© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2306.00962 · Nature

Ultracold field-linked tetratomic molecules

Xing-Yan Chen, Shrestha Biswas, Sebastian Eppelt, Andreas Schindewolf, Fulin Deng, Tao Shi, Su Yi, Timon Hilker, Immanuel Bloch, Xinyu Luo

Published Jan 31, 2024• 38 citations

Abstract

Abstract Ultracold polyatomic molecules offer opportunities 1 in cold chemistry 2,3 , precision measurements 4 and quantum information processing 5,6 , because of their rich internal structure. However, their increased complexity compared with diatomic molecules presents a challenge in using conventional cooling techniques. Here we demonstrate an approach to create weakly bound ultracold polyatomic molecules by electroassociation 7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance 8–11 . Starting from ground-state NaK molecules, we create around 1.1 × 10 3 weakly bound tetratomic (NaK) 2 molecules, with a phase space density of 0.040(3) at a temperature of 134(3) nK, more than 3,000 times colder than previously realized tetratomic molecules 12 . We observe a maximum tetramer lifetime of 8(2) ms in free space without a notable change in the presence of an optical dipole trap, indicating that these tetramers are collisionally stable. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wavefunction in momentum space. Our result demonstrates a universal tool for assembling weakly bound ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose–Einstein condensation of polyatomic molecules and towards a new crossover from a dipolar Bardeen–Cooper–Schrieffer superfluid 13–15 to a Bose–Einstein condensation of tetramers. Moreover, the long-lived field-linked state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states 16–18 .

DOI: 10.1038/s41586-023-06986-6

Related papers

Tetratomic states of microwave dressed and associated ultracold 23Na40K molecules

Zhengyu Gu, Zhou, Xuansheng, Wei Chen +5 more

Ultracold diatomic molecules have achieved significant breakthroughs in recent years, enabling the exploration of quantum chemistry, precision measurements, and strongly correlated many-body physics. Extending ultracold molecular complexity to polyatomic molecules, such as triatomic and tetratomic molecules, has attracted considerable interest. However, the realization of ultracold polyatomic molecules remains technically challenging due to their complex energy-level structures. While only a few experiments have successfully demonstrated the formation of polyatomic molecules by magnetoassociation or electroassociation, here we present the first step toward producing tetratomic molecules through the development of a microwave association technique combined with microwave dressing. When the two lowest rotational states of the molecules are dressed by a microwave field, weakly bound tetramer states emerge in the entrance channel with free dark excited states $\ket{0}$ and a dressed state $\ket{+}$. The spectroscopy of these weakly bound tetramers is probed by another microwave field that drives transitions from the populated dressed states $\ket{+}$. By precisely discriminating the complex hyperfine structure of the dark excited level $\ket{0}$ from the dressed-state spectroscopy, the binding energy of the tetratomic molecules is measured and characterized. Our work contributes to the understanding of complex few-body physics within a system of microwave-dressed molecules and may open an avenue toward the creation and control of ultracold polyatomic molecules.

arXiv:2509.23634•Sep 28, 2025•0 citations

Electroassociation of Ultracold Dipolar Molecules into Tetramer Field-Linked States

Goulven Quéméner, John L. Bohn, James F. E. Croft

The presence of electric or microwave fields can modify the long-range forces between ultracold dipolar molecules in such a way as to engineer weakly bound states of molecule pairs. These so-called field-linked states [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003).PRLTAO0031-900710.1103/PhysRevLett.90.043006; L. Lassablière and G. Quéméner, Phys. Rev. Lett. 121, 163402 (2018).PRLTAO0031-900710.1103/PhysRevLett.121.163402], in which the separation between the two bound molecules can be orders of magnitude larger than the molecules themselves, have been observed as resonances in scattering experiments [X.-Y. Chen et al., Nature (London) 614, 59 (2023).NATUAS0028-083610.1038/s41586-022-05651-8]. Here, we propose to use them as tools for the assembly of weakly bound tetramer molecules, by means of ramping an electric field, the electric-field analog of magnetoassociation in atoms. This ability would present new possibilities for constructing ultracold polyatomic molecules.

arXiv:2304.09525•Physical Review Letters•Jul 26, 2023•15 citations

Optical Excitation and Stabilization of Ultracold Field-Linked Tetratomic Molecules

