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Ultracold NaK2 Trimers: From Photoassociation to Coherent Ground-State Stabilization

Baraa Shammout

Published Jan 1, 2026• 0 citations
Publisher

Abstract

The assembly and coherent control of ultracold molecules have opened new horizons in quantum science with applications in ultracold chemistry, quantum information, quantum simulation, precision metrology and fundamental physics. While considerable progress has been achieved in controlling diatomic molecules at ultracold temperatures, extending to atom-diatom collisions and triatomic systems introduces additional internal structure, anisotropy, and interaction complexity, enabling access to many-body phenomena. This dissertation presents a detailed theoretical study on the production and stabilization of ultracold alkali-metal triatomic molecules, with a particular focus on the NaK2 molecular species. First, long-range photoassociation in ultracold NaK(X^1Σ+) + K(4s) mixtures is investigated near the molecular transition X^1Σ+ → b^3Π. Photoassociation rates into weakly bound trimers in the electronically excited 3^2A' state are evaluated under experimentally relevant conditions. The calculated photoassociation rates indicate experimentally feasible and spectrally selective routes for detecting ultracold atom–diatom photoassociation resonances, while suppressing competing diatomic loss channels. Second, a microwave-assisted association mechanism is introduced for coherently binding ultracold atoms and polar molecules into weakly bound triatomic molecules on the ground-state 1^2A' potential energy surface. This process relies on the interaction between the electric component of the microwave field and the permanent electric dipole moment of the NaK molecule. In the presence of the anisotropic atom–diatom potential, which couples the molecular rotation to the relative angular motion, the microwave field can drive transitions from scattering states to weakly bound trimer states entirely in the electronic ground-state of the triatomic molecule, without involving spontaneous emission. This process is therefore intrinsically coherent and particularly suited to closed-shell polar molecules for which magnetically tunable Feshbach resonances are weak or absent. Finally, candidate pathways toward coherent population transfer to the absolute rovibronic ground state of NaK2 are explored using bridge states belonging to the excited 3^2A' electronic state, such as those identified in [Ref.1]. The relevant potential energy surfaces, transition dipole moments, and rovibrational structures are analyzed, revealing favorable conditions for future stimulated Raman adiabatic passage scheme. The theoretical modeling combines high-level electronic-structure calculations with nuclear-motion methods across multiple energy and length scales. Three-dimensional potential energy surfaces and electronic transition dipole moment surfaces were obtained from ab initio multireference configuration interaction calculations employing effective-core pseudopotentials and core-polarization potentials. Nuclear motion was treated using coupled-channel methods for describing weakly bound states and discrete variable representation methods for deeply bound rovibrational states. The resulting wavefunctions were subsequently used to evaluate Franck–Condon factors, photo- and microwave association rates, and transition strengths relevant to experimental implementation. Overall, this dissertation provides an extensive theoretical framework for the formation, detection and ground-state stabilization of ultracold NaK2 trimers. Reference: [1] J. Cao, B.-Y. Wang, H. Yang, Z.-J. Fan, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, “Observation of photoassociation resonances in ultracold atom-molecule collisions,” Phys. Rev. Lett., vol. 132, p. 093403, 2024.

