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We present a computer program to calculate the quantised rotational and hyperfine energy levels of diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments. Program summary Program Title: Diatomic-Py CPC Library link to program files: https://doi.org/10.17632/3yfxnh5bn5.1 Developer's repository link: https://doi.org/10.5281/zenodo.6632148 Licensing provisions: BSD 3-clause Programming language: Python ≥ 3.7 Nature of problem: Calculation of the rotational and hyperfine structure of molecules in the presence of dc magnetic, dc electric, and off-resonant laser fields. Solution method: A matrix representation of the Hamiltonian is constructed in the uncoupled basis set. Eigenstates and eigenenergies are calculated by numerical diagonalization of the Hamiltonian. Additional comments including restrictions and unusual features: Restricted to calculating the Stark and Zeeman shifts with co-axial electric and magnetic fields.

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation., Comment: 14 pages, 10 figures

Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of $\arccos{(1/\sqrt{3})}\approx55^{\circ}$. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation., Comment: 19 pages, 12 figures

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.

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 also 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 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 the three broadest Feshbach resonances are universal within experimental uncertainties, consistent with observing little variation in the Efimov width parameters., 12 pages, 7 figures (including appendices)

We obtain the interaction potential for NaCs by fitting to experiments on ultracold scattering and spectroscopy in optical tweezers. The central region of the potential has been accurately determined from Fourier-Transform spectroscopy at higher temperatures, so we focus on adjusting the long-range and short-range parts. We use coupled-channel calculations of binding energies and wave functions to understand the nature of the molecular states observed in ultracold spectroscopy, and of the state that causes the Feshbach resonance used to create ultracold NaCs molecules. We elucidate the relationships between the experimental quantities and features of the interaction potential. We establish the combinations of experimental quantities that determine particular features of the potential. We find that the long-range dispersion coefficient $C_6$ must be increased by about 0.9% to 3256(1) $E_\textrm{h} a_0^6$ to fit the experimental results. We use coupled-channel calculations on the final potential to predict bound-state energies and resonance positions.

We prepare pairs of $^{133}$Cs atoms in a single optical tweezer and perform Feshbach spectroscopy for collisions of atoms in the states $(f=3, m_f=\pm3)$. 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., Comment: 18 pages, 6 figures

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.

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 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., Comment: 10 pages, 3 figures

We thank Bo Gao and Paul Julienne for discussion and Robert Moszynski for providing theoretical transition dipole moments of NaCs. This work is supported by the NSF (PHY-1806595), the AFOSR (FA9550-19-1-0089), ARO DURIP (W911NF1810194), and the Arnold and Mabel Beckman foundation. J. T. Z. is supported by a National Defense Science and Engineering Graduate Fellowship. W. B. C. is supported by a Max PlanckHarvard Research Center for Quantum Optics fellowship. K. W. is supported by an NSF GRFP fellowship. J. M. H. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grants No. EP/N007085/1, No. EP/P008275/1, and No. EP/P01058X/1. R. G.-F. acknowledges financial support of the Spanish Project FIS2017-89349-P (MINECO) and the Andalusian research group FQM-207., 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 fromtwo 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., National Science Foundation (NSF) PHY-1806595, United States Department of Defense, Air Force Office of Scientific Research (AFOSR) FA9550-19-1-0089, ARO DURIP W911NF1810194, Arnold and Mabel Beckman foundation, National Defense Science and Engineering Graduate Fellowship, Max PlanckHarvard Research Center for Quantum Optics fellowship, National Science Foundation (NSF), NSF - Office of the Director (OD), UK Research & Innovation (UKRI), Engineering & Physical Sciences Research Council (EPSRC) EP/N007085/1 EP/P008275/1 EP/P01058X/1, MINECO FIS2017-89349-P, Andalusian research group FQM-207

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 $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ 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.

