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We prepare pairs of ^133 Cs atoms in a single optical tweezer and perform Feshbach spectroscopy for collisions of atoms in the states ( f = 3, m _f = ±3). We detect enhancements in pair loss using a detection scheme where the optical tweezers are repeatedly subdivided. For atoms in the state (3, −3), we identify resonant features by performing inelastic loss spectroscopy. We carry out coupled-channel scattering calculations and show that at typical experimental temperatures the loss features are mostly centred on zeroes in the scattering length, rather than resonance centres. We measure the number of atoms remaining after a collision, elucidating how the different loss processes are influenced by the tweezer depth. These measurements probe the energy released during an inelastic collision, and thus give information on the states of the collision products. We also identify resonances with atom pairs prepared in the absolute ground state ( f = 3, m _f = 3), where two-body radiative loss is engineered by an excitation laser blue-detuned from the Cs D _2 line. These results demonstrate optical tweezers to be a versatile tool to study two-body collisions with number-resolved detection sensitivity.

We explore the properties of three-atom complexes of alkali-metal diatomic molecules with alkali-metal atoms, which may be formed in ultracold collisions. We estimate the densities of vibrational states at the energy of atom–diatom collisions, and find values ranging from 2.2 to 350 K ^−1 . However, this density does not account for electronic near-degeneracy or electron and nuclear spins. We consider the fine and hyperfine structure expected for such complexes. The Fermi contact interaction between electron and nuclear spins can cause spin exchange between atomic and molecular spins. It can drive inelastic collisions, with resonances of three distinct types, each with a characteristic width and peak height in the inelastic rate coefficient. Some of these resonances are broad enough to overlap and produce a background loss rate that is approximately proportional to the number of outgoing inelastic channels. Spin exchange can increase the density of states from which laser-induced loss may occur.

We present measurements of more than 80 magnetic Feshbach resonances in collisions of ultracold ^23 Na ^40 K with ^40 K. We assign quantum numbers to a group of low-field resonances and show that they are probably due to long-range states of the triatomic complex in which the quantum numbers of the separated atom and molecule are approximately preserved. The resonant states are not members of chaotic bath of short-range states. Similar resonances are expected to be a common feature of alkali-metal diatom + atom systems.

We report the preparation of exactly one ^87 Rb atom and one ^133 Cs atom in the same optical tweezer as the essential first step towards the construction of a tweezer array of individually trapped ^87 Rb ^133 Cs molecules. Through careful selection of the tweezer wavelengths, we show how to engineer species-selective trapping potentials suitable for high-fidelity preparation of Rb + Cs atom pairs. Using a wavelength of 814 nm to trap Rb and 938 nm to trap Cs, we achieve loading probabilities of 0.508(6) for Rb and 0.547(6) for Cs using standard red-detuned molasses cooling. Loading the traps sequentially yields exactly one Rb and one Cs atom in 28.4(6)% of experimental runs. Using a combination of an acousto-optic deflector and a piezo-controlled mirror to control the relative position of the tweezers, we merge the two tweezers, retaining the atom pair with a probability of $0.9{9}_{\left(-0.02\right)}^{\left(+0.01\right)}$ . We use this capability to study hyperfine-state-dependent collisions of Rb and Cs in the combined tweezer and compare the measured two-body loss rates with coupled-channel quantum scattering calculations.

We study inelastic collisions between CaF molecules and ^87 Rb atoms in a dual-species magneto-optical trap. The presence of atoms increases the loss rate of molecules from the trap. By measuring the loss rates and density distributions, we determine a collisional loss rate coefficient k _2 = (1.43 ± 0.29) × 10 ^−10 cm ^3 s ^−1 at a temperature of 2.4 mK. We show that this is not substantially changed by light-induced collisions or by varying the populations of excited-state atoms and molecules. The observed loss rate is close to the universal rate expected in the presence of fast loss at short range, and can be explained by rotation-changing collisions in the ground electronic state.