DOI
10.15488/22786

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The assembly and coherent control of ultracold molecules have opened new horizons in quantum science with applications in ultracold chemistry, quantum information, quantum simulation, precision metrology and fundamental physics. While considerable progress has been achieved in controlling diatomic molecules at ultracold temperatures, extending to atom-diatom collisions and triatomic systems introduces additional internal structure, anisotropy, and interaction complexity, enabling access to many-body phenomena. This dissertation presents a detailed theoretical study on the production and stabilization of ultracold alkali-metal triatomic molecules, with a particular focus on the NaK2 molecular species. First, long-range photoassociation in ultracold NaK(X^1Σ+) + K(4s) mixtures is investigated near the molecular transition X^1Σ+ → b^3Π. Photoassociation rates into weakly bound trimers in the electronically excited 3^2A' state are evaluated under experimentally relevant conditions. The calculated photoassociation rates indicate experimentally feasible and spectrally selective routes for detecting ultracold atom–diatom photoassociation resonances, while suppressing competing diatomic loss channels. Second, a microwave-assisted association mechanism is introduced for coherently binding ultracold atoms and polar molecules into weakly bound triatomic molecules on the ground-state 1^2A' potential energy surface. This process relies on the interaction between the electric component of the microwave field and the permanent electric dipole moment of the NaK molecule. In the presence of the anisotropic atom–diatom potential, which couples the molecular rotation to the relative angular motion, the microwave field can drive transitions from scattering states to weakly bound trimer states entirely in the electronic ground-state of the triatomic molecule, without involving spontaneous emission. This process is therefore intrinsically coherent and particularly suited to closed-shell polar molecules for which magnetically tunable Feshbach resonances are weak or absent. Finally, candidate pathways toward coherent population transfer to the absolute rovibronic ground state of NaK2 are explored using bridge states belonging to the excited 3^2A' electronic state, such as those identified in [Ref.1]. The relevant potential energy surfaces, transition dipole moments, and rovibrational structures are analyzed, revealing favorable conditions for future stimulated Raman adiabatic passage scheme. The theoretical modeling combines high-level electronic-structure calculations with nuclear-motion methods across multiple energy and length scales. Three-dimensional potential energy surfaces and electronic transition dipole moment surfaces were obtained from ab initio multireference configuration interaction calculations employing effective-core pseudopotentials and core-polarization potentials. Nuclear motion was treated using coupled-channel methods for describing weakly bound states and discrete variable representation methods for deeply bound rovibrational states. The resulting wavefunctions were subsequently used to evaluate Franck–Condon factors, photo- and microwave association rates, and transition strengths relevant to experimental implementation. Overall, this dissertation provides an extensive theoretical framework for the formation, detection and ground-state stabilization of ultracold NaK2 trimers. Reference: [1] J. Cao, B.-Y. Wang, H. Yang, Z.-J. Fan, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, “Observation of photoassociation resonances in ultracold atom-molecule collisions,” Phys. Rev. Lett., vol. 132, p. 093403, 2024.
The realization of rovibrationally stable dense samples of ultracold diatomic molecules remains one of the main stepping stones to achieve the next slate of major goals in the field of atomic and molecular physics. Though obtaining diatomic alkali molecules was seen as a logical next step following the optical cooling of atoms, many of the possible applications currently under investigation extend beyond atomic and molecular physics. For example, spectroscopy of ultracold molecules can help in testing extensions of the Standard Model via the search for a permanent electric dipole moment of the electron (1; 2), or the energy difference between enantiomers of chiral molecules (3). Various molecular transitions can be utilized to track the time dependence of fundamental constants, including the fine structure constant and the proton to electron mass ratio (4). They also open the way for cold and ultracold chemistry, where the interacting species and products are in a coherent quantum superposition state (5) and reactions can happen via quantum tunneling. Dipolar ultracold quantum gases promise to show a plethora of new phenomena due to anisotropic long-range dipole-dipole interactions (6). Dipolar molecules in optical lattices can be employed as a quantum simulator of condensed matter systems, and they are predicted to demonstrate new quantum phases such as a dipolar crystal, supersolid, checkerboard and collapse phases (7; 8). Ultracold polar molecules also represent an attractive platform for quantum computation (9). They offer a variety of long-lived states for qubit encoding, including rotational, spin and hyperfine (if electronic and nuclear spins are non-zero), Λ and Ω-doublet states (10) and scalability to a large number of qubits. Polar molecules can be easily controlled by DC electric and magnetic fields, as well as bymicrowave and optical fields, allowing the design of various traps (11; 12). The main appeal of polar molecules for quantum information processing, however, comes from their permanent electric dipole moment, permitting them to interact via a long-range dipole-dipole interaction. The dipole-dipole interaction offers a tool to construct two-qubit gates, required for universal quantum computation (9; 13). Ultracold molecules in their ground vibrational state v = 0 (and even in specific rotational, hyperfine or Zeeman states) are required formany of these applications since they have a large permanent electric dipole moment and are stable with respect to collisions and spontaneous emission. Currently translationally ultracold (100 nK 1 mK) molecules are produced by magneto(14) and photo-association (15) techniques. In a typical photoassociation scheme, 3
