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Many-body chemical reactions in a quantum degenerate gas


Chemical reactions in the quantum degenerate regime are described by the mixing of matter-wave fields. In many-body reactions involving bosonic reactants and products, such as coupled atomic and molecular Bose–Einstein condensates, quantum coherence and bosonic enhancement are key features of the reaction dynamics. However, the observation of these many-body phenomena, also known as ‘superchemistry’, has been elusive so far. Here we report the observation of coherent and collective reactive coupling between Bose-condensed atoms and molecules near a Feshbach resonance. Starting from an atomic condensate, the reaction begins with the rapid formation of molecules, followed by oscillations of their populations during the equilibration process. We observe faster oscillations in samples with higher densities, indicating bosonic enhancement. We present a quantum field model that captures the dynamics well and allows us to identify three-body recombination as the dominant reaction process. Our findings deepen our understanding of quantum many-body chemistry and offer insights into the control of chemical reactions at quantum degeneracy.

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Fig. 1: Reactive coupling between atomic and molecular quantum fields.
Fig. 2: Comparison of molecule formation rate in classical and quantum degenerate regimes.
Fig. 3: Coherent reaction dynamics in quantum gases of atoms and molecules across a Feshbach resonance.
Fig. 4: Bose-enhanced atom–molecule reaction dynamics on Feshbach resonance.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper are available from the corresponding author upon reasonable request.

Code availability

The codes for the analysis of data shown in this paper are available from the corresponding author upon reasonable request.


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We thank P. Julienne, K. Levin, D. Mazziotti, D. DeMille and K.-K. Ni for helpful discussions. We thank K. Patel and L. Weiss for carefully reading the paper. We thank J. Jachinowski for experimental assistance and carefully reading the paper. This work was supported by the National Science Foundation under grant nos. PHY1511696 and PHY-2103542 and by the Air Force Office of Scientific Research under award no. FA9550-21-1-0447. Z.Z. is supported by the Grainger Graduate Fellowship. S.N. acknowledges support from the Takenaka Scholarship Foundation.

Author information

Authors and Affiliations



Z.Z. and S.N. performed the experiments and analysed the data. Z.Z. built the theoretical model. K.-X.Y. contributed to the discussion of the results. C.C. supervised the work. All authors contributed to the writing of the paper.

Corresponding author

Correspondence to Cheng Chin.

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The authors declare no competing interests.

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Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Bound state energy diagram for cesium atoms in the hyperfine ground state \(\left\vert F=3,{m}_{{{{\rm{F}}}}}=3\right\rangle\) and molecular energy measurement near the g-wave Feshbach resonance around 20 G using modulation spectroscopy.

a, Energy diagram for Cs2 molecular states close to the atomic scattering continuum adapted from Fig. 22 in Ref. 19. b, Molecular energy εm obtained from modulation spectroscopy at different offset magnetic fields. The solid line is a linear fit which reaches 0 at B0 = 19.849(1) G.

Extended Data Fig. 2 Scattering length measurement near the narrow g-wave Feshbach resonance by time-of-flight.

a, Atomic density distributions after 20 ms time-of-flight at different magnetic fields near the Feshbach resonance. The images with B < 19.865 G (B > 19.865 G) come from initial BECs prepared below (above) the Feshbach resonance. b, Scattering length extracted from the Thomas-Fermi radii in the time-of-flight images, see text. The circular (diamond) data points come from initial BECs prepared below (above) the resonance. The solid line is a fit to the data excluding the points at 19.858G < B < 19.909G based on Eq. (7), from which we obtain the resonance width ΔB = 8.3(5) mG. The points at 19.855G < B < 19.909G are excluded because of the heating effect near the resonance. c, Total atom number extracted from the time-of-flight images.

Extended Data Fig. 3 Examples of atomic density evolution in a 2D flat-bottomed optical potential for the data presented in Fig. 3c.

For data below the resonance, BECs are initially prepared at 19.5 G and magnetic field is quenched to values between 0.05 and 1 G (panel a) and between 5 and 50 mG (panel c) below the resonance. Relaxation and equilibration phases are marked with different background colors in panel c. For data above the resonance, BECs are initially prepared at 20.4 G and magnetic field is quenched to values between 0.1 and 1 G (panel b) and between 10 and 50 mG (panel d) above the resonance. Solid lines are fits for extracting the atom loss rates, see text.

Extended Data Fig. 4 Molecule formation rate near the resonance complementary to the atom loss rate measurements in Fig. 3c.

Solid (empty) circles represent samples prepared below (above) the resonance.

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and Text.

Source data

Source Data Fig. 2

Source data for Fig. 2a,b.

Source Data Fig. 3

Source data for Fig. 3a–d.

Source Data Fig. 4

Source data for Fig. 4a,b,d.

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Zhang, Z., Nagata, S., Yao, KX. et al. Many-body chemical reactions in a quantum degenerate gas. Nat. Phys. 19, 1466–1470 (2023).

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