The collision dynamics of $^{17}O_2(^3Σ_g^-) +^{17}O_2(^3Σ_g^-)$ in the presence of a magnetic field is studied within the close-coupling formalism in the range between 10 nK and 50 mK. A recent global {\em ab initio} potential energy surface (PES) is employed and its effect on the dynamics is analyzed and compared with previous calculations where an experimentally derived PES was used [New J. Phys {\bf 11}, 055021 (2009)]. In contrast to the results using the older PES, magnetic field dependence of the low-field-seeking state in the ultracold regime is characterized by quite a large background scattering length, $a_{bg}$, and, in addition, cross sections exhibit broad and pronounced Feshbach resonances. The marked resonance structure is somewhat surprising considering the influence of inelastic scattering, but it can be explained by resorting to the analytical van der Waals theory, where the short range amplitude of the entrance channel wave function is enhanced by the large $a_{bg}$. This strong sensitivity to the short range of the {\em ab initio} PES persists up to relatively high energies (10 mK). After this study and despite quantitative predictions are very difficult, it can be concluded that the ratio between elastic and spin relaxation scattering is generally small, except for magnetic fields which are either low or close to an asymmetric Fano-type resonance. Some general trends found here, such as a large density of quasibound states and a propensity towards large scattering lengths, could be also characteristic of other anisotropic molecule-molecule systems.
We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between $^2Σ$ CaF molecules in the absolute ground state $|X,v=0, N=0,F=0\rangle$, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of $7(4) \times 10^{-11} \text{cm}^{3}/\text{s}$, which is below, but close to the predicted universal loss rate.
Experimental studies with ultracold atoms have enabled major breakthroughs in understanding three-body physics, historically a fundamental yet challenging problem. This is because the interactions among ultracold atoms can be precisely varied using magnetically tunable scattering resonances known as Feshbach resonances. The collisions of ultracold atoms have been discovered to have many universal aspects near the unitarity limit. Away from this limit, many quantum states are expected to be active during a three-body collision, making the collisional observables practically unpredictable. Here …
The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7$\;$D. We observe a step-wise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions. Varying t…
We report on deviations beyond the Born-Oppenheimer approximation in the potassium inter-atomic potentials. Identifying three up-to-now unknown $d$-wave Feshbach resonances, we significantly improve the understanding of the $^{39}$K inter-atomic potentials. Combining these observations with the most recent data on known inter- and intra-isotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear case appear.
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 lo…
We investigate ultracold collisions in a novel mixture of $^6$Li and $^{53}$Cr fermionic atoms, discovering more than 50 interspecies Feshbach resonances via loss spectroscopy. Building a full coupled-channel model, we unambiguously characterize the $^{6}$Li-$^{53}$Cr scattering properties and yield predictions for other isotopic pairs. In particular, we identify various Feshbach resonances that enable the controlled tuning of elastic $s$- and $p$-wave $^{6}$Li-$^{53}$Cr interactions. Our studies thus make lithium-chromium mixtures emerge as optimally-suited platforms for the experimental sear…
We report the investigation on dipolar collisions in rotational state mixtures of ultracold bosonic $^{23}$Na$^{87}$Rb molecules. The large resonant dipole-dipole interaction between molecules in rotational states of opposite parities brings about significant modifications to their collisions, even when an electric field is not present. In this work, this effect is revealed by measuring the dramatically enhanced two-body loss rate constants in the mixtures. In addition, the dipolar interaction strength can be tuned by preparing the NaRb mixture in different rotational levels with microwave spe…
We show that the lifetime of ultracold ground-state $^{87}$Rb$^{133}$Cs molecules in an optical trap is limited by fast optical excitation of long-lived two-body collision complexes. We partially suppress this loss mechanism by applying square-wave modulation to the trap intensity, such that the molecules spend 75% of each modulation cycle in the dark. By varying the modulation frequency, we show that the lifetime of the collision complex is $0.53\pm0.06$ ms in the dark. We find that the rate of optical excitation of the collision complex is $3^{+4}_{-2}\times10^{3}$ W$^{-1}$ cm$^2$ s$^{-1}$ f…
Helium atoms in the metastable $2^3{S_{1}}$ state (He$^*$) have unique advantages for ultracold atomic experiments. However, there is no known accessible Feshbach resonance in He$^*$, which could be used to manipulate the scattering length and hence unlock several new experimental possiblities. Previous experimental and theoretical studies for He$^*$ have produced contradictory results. We aimed to resolve this discrepancy with a theoretical search for Feshbach resonances, using a new close-coupled model of He$^*$ collisions in the presence of an external magnetic field. Several resonances wer…
