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arXiv:2602.11637 · Physical Review Letters

First-order phase transition in atom-molecule quantum degenerate mixtures with coherent three-body recombination

G. A. Bougas, A. Vardi, H. R. Sadeghpour, C. Chin, S. I. Mistakidis

cond-mat.quant-gasquant-phSubmitted Feb 12, 2026• Announced Feb 13, 2026• 0 citations
v1 · Feb 12, 2026v2 · Aug 25, 2026
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Abstract

We map the phase diagram of a two-mode atom-molecule Bose-Einstein condensate with Fano-Feshbach and coherent three-body recombination (cTBR) terms. The standard second order phase transition observed as the molecular energy is tuned through the Feshbach resonance, is replaced by a first order transition when cTBR becomes prominent, due to a double-well structure in the free energy landscape. This transition is associated with atom-molecule entanglement, bistability, and molecular metastability. Our results establish cTBR as a powerful knob for quantum state engineering and control of reaction dynamics in ultracold chemistry.

DOI
10.1103/llw4-tbnt
Comments
6 pages, 4 figures, Supplementary Material, 6 pages

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We map the phase diagram of a two-mode atom-molecule Bose-Einstein condensate with Fano-Feshbach and coherent three-body recombination (cTBR) terms. The standard second order phase transition observed as the molecular energy is tuned through the Feshbach resonance, is replaced by a first order transition when cTBR becomes prominent, due to a double-well structure in the free energy landscape. This transition is associated with atom-molecule entanglement, bistability, and molecular metastability. Our results establish cTBR as a powerful knob for quantum state engineering and control of reaction dynamics in ultracold chemistry.
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We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with $\text{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry, describing atoms and molecules on a two-dimensional optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean-field theory, we show that the conversion between the two species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term---the Feshbach insulator---instead of a standard Mott-insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with noncondensed atoms, and a mixed atomic-molecular condensate. Employing finite-size scaling analysis, we observe three-dimensional (3D) XYXYXY (3D Ising) transition when U(1)\text{U}(1)U(1) (Z2{\mathbb{Z}}_{2}Z2​) symmetry is broken, whereas the transition is first order when both U(1)\text{U}(1)U(1) and Z2{\mathbb{Z}}_{2}Z2​ symmetries are spontaneously broken. The finite-temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a signal compatible with a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.
Advances in atomic physics have led to the possibility of a coherent transformation between ultracold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the constituent atoms and molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these effects, along with scaling laws for the reaction yield in non-adiabatic regimes.
In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length aaa exceeds a critical value depending on the atom density nnn, na3>0.035n{a}^{3}>0.035na3>0.035, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However, when the scattering length is above another critical value, na3>0.0164n{a}^{3}>0.0164na3>0.0164, the molecular BEC state becomes an unstable coherent mixture of atoms and molecules. In both BEC states, the binding energy of diatomic molecules is reduced due to the many-body effect.
Abstract Chemical reactions in the quantum degenerate regime are described by mixing of matterwave fields. Quantum coherence and bosonic enhancement are two unique features of many-body reactions involving bosonic reactants and products. Such collective reactions of chemicals, dubbed “super-chemistry”, is an elusive goal in quantum chemistry research. 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 a rapid formation of molecules, followed by oscillations of their populations in the equilibration process. Faster oscillations are observed in samples with higher densities, indicating bosonic enhancement. We present a quantum field model which describes the dynamics well and identifies three body recombination as the dominant reaction process. Our findings exemplify the highly sought-after quantum many-body chemistry and offer a new paradigm for the control of quantum chemical reactions.
Chemical reactions in a statistical ensemble are conventionally regarded as incoherent processes driven by thermodynamics. In the quantum degenerate regime, where atoms and molecules form coherent matter waves, reactions are theoretically described by nonlinear mixing of matter-wave fields. In this scenario, we expect phase matching between reactants and products, analogous to the mixing of photonic fields in nonlinear optics. Here we report on the observation of phase coherent reaction dynamics of Bose-condensed atoms and molecules near a Feshbach resonance. Using matter-wave diffraction with optical lattices, we verify spatial coherence of both atoms and molecules and observe phase doubling when atomic waves combine into molecular waves, the matter-wave analogue of optical frequency doubling. The diffraction patterns further reveal two-atom entanglement generated during the reaction. Our observations establish phase coherence and entanglement generation as two essential features of "quantum many-body chemistry". Moreover, our work opens a pathway to control of reaction dynamics by manipulation of matter-wave phases.