We pursued four major activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions for the dispersion relation, mass, and excitation gap of magnons. These were tested experimentally.

(2) Magnon interferometry in dense Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the F=1 gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We pursued the possibility of implementing atom interferometry based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Magnon interferometry was realized and investigated.

(3) Magnon-evaporative cooling: We explored a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target was to produce and also confirm the production of quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.

(4) Quantum gas mixtures: A unique capability for quantum gas experiments in microgravity is that of overlapping quantum gases composed of different atomic species within the exact same trapping potential. On Earth, trapping requires one to overcome the force of gravity by applying electromagnetic fields to the trapped atoms. The response of each element to electromagnetic fields is different, meaning that it is impractical to place a quantum gas composed of several different atomic elements within the exact same potential. Aboard CAL or other follow-on missions, quantum gases can be admixed within potential free volumes without needing to apply an compensation against gravity. As preparation for such free-fall experiments, we explored the nature of quantum gas mixtures of lithium and rubidium atoms. Our goal here was to characterize the interaction between these gases, including the spin dependence of such interactions.

More specifically, the research impacts our knowledge of materials (through studies of superfluid turbulence), extends the frontiers of natural phenomena that we can access and explore (through the development of new thermometry and cooling techniques), and contributes to the development of high precision sensors for future scientific and technological applications (through studies of atom and magnon interferometry).

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: We focused on the nature of magnons within F=1 spinor gases of 87-Rb atoms. These gases are ferromagnetic in nature, meaning that interactions between atoms favor a state in which all atoms are magnetized, with the magnetization oriented in spatially uniform direction. Magnons are the magnetic excitations of such ferromagnetic states, i.e., a spatial ripple in the uniform magnetization. These excitations have a characteristic excitation energy that varies with the length-scale of the magnetization ripple (the wavelength of the magnon). While in many solid magnetic systems the energy of magnon excitations (i.e., their dispersion relation) is difficult to calculate from first principles, here, in the case of atomic quantum gases, there are robust theoretical predictions for the magnon energy. We conducted experiments to test these predictions.

The tests were reported in two prominent publications: a study of coherent magnon propagation [Marti et al, Physical Review Letters 113, 155302 (2014)] and a study of the phenomenon of magnon condensation [Fang et al., Physical Review Letters 116, 095301 (2016)] [Ed. note: see Cumulative Bibliography] In the former, we quantified the magnon dispersion relation in two separate measurements.

In the first, we studied the energy of uniform magnon excitations. For this, we examined a spinor Bose-Einstein condensate with a slowly varying atomic density. After exciting long-wavelength magnons in the system, via a uniform rotation of the condensate magnetization, we detected a spatial variation in the evolution of the excitation. From this, we determined that the uniform magnon excitation has an energy cost that varies with the gas density. We ascribed this energy offset (known as the magnon energy gap) to the magnetic dipole-dipole interactions in the atomic gas. By this measurement, we obtained the first direct quantitative evidence of magnetic dipolar effects in alkali-atom quantum gases. Another measurement reported in the 2014 paper focused on the magnon recoil energy, which is the added energy required to boost a magnon excitation from zero momentum to finite momentum. This recoil energy was measured through magnon interferometry, which we describe further below. The dispersion relation was found to be particle-like, characterized by a magnon mass that was slightly but significantly different from the atomic mass. There remains some theoretical controversy over this measurement result.

In our second paper, we studied the thermodynamic behavior of many magnon excitations evolving within a ferromagnetic Bose-Einstein condensate. Magnons are bosons. When a thermal gas of magnon excitations becomes sufficiently cold and dense, these magnons should themselves undergo Bose-Einstein condensation. Such condensation results in a phase transition of the ferromagnetic system, marked by the breaking of symmetry and the emergence of a macroscopic transverse magnetization. Magnon condensation is studied and observed in several magnetic systems, ranging from YIG films to superfluid helium 3 liquids. Our study was the first to examine magnon condensation in an atomic gas. Through position-space and momentum-space measurements of the quantum gas, we observed the magnon condensation phase transition. The transition point was characteristic of magnons that propagate with near-zero energy gap within the ferromagnetic condensate. The symmetry breaking phase transition was observed directly through spatially resolved measurements of the condensate spin. One remarkable finding was that the magnon condensation results only in a quasi-condensation, in which long-length-scale variations of the magnon condensate order parameter remain for very long evolution times.