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 th…
The collision of molecules at ultracold temperatures is of great importance for understanding the chemical interactions at the quantum regime. While much theoretical work has been devoted to this, experimental data are only available sparsely mainly due to the difficulty in producing ground-state molecules at ultracold temperatures. We report here the creation of optically trapped samples of ground-state bosonic sodium-rubidium molecules with precisely controlled internal states and, enabled by this, a detailed study on the inelastic loss with and without the NaRb + NaRb $\rightarrow$ Na$_2$ +…
Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photo-excitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecu…
We investigate the energy dependence and the internal-state dependence of the charge-exchange collision cross sections in a mixture of $^6$Li atoms and $^{40}$Ca$^+$ ions in the collision energy range from 0.2 mK to 1 K. Deliberately excited ion micromotion is used to control the collision energy of atoms and ions. The energy dependence of the charge-exchange collision cross section obeys the Langevin model in the temperature range of the current experiment, and the measured magnitude of the cross section is correlated to the internal state of the $^{40}$Ca$^+$ ions. Revealing the relationship…
We study ultracold atom-ion collisions in the presence of an external magnetic field. At low collision energy the field can drastically modify the translational motion of the ion, which follows quantized cyclotron orbits. We present a rigorous theoretical approach for the calculation of quantum scattering amplitudes in these conditions. Collisions in different magnetic field regimes, identified by the size of the cyclotron radius with respect to the range of the interaction potential, are investigated. Our results are important in cases where use of a magnetic field to control the atom-ion col…
We develop an analytical model for ultracold atom-ion collisions using the multichannel quantum-defect formalism. The model is based on the analytical solutions of the r^-4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of the atom-ion interaction in the ultracold domain in terms of three parameters only: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce…
We present an analytic description of ultracold collision between two spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling of the Rashba type. We show that regardless of how weak the spin-orbit coupling may be, the ultracold collision at sufficiently low energies is significantly modified, including the ubiquitous Wigner threshold behavior. We further show that the particles are preferably scattered into the lower-energy helicity state due to the break of parity conservation, thus establishing interaction with spin-orbit coupling as one mechanism for the spontaneous emergence of hand…
Collisions of $^6$Li$_2$ molecules with free $^6$Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li$_2$ closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance, and decay via two-body collisions with Li$_2$, Li, and Na. For Li$_2$+Li$_2$ and Li$_2$+Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li$_2$+Li is exceptionally small, with an upper bound ten times smaller than the universal prediction. This can be explained by…
We report on experiments investigating the collisional properties of atoms at ultralow collision energies using an all-optical atom collider. By using a pair of optical tweezers, we can manipulate two ultracold atom clouds and collide them together at energies up to three orders of magnitude larger than their thermal energy. Our experiments measure the scattering of $\rm ^{87}Rb$, $\rm ^{40}K$, and $\rm ^{40}K$-$\rm ^{87}Rb$ collisions. The versatility of our collider allows us to probe both shape resonances and Feshbach resonances in any partial wave. As examples, we present experiments demon…
Reactive or elastic two-body collisions in an ultracold gas are affected by quantum statistics. In this paper, we study ensemble-averaged collision rates for a two-species fermionic gas. The two species may have different masses, densities and temperatures. We investigate how averaged collision rates are affected by the presence of Fermi spheres in the initial states; Pauli blocking of final states is not considered. It is shown that, independently on the details of the collision, Fermi-averaged collision rates deviate from Boltzmann-averaged ones, particularly for a gas with strong imbalance …
Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well defined internal and external quantum states$^{1-4}$. In general, even cold reactions have many possible final product states$^{5-15}$ and reaction channels are therefore hard to track individually$^{16}$. In special cases, however, only a single reaction channel is essentially participating, as observed e.g. in the recombination of two atoms …
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, whi…
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 non-conservation 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. We find static electric fields as small as $10$~V/cm can lead to non-conservation of angular momentum, while we find nuclear spin is conserved during collisions. We also compute loss of collision…
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. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.