Bijit Mukherjee, Michał Tomza

We propose a coherent optical population transfer of weakly bound field-linked (FL) tetratomic molecules (tetramers) to deeper FL bound states using stimulated Raman adiabatic passage. We consider static-electric-field shielded polar alkali-metal diatomic molecules and corresponding FL tetramers in their X^{1}Σ^{+}+X^{1}Σ^{+} ground electronic state. We show that the excited metastable X^{1}Σ^{+}+b^{3}Π electronic manifold supports FL tetramers in a broader range of electric fields with collisional shielding extended to zero field. We calculate the Franck-Condon factors between the ground and excited FL tetramers and show that they are highly tunable with the electric field. We also predict photoassociation of ground-state shielded molecules to the excited FL states in free-bound optical transitions. We propose proof-of-principle experiments to implement stimulated Raman adiabatic passage and photoassociation using FL tetramers, paving the way for the formation of deeply bound ultracold polyatomic molecules.

arXiv:2506.17341•Physical Review Letters•Dec 22, 2025•5 citations

Field-linked resonances of polar molecules

Xing-Yan Chen, Andreas Schindewolf, Sebastian Eppelt +7 more

Abstract Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances 1 , which have been extensively studied in various platforms 1–7 , are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance 8–10 . Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances 11–14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium–potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole–dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids 15 and molecular supersolids 16 , as well as assembling ultracold polyatomic molecules.

arXiv:2210.13324•Nature•Feb 1, 2023•53 citations

Confinement-induced field-linked states of ultracold polar molecules

Reuben R. W. Wang, John L. Bohn

We predict the existence of stable bound states between pairs of ultracold diatomic molecules with the aid of a static electric field and 1D harmonic confinement. We focus on collisions of NaK-NaK identical fermions, for which we find that currently achievable experimental parameters allow the observation of these confinement-induced field-linked bound states as scattering resonances. The bound state is highly stable with lifetimes estimated to be tens of seconds long. With the diatomic molecules bound at distances a fraction of the dipolar length scale, these complexes allow for explorations of polyatomic chemistry and Fermi gas superfluid pairing.

arXiv:2409.08431•Sep 12, 2024•0 citations

Formation and Dissociation of Field-Linked Tetramers

Fulin Deng, Xing-Yan Chen, Xinyu Luo +3 more

We investigate the static and dynamic properties of tetratomic molecules formed by two microwave-shielded polar molecules across field-linked resonances. In particular, we focus on two-body physics and experimental techniques unexplored in the recent experiment [X.-Y. Chen {\it et al}., Nature {\bf626}, 283 (2024)]. We show that, compared to the lowest tetramer state, higher tetramer states typically have longer lifetimes, which may facilitate a further cooling of tetramer gases towards quantum degeneracy. To detect tetramers, we identify the distinctive time-of-flight images from ramp dissociation, which can be observed by lowering the ramp rate of the microwave. Remarkably, in the modulational dissociation of tetramers, we find that multi-photon processes induce dissociation even below the threshold modulation frequency when the modulation amplitude is sufficiently high. Given the universal form of the inter-molecular potential for microwave-shielded polar molecules, our results also apply to other molecular gases widely explored in recent experiments.

arXiv:2405.13645•May 22, 2024•1 citation

Abstract Ultracold polyatomic molecules offer opportunities 1 in cold chemistry 2,3 , precision measurements 4 and quantum information processing 5,6 , because of their rich internal structure. However, their increased complexity compared with diatomic molecules presents a challenge in using conventional cooling techniques. Here we demonstrate an approach to create weakly bound ultracold polyatomic molecules by electroassociation 7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance 8–11 . Starting from ground-state NaK molecules, we create around 1.1 × 10 3 weakly bound tetratomic (NaK) 2 molecules, with a phase space density of 0.040(3) at a temperature of 134(3) nK, more than 3,000 times colder than previously realized tetratomic molecules 12 . We observe a maximum tetramer lifetime of 8(2) ms in free space without a notable change in the presence of an optical dipole trap, indicating that these tetramers are collisionally stable. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wavefunction in momentum space. Our result demonstrates a universal tool for assembling weakly bound ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose–Einstein condensation of polyatomic molecules and towards a new crossover from a dipolar Bardeen–Cooper–Schrieffer superfluid 13–15 to a Bose–Einstein condensation of tetramers. Moreover, the long-lived field-linked state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states 16–18 .

