin into a bosonic molecule, (as demonstrated by Deborah Jin’s group at JILA in 2003 and 2004). In this process, a fermionic quantum Hall state can turn into a bosonic one. The result of this work has been submitted to PRX for publication and is currently under review. This work has led to a number of invited talks at international conferences including the 90th year Cebebration of Fermi’s paper on Fermi statistics at the Galileo Institute for Theoretical Physics in June 2016.

As for identifying the signature with the bosonic quantum Hall state, we have worked out the properties of quantum Hall states in rotating traps with different ellipticity. Due to the intrinsic correlation of that quantum Hall state, the surface contour of the quantum Hall droplet does not follow the equip-potential of the anisotropic trap. Rather, it is an ellipse with a different ellipticity. We are currently writing up this work. Walyon Chen will be giving a talk of this result at the upcoming American Physical Society (APS) March Meeting.

For strongly interacting Bose gas, the experiment of our team is to study the properties of the Bose gas after the interaction between bosons is increased suddenly, a process now referred to as quantum quenching. One key question is how the populations of bosons in different momentum states evolve in time. In order to obtain results that are free from uncontrolled approximations, we have been studying the quantum quenching of one dimensional Bose gas for which exact results can be obtained. The work is in progress.

One recent and exciting venture in experiments with ultracold quantum gases is the three-body problem. In 1970, theoretical physicist Vitaly Efimov predicted that, under certain conditions, three atoms can form a bound state even if the attractions between just two atoms are too weak to cause binding. It was not until 2005 that this was first demonstrated in an experiment by a group at the University of Innsbruck. This initiated significant research efforts worldwide both in theoretical and in experimental research. Despite these efforts, further experimental input is needed to assist in theoretical predictions. CAL provides a unique new environment for testing few-body systems in previously inaccessible regimes that are prerequisite for the next generation of Efimov experiments. In preparation for CAL’s launch, our collaboration has modeled actual Efimov experiments to be conducted with CAL.

In the past year, our efforts have included numerical and analytic modeling of the CAL lab magnetic field capabilities, and of predicted cold-atom dynamics in those fields. We looked at several different basic experimental strategies, including “delta-kick cooling” and adiabatic expansion. We presented these results at a Scientific Concept Review at JPL (Jet Propulsion Laboratory) in February of 2015. The bottom line result of these efforts is that everything is looking good for a precise measurement of two generations of Efimov states in Potassium-39.

While preparing for experiments in space, we have been doing a number of related experiments in our ground-based laboratories. These experiments are interesting in their own right but they also lay the groundwork for future generation space-based experiments. The most notable result we achieved was the first-ever measurement of the energy and lifetime of a Bose polariton in the strongly interacting regime. Although in our Earth-based project we are not able to reach temperatures as low as those we anticipate reaching in space, we were able to get cold enough to cause individual potassium atom impurities to become entrained in a Bose condensate made of rubidium atoms. The resulting “snow-ball” is a sort of quasi-particle, so-called because it hangs together long enough for us to be able to measure a distinct spectrum for it, much as we could if it were a real particle. In other experimental developments, we found preliminary evidence for the existence of three-body Efimov states in rubidium Bose gas even as the interactions between the atoms become so strong that, at least mathematically, they are “infinite.”

Our experimental work, the preparation for the upcoming ISS measurement, and our ground-based experiments, were complemented by an extensive theoretical efforts. These efforts including work on quantum quenching, quantum turbulence, and the quantum Hall effect. All three topics are candidate projects for future CAL flights.

1. Quantum quenching: we have been studying the quantum quenching in low dimensional systems where it is possible to obtain exact results. We have also noticed that the problem of quantum quenching can be viewed as a process of “inflation,” where the metric of space is rapidly increasing. We have worked out the evolution of density profile and momentum distribution for two and three particle systems, and are trying to the so-called Bethe Ansatz solution to study similar properties of many-particle systems.

2. Quantum turbulence: Recently, the Cambridge experimental group led by Zoran Hadzibabic has performed an experiment to shake a Bose condensate in a box trap vigorously. They found that after some period of shaking, the momentum distribution of the gas develops a power law over a wide range of momentum. (This experiment is currently under review and has not been posted on the preprint archive. We learned about it through communications with the authors.) Turbulence is one of the longest standing problems in physics. It remains unsolved after a century of studies. Once again, cold atom experiments offer a new and flexible platform to study a longstanding problem. Moreover, cold atom experiments also raise new questions. Traditional studies of turbulence have been focusing on velocity-velocity correlation functions, whereas cold atoms experiments force one to consider momentum distributions, which is a more fundamental quantity. We have recently completed a study of the analog of the Cambridge experiment for an ideal gas. The results turn out to be surprisingly rich. We have found the emergence of power law behavior at long times, which is generated by the energy cascade processes driven by the external potential. We are in the process of writing up our results.

3. Quantum Hall states: There are two classes of quantum Hall states, abelian and non-abelian. They are distinguished by the statistics of their quasi particles under exchange. For abelian quantum Hall states, the system acquires a phase factor after the exchange, whereas for non-abelian states, the quasi particles states have internal structures and the exchange process will lead to a change of these internal structures rather than the appearance of a phase factor. In solid-state systems, the descriptions of these quasi-particles are very complicated. Recently, we have found a simple way to describe the wavefunction of the quasi-particles. We are currently trying to design experimental protocols for the exchange processes of these non-abelian quasi-particles so as to reveal their properties.