(2) Magnon interferometry in dense Bose condensed gases: As reported in our paper [Marti et al, Physical Review Letters 113, 155302 (2014)] (Ed. note: See 2015 Task Book report bibliography), we realized an interferometer in which magnon waves at several different momenta propagated coherently. These magnon waves were produced by a coherent optical excitation of a ferromagnetic spinor Bose-Einstein condensate. Specifically, we produced a pattern of magnetization containing magnons at three different momenta. The interference between these magnon waves was evident in the time variation of the density of the magnon gas, which we observed directly through spin-sensitive optical imaging. A truly remarkable feature of this magnon interferometer is that the coherent evolution is obtained even as the magnons propagated within the highly dense atomic medium of the ferromagnetic spinor gas. This stands in contrast with most other approaches to atom interferometry, where atomic density must be reduced as far as possible in order to avoid deleterious effects from interactions. However, magnon waves are immune to such interaction effects on account of the rotational symmetry of atomic interactions.

(3) Magnon-evaporative cooling: In our publication [Olf et al., Nature Physics 11, 720 (2015)] (Ed. note: see 2016 Task Book report bibliography) we demonstrate the use of magnon gases for thermometry and cooling of highly degenerate Bose-Einstein gases. Precise measurement of the temperature of such degenerate gases is very difficult, requiring that one detect a small population of excited energy atoms atop a very large population of non-excited, ground-state atoms. Prior to our work, thermometry on degenerate Bose gases has been limited to temperatures that were 30% or more of the Bose-Einstein condensation transition temperature. We adopted a different approach: We added a small population of magnon excitations to the degenerate Bose gas, allowed those magnons to thermalize, and then selectively detected the magnon excitations to determine the temperature of the entire gas. By this method, we were able to measure temperatures as low as just 2% of the Bose-Einstein condensation temperature. These temperature readings confirmed that the Bose-Einstein condensed gases prepared in our experiment were at exceedingly low entropies, which is good news for efforts to use such gases to study many-body quantum physics. A byproduct of our work was the discovery of a cooling effect that occurs upon magnon thermalization. Such cooling can be implemented in experimental setups where direct evaporative cooling of the gas is difficult, e.g., for atoms in magnetic traps such as those employed in the CAL experiment on the International Space Station (ISS).

(4) Quantum gas mixtures: Toward the end of the granting period, we pivoted our efforts to study quantum gas mixtures. We were interested specifically in mixtures of lithium and rubidium atoms, which had not been studied as a gas mixture in many previous experiments, and which could perhaps be used as a precursor for LiRb diatomic molecules. The study of quantum gas mixtures is among the exciting prospects for future experiments on ultracold atomic gases in free fall, for the reason that one can study these gas mixtures without having to suspend the atoms, usually differentially, against the force of gravity.

After developing the ability to laser cool Li and Rb gases simultaneously and to load these gases together into both magnetic and optical traps, we conducted two significant experiments. In the first [Fang et al., Physical Review A 101, 012703 (2020)] (see Bibliography section), we measured the collision cross section between Li and Rb atoms with both atoms trapped in the F=1, mF = 1 hyperfine state. The measurement was performed by redistribution of momentum between different directions of motion, caused by collisions of Li atoms against a large bath of Rb atoms. The cross section was found to be small, which was bad news in terms of the prospects of cooling Li and Rb gases together via sympathetic cooling. Yet, the cross section was found to be significantly larger than was predicted by the best theoretical models of Li-Rb collisions. We worked with the theory group of Chris Greene, of Purdue University, to understand this discrepancy with theory. In the end, our analysis confirms that there is something amiss with the body of experimental measurements performed on Li-Rb gas mixtures. Hopefully this discrepancy will be cleared up by further measurements in various laboratories.