Magnetic fields can be used to change chemical reaction rates by a factor of 100

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 $k_{2} = (1.43 \pm 0.29) \times 10^{-10}$ cm$^{3}$/s 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., 14 pages, 6 figures. Added a new figure and some further details about the methods; expanded our discussion of the results

The BOUND program calculates the bound states of a complex formed from two interacting particles using coupled-channel methods. It is particularly suitable for the bound states of atom-molecule and molecule-molecule Van der Waals complexes and for the near-threshold bound states that are important in ultracold physics. It uses a basis set for all degrees of freedom except $R$, the separation of the centres of mass of the two particles. The Schr\"odinger equation is expressed as a set of coupled equations in $R$. Solutions of the coupled equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, and rigid diatom + asymmetric top. Both programs provide an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in. With appropriate plug-in routines, BOUND can take account of the effects of external electric, magnetic and electromagnetic fields, locating bound-state energies at fixed values of the fields. The related program FIELD uses the same plug-in routines and locates values of the fields where bound states exist at a specified energy. As a special case, it can locate values of the external field where bound states cross scattering thresholds and produce zero-energy Feshbach resonances. Plug-in routines are supplied to handle the bound states of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field., Comment: One of two parallel papers that document the MOLSCAT, BOUND and FIELD programs, which use closely related theoretical methods but serve different purposes. This paper and arXiv:1811.09584 therefore have substantial text overlap

We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient of $k_2 = (6.6 \pm 1.5) \times 10^{-11}$ cm$^{3}$/s at temperatures near 100~$��$K. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin relaxation rate coefficient of $k_2 < 5.8 \times 10^{-12}$ cm$^{3}$/s with 95% confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state., 9 pages, 6 figures. Minor changes following review

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 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., Comment: 21 pages, 9 figures

We explore the properties of 3-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., Comment: Accepted manuscript

We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.

We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.

We investigate the effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic $^{87}$Rb$^{133}$Cs molecules, for light of wavelength $\lambda = 1064~\mathrm{nm}$. Near this wavelength we observe unexpected two-photon transitions that may cause trap loss. We measure the ac Stark effect in external magnetic and electric fields, using microwave spectroscopy of the first rotational transition. We quantify the isotropic and anisotropic parts of the molecular polarizability at this wavelength. We demonstrate that a modest electric field can decouple the nuclear spins from the rotational angular momentum, greatly simplifying the ac Stark effect. We use this simplification to control the ac Stark shift using the polarization angle of the trapping laser.

We demonstrate the formation of a single NaCs molecule in an optical tweezer by magnetoassociation through an s-wave Feshbach resonance at 864.11(5) G. Starting from single atoms cooled to their motional ground states, we achieve conversion efficiencies of 47(1)%, and measure a molecular lifetime of 4.7(7) ms. By construction, the single molecules are predominantly [77(5)%] in the center-of-mass motional ground state of the tweezer. Furthermore, we produce a single p-wave molecule near 807 G by first preparing one of the atoms with one quantum of motional excitation. Our creation of a single weakly bound molecule in a designated internal state in the motional ground state of an optical tweezer is a crucial step towards coherent control of single molecules in optical tweezer arrays.

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 4 orders of magnitude as a function of magnetic field.

We report the observation of microwave coherent control of rotational states of ultracold $^{85}$Rb$^{133}$Cs molecules formed in their vibronic ground state by short-range photoassociation. Molecules are formed in the single rotational state $X(v=0,J=1)$ by exciting pairs of atoms to the short-range state $(2)^{3}\Pi_{0^{-}} (v=11, J=0)$, followed by spontaneous decay. We use depletion spectroscopy to record the dynamic evolution of the population distribution and observe clear Rabi oscillations while irradiating on a microwave transition between coupled neighbouring rotational levels. A density-matrix formalism that accounts for longitudinal and transverse decay times reproduces both the dynamic evolution during the coherent process and the equilibrium population. The coherent control reported here is valuable both for investigating coherent quantum effects and for applications of cold polar molecules produced by continuous short-range photoassociation., Comment: 5 pages, 4 figures

Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole-dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with $>0.999$ fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups., 13 pages, 5 figures

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 work, we dress a mixture of 85Rb and 87Rb with RF radiation, characterize the inelastic loss that occurs, and demonstrate species-selective manipulations. Our measurements show the loss is caused by two-body 87Rb+85Rb 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., 12 pages, 7 figures, 1 table

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 $0.99^{(+0.01)}_{(-0.02)}$. 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., 22 pages, 6 figures

We investigate the use of microwave radiation to produce a repulsive shield between pairs of ultracold polar molecules and prevent collisional losses that occur when molecular pairs reach short range. We carry out coupled-channels calculations on $\mathrm{RbCs}+\mathrm{RbCs}$ and $\mathrm{CaF}+\mathrm{CaF}$ collisions in microwave fields. We show that effective shielding requires predominantly circular polarization but can still be achieved with elliptical polarization that is around 90% circular.