Understanding ultracold collisions involving molecules is of fundamental importance for current experiments, where inelastic collisions typically limit the lifetime of molecular ensembles in optical traps. Here we present a broad study of optically trapped ultracold RbCs molecules in collisions with one another, in reactive collisions with Rb atoms, and in nonreactive collisions with Cs atoms. For experiments with RbCs alone, we show that by modulating the intensity of the optical trap, such that the molecules spend 75% of each modulation cycle in the dark, we partially suppress collisional loss of the molecules. This is evidence for optical excitation of molecule pairs mediated via sticky collisions. We find that the suppression is less effective for molecules not prepared in the spin-stretched hyperfine ground state. This may be due either to longer lifetimes for complexes in the dark or to laser-free decay pathways. For atom–molecule mixtures, RbCs + Rb and RbCs + Cs, we demonstrate that the rate of collisional loss of molecules scales linearly with the density of atoms. This indicates that, in both cases, the loss of molecules is rate-limited by two-body atom–molecule processes. For both mixtures, we measure loss rates that are below the thermally averaged universal limit.

We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of ^40 Ca ^19 F and ^87 Rb ^133 Cs, which are examples of molecules with ^2 Σ and ^1 Σ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a four-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension d = 4 to perform the Deutsch algorithm.

We investigate the behaviour of single-channel theoretical models of cold and ultracold collisions that take account of inelastic and reactive processes using a single parameter to represent short-range loss. We present plots of the resulting energy-dependence of elastic and inelastic or reactive cross-sections over the full parameter space of loss parameters and short-range phase shifts. We then test the single-channel model by comparing it with the results of coupled-channel calculations of rotationally inelastic collisions between LiH molecules and Li atoms. We find that the range of cross-sections predicted by the single-channel model becomes increasingly accurate as the initial LiH rotational quantum number increases, with a corresponding increase in the number of open loss channels. The results suggest that coupled-channel calculations at very low energy (in the s-wave regime) could in some cases be used to estimate a loss parameter and then to predict the range of possible loss rates at higher energy, without the need for explicit coupled-channel calculations for higher partial waves.

Ultracold polar molecules are an excellent platform for quantum science but experiments so far see fast trap losses that are poorly understood. Here the authors investigate collisional losses of nonreactive RbCs, and show they are consistent with the sticky collision hypothesis, but are slower than the universal rate.

We report coherent association of atoms into a single weakly bound NaCs molecule in an optical tweezer through an optical Raman transition. The Raman technique uses a deeply bound electronic excited intermediate state to achieve a large transition dipole moment while reducing photon scattering. Starting from two atoms in their relative motional ground state, we achieve an optical transfer efficiency of 69%. The molecules have a binding energy of 770.2 MHz at 8.83(2) G. This technique does not rely on Feshbach resonances or narrow excited-state lines and may allow a wide range of molecular species to be assembled atom by atom.

We investigate Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations. We consider both low-anisotropy and high-anisotropy limits. In both regimes, we find many resonances with a wide variety of widths. The wider resonances are suitable for tuning interatomic interactions, while some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules. These molecules might be transferred to short-range states, where they would have large magnetic moments and electric dipole moments that can be induced with very low electric fields. The results offer the opportunity to study mixed quantum gases where one species is dipolar and the other is not and open up important prospects for a new field of ultracold high-spin polar molecules.

We explore the potential energy surfaces for NH molecules interacting with alkali-metal and alkaline-earth atoms using highly correlated ab initioelectronic structure calculations. The surfaces for interaction with alkali-metal atoms have deep wells dominated by covalent forces. The resulting strong anisotropies will produce strongly inelastic collisions. The surfaces for interaction with alkaline-earth atoms have shallower wells that are dominated by induction and dispersion forces. For Be and Mg the anisotropy is small compared to the rotational constant of NH, so that collisions will be relatively weakly inelastic. Be and Mg are thus promising coolants for sympathetic cooling of NH to the ultracold regime. [ABSTRACT FROM AUTHOR]