Alkali hydride molecules are polar, exhibiting large ground-state dipole moments. As ultracold sources of alkali atoms, as well as hydrogen, have been created in the laboratory, we explore theoretically the feasibility of forming such molecules from a mixture of the ultracold atomic gases, employing various photoassociation schemes. In this work we use lithium and sodium hydride as benchmark systems to calculate molecule formation rates through stimulated one-photon radiative association directly from the continuum as well as two-photon stimulated radiative association (Raman transfer) and excitation to bound levels of an excited state followed by spontaneous emission to the ground state. Using accurate molecular potential energy curves and dipole transition moments and with laser intensities and MOT densities that are easily attainable experimentally, we have found that substantial molecule formation rates can be realized even after the effect of back-stimulation has been accounted for. We examine the spontaneous emission cascade which takes place from the upper vibrational levels of the singlet ground state on a time scale of milliseconds. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in the lowest vibrational level can be achieved. The triplet ground electronic state is of particular interest for experimental efforts since, although it has never been observed experimentally, molecular structure calculations of the a3Σ+ state for LiH and NaH predict a small van der Waals attraction, with a potential energy well so shallow that it can support only one bound rotational-vibrational level. Any molecule formed in the triplet ground state would then be immediately in the lowest and most stable level of that state and would be quite long-lived, unlike molecules in high vibrational levels which have significantly shorter lifetimes. As an analysis of our method of calculating molecule formation rates, we investigate more thoroughly the two-photon stimulated photoassociation process by employing the exact treatment of Dalgarno & Lewis to solve the Raman scattering problem. ^
This thesis reports on the construction of a novel experimental apparatus to create an ultracold sample of chemical stable 23Na40K^{23}\rm{Na}^{40}\rm{K}23Na40K polar molecules at their absolute ground states. The long range nature of the dipolar interactions between the ground state molecules, is expected to facilitate to observe new quantum many-body states and to simulate prototypical lattice spin models for exploring quantum magnetism and high TcT_cTc​ superconductivity. The experimental procedures are presented in this thesis including: trapping and cooling 23Na^{23}\rm{Na}23Na and $ ^{40}\rm{K}$ atoms to quantum degeneracy, associating weakly bound state molecules with Feshbach resonances, and transferring the Feshbach molecules to the rovibrational ground states via stimulated Raman adiabatic passage. As a result, successful transfer has been demonstrated in our experiment with a single-path transfer efficiency ≃60%\simeq 60\%≃60% via a hyperfine non-resolved intermediate state ∣d3Π,ν=5,J=1,Ω=1⟩\vert d^{3}\Pi, \nu=5, J=1, \Omega=1 \rangle∣d3Π,ν=5,J=1,Ω=1⟩. In addition, a perturbative theoretical study on the Fermi liquid properties of a single-component weakly-interacting two dimensional dipolar fermions with dipole moments ddd oriented perpendicularly to the plane of their translational motion is presented in the thesis. When the dipole moments are tilted with respect to the translational plane, the effect of anisotropic interaction appears, and collective excitations in the collisionless regime are studied in this configuration. Furthermore, stable dilute supersolid states with two-dimensional bosonic dipoles are predicted to exist with an additional three-body repulsive contact interaction. These novel quantum effects should be accessible experimentally once the NaK\rm{Na}\rm{K}NaK ground state molecules reach quantum degeneracy by further evaporative cooling.
Ultracold bialkali polar molecules play a leading part at the frontline of quantum physics. They recently attract a lot of attention in the field of ultracold quantum chemistry, quantum many-body physics and quantum simulations. The key for their success is the rich internal level structure with rotational and vibrational degrees of freedom and their large electric dipole moments. Still, only a handful of molecular species are available at ultracold temperatures until now, although it is highly desirable to produce new molecular species to further expand the range of applications. Besides direct laser cooling methods for molecules, the assembly of heteronuclear ground-state molecules from ultracold atomic mixtures is the most promising approach for the creation of polar molecules. It includes the formation of weakly bound Feshbach molecules from the diatomic mixture and the subsequent two-photon stimulated Raman adiabatic passage (STIRAP) transfer to the rovibrational ground state. This creation strategy has been successfully demonstrated for the first time in the pioneering experiments at JILA with ultracold 40K87Rb molecules. Since then, only a few more molecular species from different alkali atoms have been created, namely 6Li23Na, 23Na40K, 23Na87Rb and 87Rb133Cs. In this thesis, I report the successful creation of a new species of ultracold polar ground-state molecules: 23Na39K. Starting from an ultracold mixture of bosonic 23Na and 39K atoms, weakly bound molecules are created. For this purpose, a Feshbach resonance in a high angular momentum scattering channel is chosen, experimentally identified and characterized. Close to this resonance the weakly bound Feshbach molecules are formed using resonant radio frequency radiation. For the two-photon ground-state transfer, a unique, highly specialized two-color laser system is designed and realized. It is used for one- and two-photon spectroscopy to identify the relevant transitions for the ground-state transfer. Based on the obtained data, a local model of the singlet-triplet mixed excited state manifolds is developed, with which the hyperfine structure and the magnetic field dependence is predicted with high accuracy. According to these findings, a suitable pathway to a single hyperfine ground state is chosen considering selection rules and experimental conditions such as laser polarization and beam alignment. To precisely determine the two-photon resonance condition for STIRAP, electromagnetically induced transparency measurements are performed. The ground-state transfer is then performed using STIRAP. The experimental findings regarding the STIRAP are successfully supported theoretically by a model based on a five-level master equation. The pure molecular gas shows evidence for two-body dominated loss mechanisms, such as sticky four-body collisions. The molecule-atom mixture of 23Na39K+39K reveals an unexpectedly low loss rate coefficient although sticky three-body collisions are assumed to occur. This behavior demands further investigations regarding different hyperfine collisional chan-nels and magnetic field regions.
We report on the observation of photoassociation resonances in ultracold collisions between ^{23}Na^{40}K molecules and ^{40}K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances.
We study the rovibronic transitions in NaK 2 between its electronic ground state 1 2 A ′ and its second excited state 3 2 A ′ , to identify possible pathways for the creation of ultracold ground-state triatomic molecules. Our methodology relies on the computation of potential energy surfaces and transition dipole moment surfaces for the relevant electronic states using methods. Rovibrational energy levels and wave functions are determined using the discrete variable representation approach. A double-well structure of the potential energy surface is identified for both states, and the related transition strengths between the rovibrational levels are derived. Our calculations show that the formation of ultracold ground-state NaK 2 molecules is expected when starting from an excited electronic state of NaK 2 , which can be created by photoassociation of NaK and K, as observed by optical means by Cao, [].