Molecular quantum gases (that is, ultracold and dense molecular gases) have many potential applications, including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing1,2,3. For molecules, to reach the quantum regime usually requires efficient cooling at high densities, which is frequently hindered by fast inelastic collisions that heat and deplete the population of molecules4,5. Here we report the preparation of two-dimensional Bose–Einstein condensates (BECs) of spinning molecules by inducing pairing interactions in an atomic condensate near a g-wave Feshbach resonance6. The trap geometry and the low temperature of the molecules help to reduce inelastic loss, ensuring thermal equilibrium. From the equation-of-state measurement, we determine the molecular scattering length to be + 220(±30) Bohr radii (95% confidence interval). We also investigate the unpairing dynamics in the strong coupling regime and find that near the Feshbach resonance the dynamical timescale is consistent with the unitarity limit. Our work demonstrates the long-sought transition between atomic and molecular condensates, the bosonic analogue of the crossover from a BEC to a Bardeen−Cooper−Schrieffer (BCS) superfluid in a Fermi gas7,8,9. In addition, our experiment may shed light on condensed pairs with orbital angular momentum, where a novel anisotropic superfluid with non-zero surface current is predicted10,11, such as the A phase of 3He.
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Transition from a polaronic condensate to a degenerate Fermi gas of heteronuclear molecules
Nature Physics Open Access 13 February 2023
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
The codes for the analysis of data shown within this paper are available from the corresponding author upon reasonable request.
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We thank P. Julienne for discussions and K. Patel for carefully reading the manuscript. This work is supported by National Science Foundation (NSF) grant number PHY-1511696, the Army Research Office Multidisciplinary Research Initiative under grant W911NF-14-1-0003 and the University of Chicago Materials Research Science and Engineering Center, which is funded by the NSF under grant number DMR-1420709.
The authors declare no competing interests.
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Extended data figures and tables
Extended Data Fig. 1 Calibration of magnetic anti-trap potential from the atomic density distribution.
a, Fit of the in situ atomic density profile for determination of the magnetic anti-trap frequencies ωx and ωy using equation (2). The top and right panels show line cuts of the 2D atomic density in the x and y directions, crossing at the centre of the anti-trap. We choose the region within the red dashed circle for fit and extraction of the equation of state. b, Equation of state of atomic BEC shown in a. Each data point represents averaged density within a bin size δμ/h = 0.25 Hz and error bars represent one standard deviation. The black solid line is a linear fit to the data, while the black dashed line is an extrapolation of the fit towards the origin. Data values and error bars are estimated as in Fig. 2 from 20 measurements.
Extended Data Fig. 2 Calibration of the optical potential barrier projected by a DMD from the density response measurement of atomic BEC.
a, Images of in situ atomic column density with different central barrier heights determined by different fractions of micromirrors fDMD that are turned on in the DMD. b, Example measurements of the proportionality p(x, y) for six pixels at different locations. The solid lines are linear fits to the linear part of the data points, the slope of which gives p(x, y). Data values and error bars are estimated as in Fig. 2 from 9–11 measurements. c, Spatial dependence of the proportionality p(x, y). The upper and right panels are line cuts in the x and y directions crossing the peak value. Data values are determined from the fits and the errorbars represent 95% confidence interval.
Extended Data Fig. 3 Fast equilibration of molecules with atoms during the ramp across the Feshbach resonance.
a, Dynamics of the number of molecules during the magnetic field ramp across the Feshbach resonance at 19.87 G with different ramp speeds of 161 mG ms−1 (red), 80 mG ms−1 (blue) and 54 mG ms−1 (green). b, In situ images of molecules during the magnetic field ramp at 80 mG ms−1. Data values and error bars are estimated as in Fig.2 from 5–7 measurements.
Extended Data Fig. 4 Azimuthally averaged density profiles.
These profiles correspond to the atomic (left) and molecular (right) clouds shown in Fig. 2a. The atomic density profile is flat-topped, whereas the molecular density profile has a dip in the middle.
Extended Data Fig. 5 Dynamics of molecular density profiles in the 2D box trap with magnetic anti-trap potential.
The azimuthally averaged molecular density profiles are shown as a function of the hold time after the formation of molecules. The dips in the middle result from the magnetic anti-trap potential and persist during the first 15 ms after formation of the molecules.
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Zhang, Z., Chen, L., Yao, KX. et al. Transition from an atomic to a molecular Bose–Einstein condensate. Nature 592, 708–711 (2021). https://doi.org/10.1038/s41586-021-03443-0
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