Abstract
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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
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.
References
Köhler, T., Góral, K. & Julienne, P. S. Production of cold molecules via magnetically tunable Feshbach resonances. Rev. Mod. Phys. 78, 1311–1361 (2006).
Jones, K. M., Tiesinga, E., Lett, P. D. & Julienne, P. S. Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering. Rev. Mod. Phys. 78, 483–535 (2006).
Shuman, E. S., Barry, J. F. & DeMille, D. Laser cooling of a diatomic molecule. Nature 467, 820–823 (2010).
Yan, B. et al. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature 501, 521–525 (2013).
Cairncross, W. B. et al. Assembly of a rovibrational ground state molecule in an optical tweezer. Phys. Rev. Lett. 126, 123402 (2021).
Wolf, J. et al. State-to-state chemistry for three-body recombination in an ultracold rubidium gas. Science 358, 921–924 (2017).
Rui, J. et al. Controlled state-to-state atom-exchange reaction in an ultracold atom–dimer mixture. Nat. Phys. 13, 699–703 (2017).
Liu, Y. et al. Precision test of statistical dynamics with state-to-state ultracold chemistry. Nature 593, 379–384 (2021).
Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS–BEC crossover: from high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005).
Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008).
Marco, L. D. et al. A degenerate Fermi gas of polar molecules. Science 363, 853–856 (2019).
Zhang, Z., Chen, L., Yao, K.-X. & Chin, C. Transition from an atomic to a molecular Bose–Einstein condensate. Nature 592, 708–711 (2021).
Heinzen, D. J., Wynar, R., Drummond, P. D. & Kheruntsyan, K. V. Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates. Phys. Rev. Lett. 84, 5029–5033 (2000).
Malla, R. K., Chernyak, V. Y., Sun, C. & Sinitsyn, N. A. Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model. Phys. Rev. Lett. 129, 033201 (2022).
Moore, M. G. & Vardi, A. Bose-enhanced chemistry: amplification of selectivity in the dissociation of molecular Bose-Einstein condensates. Phys. Rev. Lett. 88, 160402 (2002).
Vardi, A., Yurovsky, V. A. & Anglin, J. R. Quantum effects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate. Phys. Rev. A 64, 063611 (2001).
Richter, F. et al. Ultracold chemistry and its reaction kinetics. New J. Phys. 17, 055005 (2015).
Clark, L. W., Gaj, A., Feng, L. & Chin, C. Collective emission of matter-wave jets from driven Bose–Einstein condensates. Nature 551, 356–359 (2017).
Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010).
Makotyn, P., Klauss, C. E., Goldberger, D. L., Cornell, E. A. & Jin, D. S. Universal dynamics of a degenerate unitary Bose gas. Nat. Phys. 10, 116–119 (2014).
Eismann, U. et al. Universal loss dynamics in a unitary Bose gas. Phys. Rev. X 6, 021025 (2016).
Burt, E. A. et al. Coherence, correlations, and collisions: what one learns about Bose-Einstein condensates from their decay. Phys. Rev. Lett. 79, 337 (1997).
Greene, C. H., Giannakeas, P. & Pérez-Ríos, J. Universal few-body physics and cluster formation. Rev. Mod. Phys. 89, 035006 (2017).
Petrov, D. S. Three-boson problem near a narrow Feshbach resonance. Phys. Rev. Lett. 93, 143201 (2004).
Chin, C. & Grimm, R. Thermal equilibrium and efficient evaporation of an ultracold atom-molecule mixture. Phys. Rev. A 69, 033612 (2004).
Pethick, C. J. & Smith, H. Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2008).
Hung, C.-L. In Situ Probing of Two-Dimensional Quantum Gases (The Univ. Chicago, 2011).
Liu, B., Fu, L.-B. & Liu, J. Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field. Phys. Rev. A 81, 013602 (2010).
Hung, C.-L., Zhang, X., Gemelke, N. & Chin, C. Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps. Phys. Rev. A 78, 011604 (2008).
Chin, C. et al. Observation of Feshbach-like resonances in collisions between ultracold molecules. Phys. Rev. Lett. 94, 123201 (2005).
Zhang, Z. Coherent Dynamics and Reactions in Atomic and Molecular Bose-Einstein Condensates (The Univ. Chicago, 2022).
Thompson, S. T., Hodby, E. & Wieman, C. E. Ultracold molecule production via a resonant oscillating magnetic field. Phys. Rev. Lett. 95, 190404 (2005).
Lange, A. D. et al. Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances. Phys. Rev. A 79, 013622 (2009).
Hung, C.-L., Zhang, X., Gemelke, N. & Chin, C. Observation of scale invariance and universality in two-dimensional Bose gases. Nature 470, 236–239 (2011).
Castin, Y. & Dum, R. Bose-Einstein condensates in time dependent traps. Phys. Rev. Lett. 77, 5315–5319 (1996).
Berninger, M. et al. Feshbach resonances, weakly bound molecular states, and coupled-channel potentials for cesium at high magnetic fields. Phys. Rev. A 87, 032517 (2013).
Mark, M. J., Meinert, F., Lauber, K. & Nagerl, H.-C. Mott-insulator-aided detection of ultra-narrow Feshbach resonances. SciPost Phys. 5, 055 (2018).
Claussen, N. R. et al. Very-high-precision bound-state spectroscopy near a 85Rb Feshbach resonance. Phys. Rev. A 67, 060701 (2003).
Acknowledgements
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
Contributions
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
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, Z., Nagata, S., Yao, KX. et al. Many-body chemical reactions in a quantum degenerate gas. Nat. Phys. 19, 1466–1470 (2023). https://doi.org/10.1038/s41567-023-02139-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-023-02139-8
This article is cited by
-
Quantum state manipulation and cooling of ultracold molecules
Nature Physics (2024)