A second experiment focused on spin-dependent interactions between Li and Rb spinor gases. Together, these gases form something known as a heteronuclear spinor Bose-Einstein gas. Such heteronuclear gases are predicted to support a wide range of interesting phenomena. In our study, we focused on spin relaxation wherein an initial spin distribution of Li atoms evolves owing to interactions with a large Rb spinor gas. From this relaxation, we were able to observe the effects of three distinctly different types of spin-dependent collisions, and then to characterize the strength of each of these processes. Our experiment represents the first complete characterization of spin-dependent collisions in a heteronuclear spinor gas, and sets an example for similar experiments to be performed on other quantum gas mixtures.

We propose four activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions that we will test precisely with interferometric measurements based on coherent magnon optics.

(2) Magnon and Bragg interferometry in dense and dilute Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the $F=1$ gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We propose to implement an atom interferometer based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Comparing the two interferometers provides a strong measurement cross-check and may allow quantitative studies of polaronic (quantum depletion) energy shifts.

(3) Imaging superflow with a magnon shear interferometer: We propose to image the magnon interference pattern to perform in-situ measurements of superfluid flow in three dimensions, akin to particle tracking velocimetry. We propose to utilize the CAL to expand a trapped Bose-Einstein condensate into a large three dimensional volume, essentially magnifying the superfluid flow pattern sufficiently that it can be imaged. A three-dimensional spatial pattern of magnons will be allowed to propagate coherently before being imaged, revealing the three-dimensional superfluid velocity field.

(4) Magnon-evaporative cooling: We will explore a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target is to produce quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.

More specifically, the research impacts our knowledge of materials (through studies of superfluid turbulence), extends the frontiers of natural phenomena that we can access and explore (through the development of new thermometry and cooling techniques), and contributes to the development of high precision sensors for future scientific and technological applications (through studies of atom and magnon interferometry).

In this year, we have managed to produce magneto-optical traps of the two atomic elements simultaneously, and to load the two gases into the same spherical quadrupole magnetic trap. With the gases co-trapped, we were hoping to see collisions between lithium and rubidium atoms that would allow the gas-mixture to thermalize. This thermalization is critical to employing sympathetic evaporative cooling, in which we cool the abundant gas (rubidium) and then have the rarer gas (lithium) also reduce its temperature. However, we observed the collision rate between lithium and rubidium to be rather slow. Given this, we performed a precise measurement of the lithium-rubidium collision cross section, using the method of cross-dimensional thermalization, and also developed theoretical models, based on molecular spectroscopy and other measurements, in order to predict the cross-section and its energy dependence. We were surprised to see significant deviations between experiment and theory. We are working now with theoretical colleagues to identify the source of this discrepancy, i.e., what is the deficiency in the theoretical model that makes it disagree with experiment. A paper on this work is being written up.

Following this observation, we are developing an alternative approach where lithium and rubidium atoms from the magneto-optical trap are loaded directly into an optical dipole trap. We have succeeded in trapping the gas mixture in this way, although we are still debugging the system in order to reduce the heating rate and increase the trap lifetime. We have also identified the need to impose a second light beam onto the gas mixtures so that we can separately control the trap depth for lithium and for rubidium atoms. We have build the appropriate light sources, and are preparing to test the operation of this kind of bichromatic optical dipole trap.

In addition, we have begun exploring ways in which lithium and rubidium atoms can be driven using laser light to form ground-state LiRb molecules. This exploration involves further development of theoretical modes for the Li-Rb molecular potential, including the excited-electronic-state potentials. We have adapted computer code from other theoretical groups to represent this potential and calculate its state structure. Based on the results of this numerical model, we have identified two different possible pathways for forming ground-state molecules, but we have also ascertained that further spectroscopic investigations of the LiRb molecule will be needed to pin down the best pathway. Again, we are collaborating with theorists to advance this work.

We propose four activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions that we will test precisely with interferometric measurements based on coherent magnon optics.

(2) Magnon and Bragg interferometry in dense and dilute Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the $F=1$ gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We propose to implement an atom interferometer based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Comparing the two interferometers provides a strong measurement cross-check and may allow quantitative studies of polaronic (quantum depletion) energy shifts.

