Linking ultracold polar molecules

Observation of Bose-Einstein condensation of dipolar molecules

Ensembles of particles governed by quantum mechanical laws exhibit intriguing emergent behaviour. Atomic quantum gases1,2, liquid helium3,4 and electrons in quantum materials5-7 all exhibit distinct properties because of their composition and interactions. Quantum degenerate samples of ultracold dipolar molecules promise the realization of new phases of matter and new avenues for quantum simulation8 and quantum computation9. However, rapid losses10, even when reduced through collisional shielding techniques11-13, have so far prevented evaporative cooling to a Bose-Einstein condensate (BEC). Here we report on the realization of a BEC of dipolar molecules. By strongly suppressing two- and three-body losses via enhanced collisional shielding, we evaporatively cool sodium-caesium molecules to quantum degeneracy and cross the phase transition to a BEC. The BEC reveals itself by a bimodal distribution when the phase-space density exceeds 1. BECs with a condensate fraction of 60(10)% and a temperature of 6(2) nK are created and found to be stable with a lifetime close to 2 s. This work opens the door to the exploration of dipolar quantum matter in regimes that have been inaccessible so far, promising the creation of exotic dipolar droplets14, self-organized crystal phases15 and dipolar spin liquids in optical lattices16.

Ultracold field-linked tetratomic molecules

Ultracold polyatomic molecules offer opportunities1 in cold chemistry2,3, precision measurements4 and quantum information processing5,6, 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 electroassociation7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance8-11. Starting from ground-state NaK molecules, we create around 1.1 × 103 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 molecules12. 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 superfluid13-15 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 states16-18.

Electroassociation of Ultracold Dipolar Molecules into Tetramer Field-Linked States

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.

Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules

We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.

Field-linked resonances of polar molecules

Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances¹, 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 superfluids¹⁵ and molecular supersolids¹⁶, as well as assembling ultracold polyatomic molecules.

Complete Quantum Coherent Control of Ultracold Molecular Collisions

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.

Controlling the Scattering Length of Ultracold Dipolar Molecules

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac field is increased, the long-range well becomes deeper and can support a certain number of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant B[over ˜]=B/s_{E_{3}} where s_{E_{3}} is a characteristic dipolar energy. We found that molecules with B[over ˜]>10^{8} are immune to any quenching losses when a sufficient ac field is applied, the ratio elastic to quenching processes can reach values above 10^{3}, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar to that for ultracold atoms.

Molecular collisions and reactive scattering in external fields: Are field-induced couplings important at short range?

We use accurate quantum scattering calculations to elucidate the role of short-range molecule-field interactions in atom-molecule inelastic collisions and abstraction chemical reactions at low temperatures. We consider two examples: elastic and inelastic scattering of NH(Σ3) molecules with Mg(S1) atoms in a magnetic field; reactive scattering LiF + H → Li + HF in an electric field. Our calculations suggest that, for non-reactive collision systems and abstraction chemical reactions, the molecule-field interactions cannot generally be neglected at short range because the atom-molecule potential passes through zero at short range. An important exception occurs for Zeeman transitions in atom-molecule collisions at magnetic fields ≲1000 G, for which the molecule-field couplings need only be included at large ρ outside the range of the atom-molecule interaction. Our results highlight the importance of an accurate description of ρ-dependent molecule-field interactions in quantum scattering calculations on molecular collisions and chemical reactions at low temperatures.

Transparent electrodes for high E-field production using a buried indium tin oxide layer

We present a design and characterization of optically transparent electrodes suitable for atomic and molecular physics experiments where high optical access is required. The electrodes can be operated in air at standard atmospheric pressure and do not suffer electrical breakdown even for electric fields far exceeding the dielectric breakdown of air. This is achieved by putting an indium tin oxide coated dielectric substrate inside a stack of dielectric substrates, which prevents ion avalanche resulting from Townsend discharge. With this design, we observe no arcing for fields of up to 120 kV/cm. Using these plates, we directly verify the production of electric fields up to 18 kV/cm inside a quartz vacuum cell by a spectroscopic measurement of the dc Stark shift of the 5(2)S(1/2) → 5(2)P(3/2) transition for a cloud of laser cooled rubidium atoms. We also report on the shielding of the electric field and on the residual electric fields that persist within the vacuum cell once the electrodes are discharged. In addition, we discuss observed atom loss that results from the motion of free charges within the vacuum. The observed asymmetry of these phenomena on the bias of the electrodes suggests that field emission of electrons within the vacuum is primarily responsible for these effects and may indicate a way of mitigating them.