We investigate magnetically tunable Feshbach resonances in ultracold collisions between ground-state Yb and Cs atoms, using coupled-channel calculations based on an interaction potential recently determined from photoassociation spectroscopy. We predict resonance positions and widths for all stable isotopes of Yb, together with resonance decay parameters where appropriate. The resonance patterns are richer and more complicated for fermionic Yb than for spin-zero isotopes, because there are additional level splittings and couplings due to scalar and tensorial Yb hyperfine interactions. We examine collisions involving Cs atoms in a variety of hyperfine states, and identify resonances that appear most promising for experimental observation and for magnetoassociation to form ultracold CsYb molecules.

We investigate $\mathrm{Cs}+\mathrm{Cs}$ scattering in excited Zeeman and hyperfine states. We calculate the real and imaginary parts of the $s$-wave scattering length; the imaginary part directly provides the rate coefficient for two-body inelastic loss, while the real part allows us to identify regions of magnetic field where three-body recombination will be slow. We identify field regions where Cs in its $(f,{m}_{f})=(3,+2)$ and $(3,+1)$ states may be stable enough to allow Bose-Einstein condensation, and additional regions for these and the (3, 0) and $(3,\ensuremath{-}3)$ states where high-density clouds should be long-lived.

Polar molecules in superpositions of rotational states exhibit long-range dipolar interactions, but maintaining their coherence in a trapped sample is a challenge. We present calculations that show many laser-coolable molecules have convenient rotational transitions that are exceptionally insensitive to magnetic fields. We verify this experimentally for CaF where we find a transition with sensitivity below $5\text{ }\text{ }\mathrm{Hz}\text{ }{\mathrm{G}}^{\ensuremath{-}1}$ and use it to demonstrate a rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest it is feasible to extend this to more than 1 s using a smaller cloud in a biased magnetic trap.

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-channels scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length, 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 $s_\textrm{res}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

We have investigated 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., Comment: Accepted version

We present the production of ultracold 87 RbCs molecules in the electronic, rovibrational and hyperfine ground state, using stimulated Raman adiabatic passage to transfer the molecules from a weakly bound Feshbach state. We measure one-way transfer efficiencies of 92(1)% and fully characterise the strengths and linewidths of the transitions used. We model the transfer, including a Monte Carlo simulation of the laser noise, and find this matches well with both the transfer efficiency and our previous measurements of the laser linewidth and frequency drifts.

We report our experimental results on the collisional physics between non-S-state atoms (ytterbium (Yb), effectively a two-electron system, in the metastable ${}^3\mathrm{P}_2$ state) and S-state atoms (lithium (Li), an alkali metal, in the ground state). At low magnetic fields, by measuring inelastic interspecies collisional losses in the double quantum degenerate mixture we reveal the strong dependence of the inelastic losses on the internal spin states of both species and suppressed losses in stretched state configurations. Increasing the magnetic field up to 800 G we further investigate the magnetic field dependence of the collisional interactions. There, smoothly increasing inelastic losses are observed towards higher fields. The combined knowledge of both the magnetic field and the spin state dependence of the collisional losses of this prototypical mixture system of non-S-state and S-state atoms provides a significant step forward towards controllable impurity physics realized in the Yb-Li ultracold system., Comment: 9 pages, 5 figures