(3) Imaging superflow with a magnon shear interferometer: We propose to image the magnon interference pattern to perform in-situ measurements of superfluid flow in three dimensions, akin to particle tracking velocimetry. We propose to utilize the CAL to expand a trapped Bose-Einstein condensate into a large three dimensional volume, essentially magnifying the superfluid flow pattern sufficiently that it can be imaged. A three-dimensional spatial pattern of magnons will be allowed to propagate coherently before being imaged, revealing the three-dimensional superfluid velocity field.

(4) Magnon-evaporative cooling: We will explore a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target is to produce quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.

More specifically, the research impacts our knowledge of materials (through studies of superfluid turbulence), extends the frontiers of natural phenomena that we can access and explore (through the development of new thermometry and cooling techniques), and contributes to the development of high precision sensors for future scientific and technological applications (through studies of atom and magnon interferometry).

We report on three activities:

1. Quantum gas mixtures of Li and Rb: In the previous reporting period, we began augmenting our experimental capabilities by adding ultracold lithium gases into our experiment. The goal of this activity is to study spinor Bose-Einstein gases and also magnon interferometry with a spinor Bose gas that has different properties than does rubidium. Compared with rubidium, lithium has the property that it should equilibrate more rapidly owing to a stronger spin-dependent interaction. We also are interested in preparing quantum-gas mixtures in optical lattices, and gases of ultracold dipolar molecules for applications in precision measurement, quantum dynamics, ultracold chemistry and quantum simulation.

Our experimental efforts during this reporting period were focused on this task. We built a laser system that delivers light at several different frequencies as are needed for slowing and laser cooling the lithium-7 isotope. We adapted our vacuum system, modifying the effusive oven source so that it emits an atomic beam containing both rubidium and lithium atoms. Operating this two-element oven adds a significant gas load to the chamber, both from the atomic beam itself and also from the additional outgassing of vacuum components at the high temperatures needed for the oven to operate. We diagnosed this higher gas load and modified the vacuum chamber to allow for ultrahigh vacuum conditions still.

We developed a method for loading both rubidium and lithium atoms into the same magneto-optical trap. We found that operating the two traps simultaneous caused light-induced losses wherein lithium and rubidium atoms collide in the presence of light near the rubidium resonance. In such a collision, a red-detuned photon is emitted, leaving behind energy that is taken up as kinetic energy by the atoms, causing both to be lost from the trap. After measuring the loss rate from such collisions, finding them to be consistent with previous measurements, we adopted a loading sequence in which the lithium and rubidium atoms accumulate in the trap while imbalanced light forces are used to offset one element from the other spatially. This arrangement allows the populations of both elements to build up. Near the end of the loading sequence, we restore the balance of optical forces on the atoms, causing the trapped gases to overlap, but for a sufficiently short time that the losses are not severe.

We implemented a recently suggested form of laser cooling to the lithium gas. In most prior experiments, laser cooling of lithium ends up being limited at the Doppler temperature because the excited-state structure of lithium prevents the atoms from being cooled by Sisyphus cooling. Thus, magneto-optical traps of lithium deliver atoms at temperatures of hundreds of microkelvin, much hotter than is achieved with other laser cooled elements. However, it was recently shown that a form of dark-state laser cooling can be applied, making use of the resolved structure of the D1 resonance line of lithium. We implemented this “D1 laser cooling” to cool all three dimensions of motion of lithium, achieving temperatures in the 10s of microkelvin range.

We have also succeeded in loading the two elements into a magnetic trap. The magnetic trap lifetime for both species is very long – on the order of two minutes – limited by the residual gas in the ultrahigh vacuum chamber. At present, we are studying the process of thermal equilibration.

2. Considering experimental tests of the validity of quantum mechanics on macroscopic scales: One of the major motivations for conducting experiments on ultracold atoms in free fall, is to perform atom interferometry experiments in which matter waves are separated by large distances for long periods of time. Increasing both quantities improves the sensitivity of atom interferometer to acceleration, perhaps permitting highly sensitive tests of the gravitational equivalence principle or measurements of gravitational waves. The microgravity environment of space-borne experiments allows interferometry experiments with freely falling atoms at larger spatial and temporal separation. In contrast, on Earth, the free-fall time of the atoms is limited by gravity.