Chemical reaction versus vibrational quenching in low energy collisions of vibrationally excited OH with O

Quantum scattering calculations are reported for state-to-state vibrational relaxation and reactive scattering in O + OH(v = 2 - 3, j = 0) collisions on the electronically adiabatic ground state (2)A'' potential energy surface of the HO2 molecule. The time-independent Schrödinger equation in hyperspherical coordinates is solved to determine energy dependent probabilities and cross sections over collision energies ranging from ultracold to 0.35 eV and for total angular momentum quantum number J = 0. A J-shifting approximation is then used to compute initial state selected reactive rate coefficients in the temperature range T = 1 - 400 K. Results are found to be in reasonable agreement with available quasiclassical trajectory calculations. Results indicate that rate coefficients for O2 formation increase with increasing the OH vibrational level except at low and ultralow temperatures where OH(v = 0) exhibits a slightly different trend. It is found that vibrational relaxation of OH in v = 2 and v = 3 vibrational levels is dominated by a multi-quantum process.

Trapping of ultracold polar molecules with a thin-wire electrostatic trap

We describe the realization of a dc electric-field trap for ultracold polar molecules, the thin-wire electrostatic trap (TWIST). The thin wires that form the electrodes of the TWIST allow us to superimpose the trap onto a magneto-optical trap (MOT). In our experiment, ultracold polar NaCs molecules in their electronic ground state are created in the MOT via photoassociation, achieving a continuous accumulation in the TWIST of molecules in low-field seeking states. Initial measurements show that the TWIST trap lifetime is limited only by the background pressure in the chamber.

Manipulating spin-dependent interactions in rotationally excited cold molecules with electric fields

We use rigorous quantum mechanical theory to study collisions of magnetically oriented cold molecules in the presence of superimposed electric and magnetic fields. It is shown that electric fields suppress the spin-rotation interaction in rotationally excited 2Sigma molecules and inhibit rotationally elastic and inelastic transitions accompanied by electron spin reorientation. We demonstrate that electric fields enhance collisional spin relaxation in 3Sigma molecules and discuss the mechanisms for electric field control of spin-changing transitions in collisions of rotationally excited CaD(2Sigma) and ND(3Sigma) molecules with helium atoms. The propensities for spin depolarization in the rotationally excited molecules are analyzed based on the calculations of collision rate constants at T=0.5 K.

Mechanism and control of the F+H2 reaction at low and ultralow collision energies

This article uses theoretical methods to study the dependence on stereodynamical factors of the mechanism and reactivity of the F+H2 reaction at low and ultralow collision energies. The impact of polarization of the H2 reactant on total and state-to-state integral and differential cross sections is analyzed. This leads to detailed pictures of the reaction mechanism in the cold and ultracold regimes, accounting, in particular, for distinctions associated with the various product states and scattering angles. The extent to which selection of reactant polarization allows for external control of the reactivity and reaction mechanism is assessed. This reveals that even the simplest of reactant polarization schemes allows for fine, product state-selective control of differential and (for reactions involving more than a single, zero orbital angular momentum partial wave) integral cross sections.

State-to-state rotational transitions in H2+H2 collisions at low temperatures

We present quantum mechanical close-coupling calculations of collisions between two hydrogen molecules over a wide range of energies, extending from the ultracold limit to the superthermal region. The two most recently published potential energy surfaces for the H(2)-H(2) complex, the so-called Diep-Johnson (DJ) [J. Chem. Phys. 112, 4465 (2000); 113, 3480 (2000)] and Boothroyd-Martin-Keogh-Peterson (BMKP) [J. Chem. Phys. 116, 666 (2002)] surfaces, are quantitatively evaluated and compared through the investigation of rotational transitions in H(2)+H(2) collisions within rigid rotor approximation. The BMKP surface is expected to be an improvement, approaching chemical accuracy, over all conformations of the potential energy surface compared to previous calculations of H(2)-H(2) interaction. We found significant differences in rotational excitation/deexcitation cross sections computed on the two surfaces in collisions between two para-H(2) molecules. The discrepancy persists over a large range of energies from the ultracold regime to thermal energies and occurs for several low-lying initial rotational levels. Good agreement is found with experiment B. Mate et al., [J. Chem. Phys. 122, 064313 (2005)] for the lowest rotational excitation process, but only with the use of the DJ potential. Rate coefficients computed with the BMKP potential are an order of magnitude smaller.

