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arXiv:2304.09525 · Physical Review Letters

Electroassociation of Ultracold Dipolar Molecules into Tetramer Field-Linked States

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

Published Jul 26, 2023• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.131.043402

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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.
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 .
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 explore the character of a novel set of ``field-linked'' states that were predicted by Avdeenkov and Bohn [Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasibound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the two-dimensional Schr\"odinger equation to find bound states, whose energies correlate well with resonance features found in fully converged multichannel scattering calculations.
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 ∣0⟩\ket{0}∣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 ∣0⟩\ket{0}∣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.
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.