Stretching the bounds of atom interferometry also tests our assumption that quantum mechanics continues to be valid at ever-larger length and timescales. Several theories have been offered that consider the possibility that quantum mechanics does not retain its validity under such macroscopic separations, citing the empirical fact that macroscopic objects appear to be described perfectly well by classical, rather than quantum, mechanics. One such theory is the theory of continuous spontaneous localization (CSL), which posits that massive objects that are placed in superpositions of spatially separated states will decohere naturally. While it has been experimentally verified that massless particles (photons) can remain in coherent superpositions with macroscopic length and time scales, it remains untested whether massive particles can retain coherence under such conditions.

A recent paper by the Kasevich group at Stanford has claimed to test the validity of quantum mechanics for rubidium atoms placed in superpositions with meter-scale spatial and second-scale temporal separations. However, as described in our publication [Dan M. Stamper-Kurn, G. Edward Marti, Holger Müller, “Brief Communication Arising: Verifying quantum superpositions at metre scales,” Nature 537, http://dx.doi.org/10.1038/nature19108 (2016)], the Stanford group’s interpretation is flawed. In their experiment, they observe high contrast interference for two Bose-Einstein condensed gases that are separated by large distances and large times. However, the interference phase is not stable between measurements. The instability of the interference phase is, in fact, completely consistent with spontaneous localization of the spatially separated clouds, causing them to interfere just like two independently produced, and entire phase-incoherent, Bose-Einstein condensates. We show that their experiment sets only a modest bound on spontaneous localization theories – at spatial separations of just a millimeter scale – matching bounds that had already been set by prior experiments. Our correct interpretation of their work is highly significant for future efforts to test CSL theories with space-borne experiments, i.e., we show that the validity quantum mechanics at macroscopic scales remains untested.

3. Defining future space-based ultracold atom experiments: NASA has begun discussions with the German space agency (DLR) about a joint mission that will be a follow-on to the Cold Atom Laboratory. I contributed to these discussions by attending a joint planning workshop in Bremen, Germany in December 2016. I presented a scientific proposal to use a new mission to study ultracold atomic gases in large volume, blue-detuned optical traps. Such a capability would allow one to study the dynamics and thermodynamics of homogeneous quantum gases. I contributed to the planning documentation. The ideas I brought to the meeting do not constitute a recognized scientific direction for the proposed mission.

We propose four activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions that we will test precisely with interferometric measurements based on coherent magnon optics.

(2) Magnon and Bragg interferometry in dense and dilute Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the $F=1$ gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We propose to implement an atom interferometer based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Comparing the two interferometers provides a strong measurement cross-check and may allow quantitative studies of polaronic (quantum depletion) energy shifts.

(3) Imaging superflow with a magnon shear interferometer: We propose to image the magnon interference pattern to perform in-situ measurements of superfluid flow in three dimensions, akin to particle tracking velocimetry. We propose to utilize the CAL to expand a trapped Bose-Einstein condensate into a large three dimensional volume, essentially magnifying the superfluid flow pattern sufficiently that it can be imaged. A three-dimensional spatial pattern of magnons will be allowed to propagate coherently before being imaged, revealing the three-dimensional superfluid velocity field.

(4) Magnon-evaporative cooling: We will explore a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target is to produce quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.

More specifically, the research impacts our knowledge of materials (through studies of superfluid turbulence), extends the frontiers of natural phenomena that we can access and explore (through the development of new thermometry and cooling techniques), and contributes to the development of high precision sensors for future scientific and technological applications (through studies of atom and magnon interferometry).