Abstract Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology and quantum computing. For stability reasons, in the majority of cases the energetically lowest-lying atomic spin state is used. Here, we report the Bose-Einstein condensation of caesium atoms in the Zeeman-excited m f = 2 state, realizing a non-ground-state Bose-Einstein condensate with tunable interactions and tunable loss. We identify two regions of magnetic field in which the two-body relaxation rate is low enough that condensation is possible. We characterize the phase transition and quantify the loss processes, finding unusually high three-body losses in one of the two regions. Our results open up new possibilities for the mixing of quantum-degenerate gases, for polaron and impurity physics, and in particular for the study of impurity transport in strongly correlated one-dimensional quantum wires.

Trapped samples of ultracold molecules are often short-lived because close collisions between them result in trap loss. We investigate the use of shielding with static electric fields to create repulsive barriers between polar molecules to prevent such loss. Shielding is very effective even for RbCs, with a relatively low dipole moment, and even more effective for molecules such as NaK, NaRb, and NaCs, with progressively larger dipoles. Varying the electric field allows substantial control over the scattering length, which will be crucial for the stability or collapse of molecular Bose-Einstein condensates. This arises because the dipole-dipole interaction creates a long-range attraction that is tunable with electric field. For RbCs, the scattering length is positive across the range where shielding is effective because the repulsion responsible for shielding dominates. For NaK, the scattering length can be tuned across zero to negative values. For NaRb and NaCs, the attraction is strong enough to support tetra-atomic bound states, and the scattering length passes through resonant poles where these states cross threshold. For KAg and CsAg, there are multiple bound states and multiple poles. For each molecule, we calculate the variation of the scattering length with field and comment on the possibilities for exploring new physics.

We identify a route for the production of $^{87}$Rb$^{133}$Cs molecules in the $X^1\Sigma^+$ rovibronic ground state that is compatible with efficient mixing of the atoms in optical lattices. We first construct a model for the excited-state structure using constants found by fitting to spectroscopy of the relevant $a\,^3 \Sigma^+ → b\, ^3\Pi_1$ transitions at 181.5 G and 217.1 G. We then compare the predicted transition dipole moments from this model to those found for the transitions that have been successfully used for STIRAP at 181.5 G. We form molecules by magnetoassociation on a broad interspecies Feshbach resonance at 352.7 G and explore the pattern of Feshbach states near 305 G. This allows us to navigate to a suitable initial state for STIRAP by jumping across an avoided crossing with radiofrequency radiation. We identify suitable transitions for STIRAP at 305 G. We characterize these transitions experimentally and demonstrate STIRAP to a single hyperfine level of the ground state with a one-way efficiency of 85(4)%.

Mergoassociation of two ultracold atoms to form a weakly bound molecule can occur when two optical traps that each contain a single atom are merged. Molecule formation occurs at an avoided crossing between a molecular state and the lowest motional state of the atom pair. We develop the theory of mergoassociation for pairs of nonidentical nonspherical traps. We develop a coupled-channel approach for the relative motion of the two atoms and present results for pairs of cylindrically symmetrical traps as a function of their anisotropy. We focus on the strength of the avoided crossing responsible for mergoassociation. We also develop an approximate method that gives insight into the dependence of the crossing strength on aspect ratio.

We study collisions of ultracold CaF molecules in strong static electric fields. These fields allow the creation of long-range barriers in the interaction potential, effectively preventing the molecules from reaching the short-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channel calculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for including energetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show that shielding is particularly efficient for CaF and allows the rate of two-body loss processes to be reduced by a factor of 10^{7} or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron and nuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. These results pave the way for evaporative cooling of CaF towards quantum degeneracy.

We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of molecules in ^{2}Σ states and alkali-metal atoms. We focus on Rb+CaF as a prototype system. There are likely to be Feshbach resonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-threshold states and the resonances that they cause, using coupled-channel calculations of the bound states and low-energy scattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknown potential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G, and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation. We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they may produce additional resonances but should not affect the existence of rotation-free resonances.

We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of ^{40}K^{87}Rb+^{87}Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.

Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in ^{39}K, as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length a and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the a^{4} scaling of the three-body loss coefficient for both a0, as well as the many-body loss dynamics at unitarity (where a diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov–van der Waals universality in ^{39}K, while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.

Magnetically tunable Feshbach resonances exist in ultracold collisions between atoms in ^{2}S and ^{3}P_{0} states, such as an alkali-metal atom colliding with Yb or Sr in a clock state. We investigate the mechanisms of these resonances and identify the terms in the collision Hamiltonian responsible for them. They involve indirect coupling between the open and closed channels, via intermediate channels involving atoms in ^{3}P_{1} states. The resonance widths are generally proportional to the square of the magnetic field and are strongly enhanced when the magnitude of the background scattering length is large. For any given pair of atoms, the scattering length can be tuned discretely by choosing different isotopes of the ^{3}P_{0} atom. For each combination of an alkali-metal atom and either Yb or Sr, we consider the prospects of finding an isotopic combination that has both a large background scattering length and resonances at a high but experimentally accessible field. We conclude that ^{87}Rb+Yb, Cs+Yb, and ^{85}Rb+Sr are particularly promising combinations.

We report the observation of magnetic Feshbach resonances between ^{173}Yb and ^{133}Cs. In a mixture of Cs atoms prepared in the (f=3,m_{f}=3) state and unpolarized fermionic ^{173}Yb, we observe resonant atom loss due to two sets of magnetic Feshbach resonances around 622 and 702 G. Resonances for individual Yb nuclear spin components m_{i,Yb} are split by its interaction with the Cs electronic spin, which also provides the main coupling mechanism for the observed resonances. The observed splittings and relative resonance strengths are in good agreement with theoretical predictions from coupled-channel calculations.

The beyond-mean-field Lee-Huang-Yang (LHY) correction is ubiquitous in dilute ultracold quantum gases. However, its effects are often elusive due to the typically much larger influence of the mean-field (MF) energy. In this work, we study an ultracold mixture of ^{23}Na and ^{87}Rb with tunable attractive interspecies interactions. The LHY effects manifest in the formation of self-bound quantum liquid droplets and the expansion dynamics of the gas-phase sample. A liquid-to-gas-phase diagram is obtained by measuring the critical atom numbers below which the self-bound behavior disappears. In stark contrast to trapped gas-phase condensates, the gas-phase mixture formed following the liquid-to-gas-phase transition shows an anomalous expansion featuring a larger release energy for increasing MF attractions.

Radiofrequency (rf) -dressed potentials are a promising technique for manipulating atomic mixtures, but so far little work has been undertaken to understand the collisions of atoms held within these traps. In this paper, we dress a mixture of ^{85}Rb and ^{87}Rb with rf radiation, characterize the inelastic loss that occurs, and demonstrate species-selective manipulations. Our measurements show the loss is caused by two-body ^{87}Rb+^{85}Rb collisions, and we show the inelastic rate coefficient varies with detuning from the rf resonance. We explain our observations using quantum scattering calculations, which give reasonable agreement with the measurements. The calculations consider magnetic fields both perpendicular to the plane of rf polarization and tilted with respect to it. Our findings have important consequences for future experiments that dress mixtures with rf fields.

Characterizing quasibound states from coupled-channel scattering calculations can be a laborious task, involving extensive manual iteration and fitting. We present an automated procedure, based on the phase shift or S-matrix eigenphase sum, that reliably converges on a quasibound state (or scattering resonance) from some distance away. It may be used for both single-channel and multichannel scattering. It produces the energy and width of the state and the phase shift of the background scattering, and hence the lifetime of the state. It also allows extraction of partial widths for decay to individual open channels. We demonstrate the method on a very narrow state in the Van der Waals complex Ar–H_{2}, which decays only by vibrational predissociation, and on near-threshold states of ^{85}Rb_{2}, whose lifetime varies over four orders of magnitude as a function of magnetic field.

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channel scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length and so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter s_{res}. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.