Observation of Bose-Einstein condensation of dipolar molecules.

Ensembles of particles governed by quantum mechanical laws exhibit intriguing emergent behaviour. Atomic quantum gases, liquid helium and electrons in quantum materials 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 simulation and quantum computation.

Quantum state-resolved molecular dipolar collisions over four decades of energy.

Collisions between cold polar molecules represent a fascinating research frontier but have proven hard to probe experimentally. We report measurements of inelastic cross sections for collisions between nitric oxide (NO) and deuterated ammonia (ND) molecules at energies between 0.1 and 580 centimeter, with full quantum state resolution.

Resonances in Non-universal Dipolar Collisions.

Scattering resonances due to the dipole-dipole interaction between ultracold molecules, induced by static or microwave fields, are studied theoretically. We develop a method for coupled-channel calculations that can efficiently impose many short-range boundary conditions, defined by a short-range phase shift and loss probability as in quantum defect theory. We study how resonances appear as the short-range loss probability is lowered below the universal unit probability.

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 resonances, which have been extensively studied in various platforms, 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. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules.

Symmetry Breaking in Sticky Collisions between Ultracold Molecules.

Ultracold molecules undergo "sticky collisions" that result in loss even for chemically nonreactive molecules. Sticking times can be enhanced by orders of magnitude by interactions that lead to nonconservation of nuclear spin or total angular momentum. We present a quantitative theory of the required strength of such symmetry-breaking interactions based on classical simulation of collision complexes.

Evaporation of microwave-shielded polar molecules to quantum degeneracy.

Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter, implement quantum information schemes and test the fundamental symmetries of nature. Realizing their full potential requires cooling interacting molecular gases deeply into the quantum-degenerate regime. However, the intrinsically unstable collisions between molecules at short range have so far prevented direct cooling through elastic collisions to quantum degeneracy in three dimensions.

Correlated rotational excitations in NO-CO inelastic collisions.

We present a joint experimental and theoretical study of rotationally inelastic collisions between NO (XΠ, ν = 0, j = 1/2, f) radicals and CO (XΣ, ν = 0, j = 0) molecules at a collision energy of 220 cm. State-to-state scattering images for excitation of NO radicals into various final states were measured with high resolution by combining the Stark deceleration and velocity map imaging techniques. The high image resolution afforded the observation of correlated rotational excitations of NO-CO pairs, which revealed a number of striking scattering phenomena.

Glory scattering in deeply inelastic molecular collisions.

For molecular collisions, the deflection of a molecule's trajectory provides one of the most sensitive probes of the interaction potential and there are general rules of thumb that relate the direction of deflection to precollision conditions. Following intuition, forward scattering results from glancing collisions, whereas near head-on collisions result in back scattering. Here we present the observation of forward scattering in inelastic processes that defies this common wisdom.

Control of reactive collisions by quantum interference.

In this study, we achieved magnetic control of reactive scattering in an ultracold mixture of Na atoms and NaLi molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na + NaLi system was shown to have only ~4% loss probability in a fully spin-polarized state.

Observation of microwave shielding of ultracold molecules.

Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we used microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probed collisions in three dimensions.

Resonant Dipolar Collisions of Ultracold Molecules Induced by Microwave Dressing.

We demonstrate microwave dressing on ultracold, fermionic ^{23}Na^{40}K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding 3 times the s-wave unitarity limit. The origin of these interactions is the resonant alignment of the approaching molecules' dipoles along the intermolecular axis, which leads to strong attraction. We explain our observations with a conceptually simple two-state picture based on the Condon approximation.

Rotational-vibrational resonance states.

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments.

Imaging the onset of the resonance regime in low-energy NO-He collisions.

At low energies, the quantum wave-like nature of molecular interactions results in distinctive scattering behavior, ranging from the universal Wigner laws near 0 kelvin to the occurrence of scattering resonances at higher energies. It has proven challenging to experimentally probe the individual waves underlying these phenomena. We report measurements of state-to-state integral and differential cross sections for inelastic NO-He collisions in the 0.