1) Magnon evaporative cooling and thermometry. Here, we accomplished the goals of Task 4 as listed in our proposal. We found that spin impurities within a Bose-Einstein condensed gas can serve both as a medium for precise thermometry down to very low temperatures, and also as a coolant to reduce the temperature of the trapped gas. In this work, we began with a gas of atoms occupying a single internal atomic state, and cooled down to temperature near or below the Bose-Einstein condensation temperature. We then applied a radio-frequency magnetic pulse to flip the spins of a small fraction of the atoms, creating a minority population of trapped atoms in a different internal atomic state. After allowing the gas to equilibrate at near-constant magnetization, we made state-selective measurements of the atomic momentum distribution. Characterizing the distribution of the minority spin population allowed us to determine the gas temperature down 1 nanokelvin, corresponding to 0.02 times the Bose-Einstein condensation transition temperature. We calculate that, under these conditions, the gas entropy is just S/N = 10^(-3) k_B, meaning that only one out of a thousand atoms in the gas are thermally excited. This is the lowest entropy (quietest) gas ever produced. Previously existing thermometry methods were inadequate to measure such low temperatures/entropies. We observed also that the thermalization of the spin impurities had the effect of cooling the gas. We describe this cooling as an isoenergetic demagnetization cooling effect. Our techniques for thermometry and cooling are compatible with, and have benefits for, the planned CAL instrument. This work is described in Olf et al., Nature Physics 11, 720–723 (2015).

2) Magnon condensation. This activity addresses Task 1 as listed in the proposal (precise characterization of magnons). Magnon condensation describes various equilibrium and non-equilibrium transitions in solid-state materials, in which the population of magnetic excitations in a magnetically ordered system rises above the Bose-Einstein condensation critical number. The ensuing condensation of magnons appears as a spontaneous transverse magnetization, breaking rotational symmetry. We explored this phenomenon within a spinor Bose-Einstein condensate. We introduce a population of magnons into a longitudinally magnetized ferromagnetic spinor condensate. After allowing this magnon population to equilibrate at high temperature, we cool the gas. In this process, the critical number for magnon condensation drops, causing the thermalized magnon cloud to condense within the ferromagnetic gas. We report two main findings. First, magnon condensation occurs as the condensation of free particles in a uniform potential volume defined by the volume of the ferromagnetic condensate. The flat-box effective potential reflects the fundamental property of magnons being gapless excitations. We confirm this description by measuring precisely the position and momentum-space magnon distribution, and also the critical number for magnon condensation. Second, we observe the magnon condensate order parameter directly by imaging the transverse magentization of the gas. We find the order parameter to lack long-range order, with the magnons forming a quasi-condensate. We suspect that the origin of this quasi-condensation is that the Bose-Einstein condensation transition is crossed simultaneously throughout the volume of the ferromagnetic condensate, leading to inhomogeneous symmetry breaking. The dynamics of such symmetry breaking and consequent phase-ordering kinetics, relevant to systems ranging from solids and liquids to the dynamics of the early universe, may be studied in future works. This work is described in our publication Fang et al., PRL 116, 095301 (2016).

3) Quantum gas mixtures of Li and Rb. We are augmenting our experimental capabilities by adding ultracold lithium gases into our experiment. The goal of this activity is to study spinor Bose-Einstein gases with different properties -- e.g., lithium gases in their F=1 state should equilibrate more rapidly than do rubidium gases. We also are interested in preparing gases of ultracold dipolar molecules for applications in precision measurement, quantum dynamics, ultracold chemistry and quantum simulation.

We propose four activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions that we will test precisely with interferometric measurements based on coherent magnon optics.

(2) Magnon and Bragg interferometry in dense and dilute Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the $F=1$ gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We propose to implement an atom interferometer based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Comparing the two interferometers provides a strong measurement cross-check and may allow quantitative studies of polaronic (quantum depletion) energy shifts.

(3) Imaging superflow with a magnon shear interferometer: We propose to image the magnon interference pattern to perform in-situ measurements of superfluid flow in three dimensions, akin to particle tracking velocimetry. We propose to utilize the CAL to expand a trapped Bose-Einstein condensate into a large three dimensional volume, essentially magnifying the superfluid flow pattern sufficiently that it can be imaged. A three-dimensional spatial pattern of magnons will be allowed to propagate coherently before being imaged, revealing the three-dimensional superfluid velocity field.

(4) Magnon-evaporative cooling: We will explore a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target is to produce quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.

More specifically, the research impacts our knowledge of materials (through studies of superfluid turbulence), extends the frontiers of natural phenomena that we can access and explore (through the development of new thermometry and cooling techniques), and contributes to the development of high precision sensors for future scientific and technological applications (through studies of atom and magnon interferometry).