One recent and exciting venture in experiments with ultracold quantum gases has been the three-body problem. In 1970, theoretical physicist Vitaly Efimov predicted that, under certain conditions, three atoms can form a bound state even if the attractions between just two atoms are too weak to cause binding. It was not until 2005 that this was first demonstrated in an experiment by a group at the University of Innsbruck. This initiated significant research efforts worldwide both in theoretical and in experimental research. Despite these efforts, further experimental input is needed to assist in theoretical predictions, which fluctuate widely. CAL provides a unique new environment for testing few-body systems in new and previously inaccessible regimes that are prerequisite for the next generation of Efimov experiments. In preparation for CAL’s launch in 2016, our work-to-date for this project has involved analytic calculations and numerical modeling of actual Efimov experiments to be conducted with CAL.

We are currently conducting numerical analyses addressing the question of how we can attain optimum data while keeping the complexity of the experiment low. To this goal, our numerical calculations simulate exactly what the cloud of atoms will act like in a micro-gravity environment by using actual design parameters of the CAL facility. The planned experiments begin with an ultracold cloud of atoms trapped by a suitably tailored magnetic field. This cloud is prepared using evaporative cooling techniques similar to those used in Earth based experiments. From there, different pathways can be followed to reach the extreme regimes required for next-generation Efimov experiments. First, one can slowly ramp down the trapping confinement, during which the cloud cools in process called adiabatic cooling. Alternatively, one can suddenly turn the trapping confinement off so that the cloud expands ballistically. A subsequent “magnetic field delta-kick,” during which the trapping confinement is switched on again for a very brief period of time, then stops the ballistic expansion and leads to a super cooled cloud. A combination of these two techniques is also possible. In our thermodynamic calculations we are assessing the efficiencies of these methods and matching them to the experimental design parameters of CAL. The final cooling procedure establishes clouds that are very dilute and ultracold, with temperatures on the order of 100pK, the perfect regime for Efimov studies. After this, we plan to apply a homogeneous magnetic field for a set time. This homogeneous field determines how strongly atoms interact with each other, through an effect called Fano-Feshbach resonance. We then will observe how the cloud loses atoms over time as collisions in the cloud occur. When plotted as a function of the atomic interaction strength (determined by the applied homogeneous magnetic field), these losses contain signatures of the Efimov states under investigation.

The research conducted in the frame of this project lays the groundwork for future investigations of few-body physics using NASA’s planned CAL facility onboard the ISS. While CAL is currently under construction at JPL, our modeling, based on actual design parameters of CAL, paves the way for the next-generation Efimov experiments. We have identified successful pathways to generate atomic clouds with sufficiently low density and temperature and have determined realistic parameters to be used in these studies.

To develop the intricate patterns of atoms we want to study, we need low temperatures, yes, but also we need to get the atoms to clump together in interesting ways. Towards this end, and in parallel with our work on Efimov resonances, we are spinning the cloud of atoms at ever higher rates. The individual atoms, like strands of wool being spun into yarn, become increasingly more entangled. This year we have succeeded in spinning atoms rapidly in a novel atomic trap, a sort of bowl for atoms constructed of laser beams. Our hope is to do a similar experiment in a second-generation Cold Atom Laboratory, on the ISS. In other progress this year, we have improved our ability to take pictures of the cold atoms. Going into this past year, if two clumps of atoms were closer together than about four ten thousandths of an inch, they would appear us a single blurry clump. Now we can see patterns of atoms that are two times smaller than before. This will help us better understand what’s going on at extremely low temperatures.

To interpret our results from CAL, both the Efimov state work and the high-rotation work, we will need to have extensive theoretical understanding. We have been making progress in this area over the last year.

Together with Dr. Ran Qi (NIST), we have studied the quantum quenching of two and three particle systems in a trap. Specially, we study the time evolution of the system after the interaction between particles suddenly jumped from being weakly repulsive to being strongly repulsive. We have investigated this evolution for different kind of confining potential. We have completed the study for the two-particle case, and is in the process of studying the three particle case. The study of the two-particle case reveals a universal structure of the time evolution. The study of the three-particle case will illustrate the relative role between two- and three-particle contributions in quantum quenching. Our long term goal is to use the insight from a few body study to construct a general description (like that renormalization group) for systems with a large number of particles, which will form a solution of this class of long-standing non-equilibrium problems.

Theoretically, it is known that a rotating quantum gas will reach the so-called quantum Hall state when it gains sufficiently large angular momentum. A necessary condition to realize quantum Hall states is to reach the fast rotating regime where the energy levels of the particles are organized into almost degenerate levels (called Landau levels). This regime has been achieved by the lead P.I. (E. Cornell) of our team. The next step is to increase the angular momentum further to reach the quantum Hall state. For Bose gases, this turns out to be a difficult step as Bose-Einstein condensation competes strongly with the formation of quantum Hall states. In contrast, it is much easier for Fermi gases to go into quantum Hall states, since their formations are helped by Fermi statistics. On the other hand, another member of our team (D. Jin) has pioneered the technique of associating fermion pairs into bosons by changing the interaction of the system, which can be achieved by simply varying an external magnetic field. This then create a new path for us to achieve the bosonic quantum Hall states. One can first produce a fermionic quantum Hall state, and then associate the fermionic quantum Hall states into bosonic ones by changing the interaction between particles. At present, our theory group, led by T.-L. Ho, has been performing theoretical studies of this association process, as well as methods to identify the presence of quantum Hall states. We have demonstrated the success forming bosonic quantum Hall states in this association process. We are now trying to extend the study to systems with larger number of particles. Together with our students, we have also shown that the presence of quantum Hall states can be easily identified through their density profiles and local density fluctuations.