Photoinduced Two-Body Loss of Ultracold Molecules.

The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss.

Six-dimensional potential energy surface for NaK-NaK collisions: Gaussian process representation with correct asymptotic form.

Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three- and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range.

Microwave Shielding of Ultracold Polar Molecules.

We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10^{-14}  cm^{3} s^{-1}.

Energy dependent parity-pair behavior in NO + He collisions.

Colliding molecules behave fundamentally differently at high and low collision energies. At high energies, a collision can be described to a large extent using classical mechanics, and the scattering process can be compared to a billiard-ball-like collision. At low collision energies, the wave character of the collision partners dominates, and only quantum mechanics can predict the outcome of an encounter.

Publisher Correction: O-O and O-N collision-induced absorption mechanisms unravelled.

In the version of this Article originally published, Figures 3 and 4 were erroneously swapped, this has been corrected in all versions of the Article.

Correlated energy transfer in rotationally and spin-orbit inelastic collisions of NO(XΠ, j = 1/2f) with O(XΣ).

We present a combined experimental and theoretical study of state-to-state inelastic scattering of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-) molecules at a collision energy of 480 cm-1, focusing in particular on the observation and interpretation of correlated excitations in both NO and O2. Various final states of the NO radical, in both spin-orbit manifolds, were measured with high resolution using a crossed molecular beam apparatus which employs a combination of Stark deceleration and velocity map imaging. Velocity map imaging directly measures both the angular distribution and the radial velocity distribution of the scattered NO molecules, which probes the kinetic energy uptake or release and hence correlated excitations of NO-O2 pairs.

O-O and O-N collision-induced absorption mechanisms unravelled.

Collision-induced absorption is the phenomenon in which interactions between colliding molecules lead to absorption of light, even for transitions that are forbidden for the isolated molecules. Collision-induced absorption contributes to the atmospheric heat balance and is important for the electronic excitations of O that are used for remote sensing. Here, we present a theoretical study of five vibronic transitions in O-O and O-N, using analytical models and numerical quantum scattering calculations.

Observation of correlated excitations in bimolecular collisions.

Although collisions between atoms and molecules are largely understood, collisions between two molecules have proven much harder to study. In both experiment and theory, our ability to determine quantum-state-resolved bimolecular cross-sections lags behind their atom-molecule counterparts by decades. For many bimolecular systems, even rules of thumb-much less intuitive understanding-of scattering cross sections are lacking.

Scattering resonances in bimolecular collisions between NO radicals and H challenge the theoretical gold standard.

Over the last 25 years, the formalism known as coupled-cluster (CC) theory has emerged as the method of choice for the ab initio calculation of intermolecular interaction potentials. The implementation known as CCSD(T) is often referred to as the gold standard in quantum chemistry. It gives excellent agreement with experimental observations for a variety of energy-transfer processes in molecular collisions, and it is used to calibrate density functional theory.

State-to-State Differential Cross Sections for Inelastic Collisions of NO Radicals with para-H and ortho-D.

We present state-to-state differential cross sections for collisions of NO molecules (XΠ, j = 1/2f) with para-H and ortho-D molecules, at a collision energy of 510 and 450 cm, respectively. The angular scattering distributions for various final states of the NO radical are measured with high resolution using a crossed molecular beam apparatus that employs the combination of Stark deceleration and velocity map imaging. Rotational rainbows as well as diffraction oscillations are fully resolved in the scattering images.

Line-shape theory of the XΣ→aΔ,bΣ transitions in O-O collision-induced absorption.

We derive the theory of collision-induced absorption for electronic transitions in the approximation of an isotropic interaction potential. We apply this theory to the spin-forbidden XΣ→aΔ and XΣ→bΣ transitions in O-O, which are relevant for calibration in atmospheric studies. We consider two mechanisms for breaking the spin symmetry, either by the intermolecular exchange interaction between paramagnetic collision partners or by the intramolecular spin-orbit coupling.