Quantum Gas Mixtures and Dual-Species Atom Interferometry in Space

Abstract

The capability to reach ultracold atomic temperatures in compact instruments has recently been extended into space. Ultracold temperatures amplify quantum effects, while free-fall allows further cooling and longer interactions time with gravity - the final force without a quantum description. On Earth, these devices have produced macroscopic quantum phenomena such as Bose-Einstein condensation (BECs), superfluidity, and strongly interacting quantum gases. Quantum sensors interfering the superposition of two ultracold atomic isotopes have tested the Universality of Free Fall (UFF), a core tenet of Einstein's classical gravitational theory, at the $10^{-12}$ level. In space, cooling the elements needed to explore the rich physics of strong interactions and preparing the multiple species required for quantum tests of the UFF has remained elusive. Here, utilizing upgraded capabilities of the multi-user Cold Atom Lab (CAL) instrument within the International Space Station (ISS), we report the first simultaneous production of a dual species Bose-Einstein condensate in space (formed from $^{87}$Rb and $^{41}$K), observation of interspecies interactions, as well as the production of $^{39}$K ultracold gases. We have further achieved the first space-borne demonstration of simultaneous atom interferometry with two atomic species ($^{87}$Rb and $^{41}$K). These results are an important step towards quantum tests of UFF in space, and will allow scientists to investigate aspects of few-body physics, quantum chemistry, and fundamental physics in novel regimes without the perturbing asymmetry of gravity.

Figures (6)