Understanding the sources of losses and chemical reactions of ultracold alkali-metal molecules is among the critical elements needed for their application in precision measurements and quantum technologies. Recent experiments with nonreactive systems have reported unexpectedly large loss rates, posing a challenge for theoretical explanation. Here, we examine the dynamics of intermediate four-atom complexes formed in bimolecular collisions. We calculate the nuclear spin--rotation, spin--spin, and quadrupole coupling constants for bialkali tetramers using ab intio quantum-chemical methods. We sh…
Understanding and controlling collisions is crucial to the burgeoning field of ultracold molecules. All experiments so far have observed fast loss of molecules from the trap. However, the dominant mechanism for collisional loss is not well understood when there are no allowed 2-body loss processes. Here we experimentally investigate collisional losses of nonreactive ultracold RbCs molecules, and compare our findings with the sticky collision hypothesis that pairs of molecules form long-lived collision complexes. We demonstrate that loss of molecules occupying their rotational and hyperfine gro…
Interactions between particles can be strongly altered by their environment. We demonstrate a technique for modifying interactions between ultracold atoms by dressing the bare atomic states with light, creating an effective interaction of vastly increased range that scatters states of finite relative angular momentum at collision energies where only s-wave scattering would normally be expected. We collided two optically dressed neutral atomic Bose-Einstein condensates with equal, and opposite, momenta and observed that the usual s-wave distribution of scattered atoms was altered by the appeara…
We demonstrate microwave dressing on ultracold, fermionic ${}^{23}$Na${}^{40}$K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding three times the $s$-wave unitarity limit. The origin of these collisions 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. Furthermore, we perform coupled-channels calculations that agree well with the experimentally observed collision rate…
We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more…
Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions and collisions between Feshbach molecules which are very weakly bound. Whether such resonances exist for ultracold ground state molecules has been debated due to the possibly high density of states and/or rapid decay of the resonant complex. Here we report a v…
We calculate and analyze Feshbach resonance spectra for ultracold Yb($^1$S$_0$) + Yb($^3$P$_2$) collisions as a function of an interatomic potential scaling factor $λ$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $λ$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances in magnetic field in the experimentally accessible range 400 to 2000~G are chaoticall…
We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in K. Jachymski \emph{et al.}, Phys. Rev. Lett. {\bf 120}, 013401 (2018), is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect …
Atomic and molecular samples reduced to temperatures below 1 microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating how their constituent particles interact with one another. For simple atoms, such as alkalis, scattering resonances are extremely well-characterized. However, ultracold physics is now poised to enter a new regime, where far more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense forest of resonances in ultracold collision cross se…
We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, $N$-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the K$_2$-Rb and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124~$μ$K$^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus (RRKM) sticking time of 6.0~$μ$s. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scali…
Access to single-particle momenta provides new means of studying the dynamics of a few interacting particles. In a joint theoretical and experimental effort, we observe and analyze the effects of a finite number of ultracold two-body collisions on the relative and single-particle densities by quenching two ultracold atoms with an initial narrow wave packet into a wide trap with an inverted aspect ratio. The experimentally observed spatial oscillations of the relative density are reproduced by a parameter-free zero-range theory and interpreted in terms of cross-dimensional flux. We theoreticall…
Arrays of single ultracold molecules promise to be a powerful platform for many applications ranging from quantum simulation to precision measurement. Here we report on the creation of an optical tweezer array of single ultracold CaF molecules. By utilizing light-induced collisions during the laser cooling process, we trap single molecules. The high densities attained inside the tweezer traps have also enabled us to observe in the absence of light molecule-molecule collisions of laser cooled molecules for the first time.