Controlling electronic spin relaxation of cold molecules with electric fields

We present a theoretical study of atom-molecule collisions in superimposed electric and magnetic fields and show that dynamics of electronic spin relaxation in molecules at temperatures below 0.5 K can be manipulated by varying the strength and the relative orientation of the applied fields. The mechanism of electric field control of Zeeman transitions is based on an intricate interplay between intramolecular spin-rotation couplings and molecule-field interactions. We suggest that electric fields may affect chemical reactions through inducing nonadiabatic spin transitions and facilitate evaporative cooling of molecules in a magnetic trap.

STARK DECELERATION AND TRAPPING OF OH RADICALS

▪ Abstract  The motion of polar molecules can be controlled by time-varying inhomogeneous electric fields. In a Stark decelerator, this is exploited to accelerate, transport, or decelerate a fraction of a molecular beam. When combined with a trap, the decelerator provides a means to store the molecules for times up to seconds. Here, we review our efforts to produce cold molecules via this technique. In particular, we present a new generation Stark decelerator and electrostatic trap that selects a significant part of a molecular beam pulse that can be loaded into the trap. Deceleration and trapping experiments using a beam of OH radicals are discussed.

Continuous loading of an electrostatic trap for polar molecules

A continuously operated electrostatic trap for polar molecules is demonstrated. The trap has a volume of approximately 0.6 cm3 and holds molecules with a positive Stark shift. With deuterated ammonia from a quadrupole velocity filter, a trap density of approximately 10(8) cm(-3) is achieved with an average lifetime of 130 ms and a motional temperature of approximately 300 mK. The trap offers good starting conditions for high-precision measurements, and can be used as a first stage in cooling schemes for molecules and as a "reaction vessel" in cold chemistry.

Deceleration and electrostatic trapping of OH radicals

A pulsed beam of ground state OH radicals is slowed down using a Stark decelerator and is subsequently loaded into an electrostatic trap. Characterization of the molecular beam production, deceleration, and trap loading process is performed via laser induced fluorescence detection inside the quadrupole trap. Depending on the details of the trap loading sequence, typically 10(5) OH (X2Pi(3/2),J=3/2) radicals are trapped at a density of around 10(7) cm(-3) and at temperatures in the 50-500 mK range. The 1/e trap lifetime is around 1.0 s.

Interaction of NH(X3Sigma-) molecules with rubidium atoms: implications for sympathetic cooling and the formation of extremely polar molecules

The Rb-NH interaction is investigated as a prototype for interactions between alkali-metal atoms and stable molecules. For spin-aligned Rb and NH that interact on a quartet surface (4A"), the interaction is relatively weak, with a well depth of 0.078 eV. However, there are also doublet surfaces of ion-pair character that are very much deeper (well depth 1.372 eV). They may be important for atom-molecule collision rates and offer the possibility of forming strongly dipolar molecules by photoassociation. Similar deeply bound ion-pair states are likely to exist for other alkali atom-molecule pairs.

Quantum-mechanical theory of atom-molecule and molecular collisions in a magnetic field: Spin depolarization

A theory for quantum-mechanical calculations of cross sections for atom-molecule and molecular collisions in a magnetic field is presented. The formalism is based on the representation of the wave function as an expansion in a fully uncoupled space-fixed basis. The systems considered include 1S-atom-2Sigma-molecule, 1S-atom-3Sigma-molecule, 2Sigma-molecule-2Sigma-molecule, and 3Sigma-molecule-3Sigma-molecule. The theory is used to elucidate the mechanisms for collisionally induced spin depolarization.

Production of ultracold, polar RbCs* molecules via photoassociation

We have produced ultracold, polar RbCs* molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs* molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound X(1)Sigma(+) ground-state RbCs vibrational levels as high as 5 x 10(5) s(-1) per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.

Phase space manipulation of cold free radical OH molecules

We report bunching, slowing, and acceleration of a supersonically cooled beam of diatomic hydroxyl radicals (OH). In situ observation of laser-induced fluorescence along the beam propagation path allows for detailed characterization of longitudinal phase-space manipulation of OH molecules through the Stark effect by precisely sequenced inhomogeneous electric fields.

Ultracold collision properties of metastable alkaline-earth atoms

Ultracold collisions of spin-polarized 24Mg, 40Ca, and 88Sr in the metastable 3P2 excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.