Ultracold diatomic molecules have achieved significant breakthroughs in recent years, enabling the exploration of quantum chemistry, precision measurements, and strongly correlated many-body physics. Extending ultracold molecular complexity to polyatomic molecules, such as triatomic and tetratomic molecules, has attracted considerable interest. However, the realization of ultracold polyatomic molecules remains technically challenging due to their complex energy-level structures. While only a few experiments have successfully demonstrated the formation of polyatomic molecules by magnetoassociation or electroassociation, here we present the first step toward producing tetratomic molecules through the development of a microwave association technique combined with microwave dressing. When the two lowest rotational states of the molecules are dressed by a microwave field, weakly bound tetramer states emerge in the entrance channel with free dark excited states

\ket{0}

and a dressed state

\ket{+}

. The spectroscopy of these weakly bound tetramers is probed by another microwave field that drives transitions from the populated dressed states

\ket{+}

. By precisely discriminating the complex hyperfine structure of the dark excited level

\ket{0}

from the dressed-state spectroscopy, the binding energy of the tetratomic molecules is measured and characterized. Our work contributes to the understanding of complex few-body physics within a system of microwave-dressed molecules and may open an avenue toward the creation and control of ultracold polyatomic molecules.

The presence of electric or microwave fields can modify the long-range forces between ultracold dipolar molecules in such a way as to engineer weakly bound states of molecule pairs. These so-called field-linked states [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003).PRLTAO0031-900710.1103/PhysRevLett.90.043006; L. Lassablière and G. Quéméner, Phys. Rev. Lett. 121, 163402 (2018).PRLTAO0031-900710.1103/PhysRevLett.121.163402], in which the separation between the two bound molecules can be orders of magnitude larger than the molecules themselves, have been observed as resonances in scattering experiments [X.-Y. Chen et al., Nature (London) 614, 59 (2023).NATUAS0028-083610.1038/s41586-022-05651-8]. Here, we propose to use them as tools for the assembly of weakly bound tetramer molecules, by means of ramping an electric field, the electric-field analog of magnetoassociation in atoms. This ability would present new possibilities for constructing ultracold polyatomic molecules.

We propose a coherent optical population transfer of weakly bound field-linked (FL) tetratomic molecules (tetramers) to deeper FL bound states using stimulated Raman adiabatic passage. We consider static-electric-field shielded polar alkali-metal diatomic molecules and corresponding FL tetramers in their X^{1}Σ^{+}+X^{1}Σ^{+} ground electronic state. We show that the excited metastable X^{1}Σ^{+}+b^{3}Π electronic manifold supports FL tetramers in a broader range of electric fields with collisional shielding extended to zero field. We calculate the Franck-Condon factors between the ground and excited FL tetramers and show that they are highly tunable with the electric field. We also predict photoassociation of ground-state shielded molecules to the excited FL states in free-bound optical transitions. We propose proof-of-principle experiments to implement stimulated Raman adiabatic passage and photoassociation using FL tetramers, paving the way for the formation of deeply bound ultracold polyatomic molecules.

Abstract Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances 1 , which have been extensively studied in various platforms 1–7 , are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance 8–10 . Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances 11–14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium–potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole–dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids 15 and molecular supersolids 16 , as well as assembling ultracold polyatomic molecules.

We predict the existence of stable bound states between pairs of ultracold diatomic molecules with the aid of a static electric field and 1D harmonic confinement. We focus on collisions of NaK-NaK identical fermions, for which we find that currently achievable experimental parameters allow the observation of these confinement-induced field-linked bound states as scattering resonances. The bound state is highly stable with lifetimes estimated to be tens of seconds long. With the diatomic molecules bound at distances a fraction of the dipolar length scale, these complexes allow for explorations of polyatomic chemistry and Fermi gas superfluid pairing.

We investigate the static and dynamic properties of tetratomic molecules formed by two microwave-shielded polar molecules across field-linked resonances. In particular, we focus on two-body physics and experimental techniques unexplored in the recent experiment [X.-Y. Chen {\it et al}., Nature {\bf626}, 283 (2024)]. We show that, compared to the lowest tetramer state, higher tetramer states typically have longer lifetimes, which may facilitate a further cooling of tetramer gases towards quantum degeneracy. To detect tetramers, we identify the distinctive time-of-flight images from ramp dissociation, which can be observed by lowering the ramp rate of the microwave. Remarkably, in the modulational dissociation of tetramers, we find that multi-photon processes induce dissociation even below the threshold modulation frequency when the modulation amplitude is sufficiently high. Given the universal form of the inter-molecular potential for microwave-shielded polar molecules, our results also apply to other molecular gases widely explored in recent experiments.