MOLSCAT is a general-purpose program for quantum-mechanical calculations on nonreactive atom-atom, atom-molecule and molecule-molecule collisions. It constructs the coupled-channel equations of atomic and molecular scattering theory, and solves them by propagating the wavefunction or log-derivative matrix outwards from short range to the asymptotic region. It then applies scattering boundary conditions to extract the scattering matrix (S matrix). Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, rigid diatom + asymmetric top, and diffractive scattering of an atom from a crystal surface. Interaction potentials may be specified either in program input (for simple cases) or with user-supplied routines. For the built-in coupling cases, MOLSCAT can loop over partial wave (or total angular momentum) to calculate elastic and inelastic cross integral sections and spectroscopic line-shape cross sections. Post-processors are available to calculate differential cross sections, transport, relaxation and Senftleben-Beenakker cross sections, and to fit the parameters of scattering resonances. MOLSCAT also provides an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in; plug-in routines are supplied to handle collisions of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. For low-energy scattering, MOLSCAT can calculate scattering lengths and effective ranges and can locate and characterize scattering resonances as a function of an external variable such as the magnetic field., arXiv admin note: substantial text overlap with arXiv:1811.09111 This is because these are two parallel papers that describe related programs with the same theoretical basis but for different purposes

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 ${10}^{\ensuremath{-}14}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)], and do not require cancellation of the long-range dipole-dipole interaction that is vital to many applications.

Magnetic Feshbach resonances are an invaluable tool for controlling ultracold atoms and molecules. They can be used to tune atomic interactions and have been used extensively to explore few- and many-body phenomena. They can also be used for magnetoassociation, in which pairs of atoms are converted into molecules by ramping an applied magnetic field across a resonance. Pairs of open-shell atoms, such as the alkalis, chromium, and some lanthanides, exhibit broad resonances because the corresponding molecule has multiple electronic states. However, molecules formed between alkali and closed-shell atoms have only one electronic state and no broad resonances. Narrow resonances have been predicted in such systems, but until now have eluded observation. Here we present the first observation of magnetic Feshbach resonances in a system containing a closed-shell atom, Sr, interacting with an alkali atom, Rb. These resonances pave the way to creating an ultracold gas of strongly polar, open-shell molecules, which will open up new possibilities for designing quantum many-body systems and for tests of fundamental symmetries., Comment: 5 pages, 3 figures, 2 tables

We study the two-body bound states of a model Hamiltonian that describes the interaction between two field-oriented dipole moments. This model has been used extensively in the many-body physics of ultracold polar molecules and magnetic atoms, but its few-body physics has been explored less fully. With a hard-wall short-range boundary condition, the dipole-dipole bound states are universal and exhibit a complicated pattern of avoided crossings between states of different character. For more realistic Lennard–Jones short-range interactions, we consider parameters representative of magnetic atoms and polar molecules. For magnetic atoms, the bound states are dominated by the Lennard–Jones potential, and the perturbative dipole-dipole interaction is suppressed by the special structure of van der Waals bound states. For polar molecules, we find a dense manifold of dipole-dipole bound states with many avoided crossings as a function of induced dipole or applied field, similar to those for hard-wall boundary conditions. This universal pattern of states may be observable spectroscopically for pairs of ultracold polar molecules.

We report the production of ultracold heteronuclear Cs$^*$Yb molecules through one-photon photoassociation applied to an ultracold atomic mixture of Cs and Yb confined in an optical dipole trap. We use trap-loss spectroscopy to detect molecular states below the Cs($^{2}P_{1/2}$) + Yb($^{1}S_{0}$) asymptote. For $^{133}$Cs$^{174}$Yb, we observe 13 rovibrational states with binding energies up to $\sim$500 GHz. For each rovibrational state we observe two resonances associated with the Cs hyperfine structure and show that the hyperfine splitting in the diatomic molecule decreases for more deeply bound states. In addition, we produce ultracold fermionic $^{133}$Cs$^{173}$Yb and bosonic $^{133}$Cs$^{172}$Yb and $^{133}$Cs$^{170}$Yb molecules. From mass scaling, we determine the number of bound states supported by the 2(1/2) excited-state potential to be 154 or 155., Comment: 9 Pages, 5 Figures

Ultracold molecules with both electron spin and an electric dipole moment offer new possibilities in quantum science. We use density-functional theory to calculate hyperfine coupling constants for a selection of molecules important in this area, including RbSr, LiYb, RbYb, CaF, and SrF. We find substantial hyperfine coupling constants for the fermionic isotopes of the alkaline-earth-metal and Yb atoms. We discuss the hyperfine level patterns and Zeeman splittings expected for these molecules. The results will be important both to experiments aimed at forming ultracold open-shell molecules and to their applications.