We completed our first study of the properties of magnon excitations in a spinor Bose-Einstein condensed gas, these being the low-energy magnetic excitations of a system that is both ferromagnetic and also superfluid. We developed an optical method for producing coherent waves of magnons and then a spin-specific imaging method that allowed us to visualize the evolution of these waves. These methods were used to construct a magnon-wave interferometer that was suited to measuring the magnon recoil energy -- the extra kinetic energy that a magnon acquires as a function of its wavelength or velocity. We were testing theoretical predictions that the recoil energy should scale quadratically with the wavevector of the magnon and that the effective mass of a magnon should be very close to (with about 0.3%) the mass of a bare rubidium atom. Our data supported the prediction of a quadratic dispersion relation, but identified the magnon mass to be significantly higher than was predicted. We do not understand the reason for this heavy mass yet. In addition, we measured the magnon energy gap -- the energy required to create a stationary magnon. Applying the cold atomic gas as a magnetic field sensor, we measured the field produced by the gas itself and identified this field as the origin for the magnon energy gap. The gap was measured to be around 1 Hertz (in units of frequency), in good agreement with predictions.

We also made significant progress on the project's aim of developing techniques to measure and to lower the temperature of ultracold trapped atomic gases. Here, we aim to overcome limitations of current schemes of thermometry and cooling, both of which require one to identify the rare thermally excited atoms that exist in a highly degenerate atomic gas. We found that introducing an incoherent population of magnon excitations to the gas allowed one to measure the temperature in regimes that were hitherto inaccessible to measurement. From such measurements, we found that atomic Bose gases can be produced at extremely low values of the entropy per particle, a finding that bodes well for experiments that seek to model low-temperature materials using gases of cold atoms. In addition, we found that the very act of producing this incoherent magnon gas, out of an initially coherent wave of magnons, tended to lower the temperature of the gas. We identified this as a form of isoenergetic demagnetization cooling, and demonstrated it to be efficient in reducing the temperature and entropy of gases trapped in deep traps. Both the thermometry and the magnon cooling methods can be adapted in a straightforward manner to experiments being planned aboard the Cold Atom Laboratory on the International Space Station.

Recently, we have begun a new effort to characterize the re-condensation of magnons within a spinor Bose-Einstein condensate. The project has just gotten underway, but we are already seeing key features that are expected of this magnon condensation transition, such as the dependence of the critical atom number on system parameters, and the spontaneous symmetry breaking that occurs at such condensation.

We propose four activities:

(1) Precise characterization of magnons in spinor Bose-Einstein condensates: Magnons are low energy spin excitations in spinor condensates. Theories of symmetry breaking, as well as mean-field and beyond-mean-field mean-field treatments of Bose gases provide strong predictions that we will test precisely with interferometric measurements based on coherent magnon optics.

(2) Magnon and Bragg interferometry in dense and dilute Bose condensed gases: magnons in ferromagnetic spinor condensates, such as the $F=1$ gases of 87Rb and 41K, are by necessity gapless and quadratically dispersing, with an effective mass that, within mean field theory that is applicable to weakly interacting gases, is equal to the atomic mass. In other words, magnons propagate just like free particles. We propose to implement an atom interferometer based on coherent magnon optics. Compared to a Bragg interferometer, a magnon interferometer has no mean-field interaction shift. Comparing the two interferometers provides a strong measurement cross-check and may allow quantitative studies of polaronic (quantum depletion) energy shifts.

(3) Imaging superflow with a magnon shear interferometer: We propose to image the magnon interference pattern to perform in-situ measurements of superfluid flow in three dimensions, akin to particle tracking velocimetry. We propose to utilize the CAL to expand a trapped Bose-Einstein condensate into a large three dimensional volume, essentially magnifying the superfluid flow pattern sufficiently that it can be imaged. A three-dimensional spatial pattern of magnons will be allowed to propagate coherently before being imaged, revealing the three-dimensional superfluid velocity field.

(4) Magnon-evaporative cooling: We will explore a novel cooling technique in which magnon excitations are used to absorb, and then expel entropy from a highly degenerate spinor Bose-Einstein condensate. Our target it to produce quantum gases at the lowest entropy per particle, with a method that can be applied in the CAL apparatus.