• Figure 1: CAL On-orbit Hardware Upgrades: (A) The CAL payload, housed in EXPRESS Rack 7 within the US Lab Destiny Module of the ISS, undergoing preparation for removal of the science module launched with CAL in 2018 (image source: NASA). This original science module, designated "SM2", was utilized for the results reported in CAL_nature_20Carollo2022CassDecompGaaloul2022), and was replaced with science module "SM3" by ISS crew in January 2020 (astronaut Christina Koch pictured). The novel capabilities of SM3 and the multi-tone microwave were necessary for the results reported here, and their locations are emphasized. (B) From the outside, SM2 and SM3 are virtually identical, but SM3 features a new atom chip layout and additional optics necessary for atom interferometry. (C) A cross section of SM3 revealing the interior of the vacuum chamber ("science cell") where atom cooling and interferometry occurs (purple). (D) Enlarged view of the "AI platform" above the science cell. The red line indicates the path of the 1-mm diameter Bragg beam operating at 785 nm, propagating approximately along the direction of Earth's gravity vector, labeled as the z-direction. The Bragg beam exits an optical fiber, passes through an optical filter, reflects off a polarizing beam splitter down through a 2 mm $\times$ 3 mm aperture in the atom chip surface which forms the upper cell wall, and finally retro-reflects from a mirror attached to the lower surface of the cell. The location of the overlapped rubidium and potassium MOT, from where atoms are magnetically transferred to the chip trap, is noted as a red cross. (E) The multi-tone microwave source installed in July 2021, featuring two synthesizers shown in red. The longest dimension is 38 cm. (F) The microwave spectrum of the multi-tone microwave source, where tones (c) and (k) are the mixed outputs of two independently tunable frequency synthesizers near 6.834 GHz and 15 MHz, yielding frequencies of order 6.834 GHz and 6.834 GHz + 15 MHz, respectively. Additional mixing harmonics are shown in gray. Tone (c) can act alone to transfer $^{87}$Rb atoms in the $\ket{2,2}$ state to state $\ket{1,1}$ to drive radiative evaporation, or it can be set to remove $^{87}$Rb atoms in the $\ket{2,1}$ state while sideband (k(t)) becomes a time dependent frequency to evaporates atoms from the $\ket{2,2}$ to $\ket{1,1}$ state. This later case is shown in (G).
• Figure 2: Production of Degenerate Quantum Mixtures in Space: False-colour absorption images of $^{87}$Rb, $^{41}$K, and $^{39}$K atomic clouds following microwave evaporation, decompression, and release from CAL’s magnetic chip trap (see Methods). All images are 244 by 406 µm (60 by 100 pixels) in the $z$- by $x$-directions, respectively, where $z$ is along the direction of Earth's gravity gradient. The potassium cloud is imaged following the indicated time of flight in free expansion (TOF), and then a separate laser frequency images $^{87}$Rb after a 2.1 ms delay. The vertical axis of all 3D surface plots is optical density (OD), and height is referenced to a common scale with a maximum of 3.5. Each atomic species then has a separate relation between height and color, where a different false color map is assigned to each species with the color limits corresponding to the OD ranges indicated. (A) Preparation of a dual species degenerate gas. From left to right, the final frequency of an evaporative cooling ramp using a multi-tone microwave source is lowered, with the microwave evaporation supplemented by an additional RF source. In this example, $^{87}$Rb condenses first at a critical temperature at 70 nK (second from left). Further evaporation (third from left) lowers the $^{87}$Rb temperature to 59 nK, remaining below a lower critical temperature as the atom number simultaneously drops. The final evaporation step lowers the $^{87}$Rb atom number to $1.25 \times 10^4$ and temperature to 46 nK, producing a $^{41}$K BEC with $1.45 \times 10^3$ atoms at 37 nK. Temperatures are calculated from the measured BEC fraction, atom number, and trap frequencies. One dimensional density plots (light blue points), obtained by integrating along the $z$-direction (radial dimension of the trap) show the bimodal fit for the BEC component (blue) and the thermal component (red) in the final evaporation stage. (B) Potassium performance is prioritized by evaporating with only microwaves and a $^{87}$Rb BEC never forms. The atom number of $^{41}$K is maintained at $\sim 1.32 \times 10^4$ in all three images as the critical temperature of 95 nK is passed in the middle image, with a final temperature of 70 nK in the right image. (C) $^{39}$K sympathetically cooled to ultracold temperatures, with no $^{87}$Rb remaining.
• Figure 3: Interactions of degenerate $^{87}$Rb and $^{41}$K mixtures: Blue traces are $^{87}$Rb and $^{41}$K absorption profiles from the final evaporation stages of Figure \ref{['fig:dual_BEC']} (A) and (B), integrated along the $x$- and $z$-directions respectively. Red traces are theoretical models obtained by solving for the ground state configuration of the trap, and then propagating the initial states through the processes of trap decompression, release, and free expansion. The distributions are convolved with a 15 µm-Gaussian to account for the resolution of the camera. Position 0 is defined as the center of the condensate component for $^{41}$K, where the positive z-direction points away from the chip, consistent across figures. The solid vertical lines show the center position of the condensate component for each species. Green dashed traces are Gaussian fits to the data, showing the non-condensed atoms in the gas. The dashed vertical lines show the center of the non-condensed component. For the dual-species case, (A), (B), (C), and (D) we see that the Rb atoms share a nearly common center. In contrast, the $^{41}$K condensate is offset relative to the $^{41}$K thermal component by $\sim$30 µm along $z$ (normal to the atom chip). This displacement is consistent with model calculations that take into account mean-field interactions between the two condensates. (E) and (F), where no $^{87}$Rb is present, displays the overlap of the $^{41}$K condensate and $^{41}$K thermal component restored.
• Figure 4: Dual Species Atom Interferometry in Space: (Left) Normalized population for ultracold samples of $^{41}$K (blue) and $^{87}$Rb (red) in the excited momentum state $2\hbar k$ following the application of three Bragg pulses in a Mach-Zehnder configuration. The time between pulses is $T = 0.5$ ms, and the pulse durations are 270 µs, 580 µs, and 270 µs, respectively. Each pulse interacts with both atomic species simultaneously, and contains three frequency components configured to drive Bragg transitions in both species with equal Rabi rates. For the third pulse, the same variable phase shift (degrees) is applied to components addressing each species, in steps of 30$^\circ$. Interference causes the population of the output states to vary sinusoidally, as observed. The offset and amplitude of the oscillation agrees very well with the expected minimal and maximal populations in the excited momentum state obtained by modelling the efficiencies of all three pulses (see Methods). Each data point and error bar represents the average and standard deviation of between 5 and 15 independent experimental runs respectively for a chosen phase shift. (Right) Comparison of the relative population in the excited momentum state of $^{41}$K and $^{87}$Rb showing a correlation between both species. Fitting an ellipse (black) to the data yields a vanishing differential phase of $0.37^{+0.45}_{-1.19}$ indicating that both interferometers measured the same phase.
• Figure 5: Rabi scan: Relative population of the excited momentum state $2\hbar k$ of a cloud of $^{41}$K (left) and $^{87}$Rb (right) atoms as a function of the pulse duration of a single Bragg pulse. Each data point and error bar represents the average and standard deviation of 3 independent experimental runs for a chosen pulse duration. The sequence uses the tri-tone configuration that was also applied in the full interferometer shown in Figure \ref{['fig:Dual_AI']}. By fitting a theory model to the data set the Rabi frequency and the momentum width of the atom cloud was determined (see Methods).