We perform two-photon photoassociation spectroscopy of the heteronuclear CsYb molecule to measure the binding energies of near-threshold vibrational levels of the $X~^{2}\Sigma_{1/2}^{+}$ molecular ground state. We report results for $^{133}$Cs$^{170}$Yb, $^{133}$Cs$^{173}$Yb and $^{133}$Cs$^{174}$Yb, in each case determining the energy of several vibrational levels including the least-bound state. We fit an interaction potential based on electronic structure calculations to the binding energies for all three isotopologs and find that the ground-state potential supports 77 vibrational levels. We use the fitted potential to predict the interspecies s-wave scattering lengths for all seven Cs+Yb isotopic mixtures., Comment: 11 pages, 8 figures, 4 tables

We present calculations of the hyperfine coupling constants for all the heteronuclear alkali-metal diatomic molecules at the equilibrium geometry of the electronic ground state. These constants are important in developing methods to control ultracold polar molecules. The results are based on electronic structure calculations using density-functional theory, and are in good agreement with experiment for the limited set of molecules for which experiments are so far available.

We describe procedures for converging on and characterizing zero-energy Feshbach resonances that appear in scattering lengths as a function of an external field. The elastic procedure is appropriate for purely elastic scattering, where the scattering length is real and displays a true pole. The regularized scattering length (RSL) procedure is appropriate when there is weak background inelasticity, so that the scattering length is complex and displays an oscillation rather than a pole, but the resonant scattering length $a_{\rm res}$ is close to real. The fully complex procedure is appropriate when there is substantial background inelasticity and the real and complex parts of $a_{\rm res}$ are required. We demonstrate these procedures for scattering of ultracold $^{85}$Rb in various initial states. All of them can converge on and provide full characterization of resonances, from initial guesses many thousands of widths away, using scattering calculations at only about 10 values of the external field., 9 pages, 5 figures

We use an atomic fountain clock to measure quantum scattering phase shifts precisely through a series of narrow, low-field Feshbach resonances at average collision energies below $1\,\mu$K. Our low spread in collision energy yields phase variations of order $\pm \pi/2$ for target atoms in several $F,m_F$ states. We compare them to a theoretical model and establish the accuracy of the measurements and the theoretical uncertainties from the fitted potential. We find overall excellent agreement, with small statistically significant differences that remain unexplained.

We calculate the rates of inelastic collisions for ultracold alkali-metal atoms in radio-frequency-dressed traps, using coupled-channel scattering calculations on accurate potential energy surfaces. We identify a radio-frequency-induced loss mechanism that does not exist in the absence of radio frequency (rf) radiation. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings, and the strength of the rf field. We interpret the results in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. $^{87}\mathrm{Rb}$ is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate.

We investigate the effect of far-off-resonant trapping light on ultracold bosonic 87Rb133Cs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC~Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating measurements allows complete characterization of the molecule polarizability at a wavelength of 1550~nm in both the ground and first excited rotational states.

We present measurements of interspecies thermalization between ultracold samples of $^{133}$Cs and either $^{174}$Yb or $^{170}$Yb. The two species are trapped in a far-off-resonance optical dipole trap and $^{133}$Cs is sympathetically cooled by Yb. We extract effective interspecies thermalization cross sections by fitting the thermalization measurements to a rate equation model, giving $\sigma_{\mathrm{Cs^{174}Yb}} = \left(5 \pm 2\right) \times 10^{-13} \, \mathrm{cm^{2}}$ and $\sigma_{\mathrm{Cs^{170}Yb}} = \left(18 \pm 8\right) \times 10^{-13} \, \mathrm{cm^{2}}$. We perform quantum scattering calculations of the thermalization cross sections and optimize the CsYb interaction potential to reproduce the measurements. We predict scattering lengths for all isotopic combinations of Cs and Yb. We also demonstrate the independent production of $^{174}$Yb and $^{133}$Cs Bose-Einstein condensates using the same optical dipole trap, an important step towards the realization of a quantum-degenerate mixture of the two species., Comment: 12 pages, 7 figures