We investigate collisional loss in an ultracold mixture of $^{40}$K$^{87}$Rb molecules and $^{87}$Rb atoms, where chemical reactions between the two species are energetically forbidden. Through direct detection of the KRb$_{2}^{*}$ intermediate complexes formed from atom-molecule collisions, we show that a $1064$ nm laser source used for optical trapping of the sample can efficiently deplete the complex population via photo-excitation, an effect which can explain the universal two-body loss observed in the mixture. By monitoring the time-evolution of the KRb$_{2}^{*}$ population after a sudden…
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system, and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of the four-body bound states in the adiabatic approximation (i.e. no coupling between adiabatic channels). It is found that while the adiabatic potential distribution transitions from chaotic to non-chaotic as th…
The Fano effect (U. Fano, Phys. Rev. \textbf{15},1866 (1961) shows that an inelastic scattering process can be suppressed when the output channel (OC) is coupled to an isolated bound state. In this paper we investigate the application of this effect for the suppression of two-body collisional losses of ultracold atoms. The Fano effect is originally derived via a first-order perturbation treatment for coupling between the incident channel (IC) and the OC. We generalize the Fano effect to systems with arbitrarily strong IC--OC couplings. We analytically prove that, in a system with one IC and on…
We study collisions in an optically trapped, pure sample of ultracold Cs$_2$ molecules in various internal states. The molecular gas is created by Feshbach association from a near-degenerate atomic gas, with adjustable temperatures in the nanokelvin range. We identify several narrow loss resonances, which point to the coupling to more complex molecular states and may be interpreted as Feshbach resonances in dimer-dimer interactions. Moreover, in some molecular states we observe a surprising temperature dependence in collisional loss. This shows that the situation cannot be understood in terms …
Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vi…
The control of the ultracold collisions between neutral atoms is an extensive and successful field of study. The tools developed allow for ultracold chemical reactions to be managed using magnetic fields, light fields and spin-state manipulation of the colliding particles among other methods. The control of chemical reactions in ultracold atom-ion collisions is a young and growing field of research. Recently, the collision energy and the ion electronic state were used to control atom-ion interactions. Here, we demonstrate spin-controlled atom-ion inelastic processes. In our experiment, both sp…
Collisional complexes, which are formed as intermediate states in molecular collisions, are typically short-lived and decay within picoseconds. However, in ultracold collisions involving bialkali molecules, complexes can live for milliseconds, completely changing the collision dynamics. This can lead to unexpected two-body loss in samples of nonreactive molecules. During the last decade, such "sticky" collisons have been a major hindrance in the preparation of dense and stable molecular samples, especially in the quantum-degenerate regime. Currently, the behavior of the complexes is not fully …
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a $C_6$ coefficient) for each asymptotic value of partial wave quantum numbers $|L,M \rangle$. From this,…
We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach reso…
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T \sim 10^{-8}$ K. A global six-dimensional H$_2$-H$_2$ potential energy surface is adopted from a previous work [Boothroyd {\it et al.}, J. Chem. Phys., {\bf 116}, 666 (2002).] State-resolved integral cross sections $σ_{ij\rightarrow i'j'}(\varepsilon_{kin})$ of different quantum-mechanical rotational transitions $ij\rightarrow i'j'$ in the HD molecules and corresponding state-resolved thermal rate coefficients $k_{ij\rightar…
We consider the low-energy scattering of two ultracold polarized dipoles with both a short-range interaction (SRI) and a weak dipole-dipole interaction (DDI) which is far away from shape-resonances. In previous analytical studies, the scattering amplitude in this system was often calculated via the first-order Born approximation (FBA). Our results show that significant derivations from this approximation can arise in some cases. In these cases, the SRI can significantly modify the inter-dipole scattering amplitudes even if the scattering amplitudes for the SRI alone are much smaller than the d…
We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting h…
Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known r…
We study cavity optomechanics of a mixture of ultracold atoms with tunable nonlinear collisions. We show that atomic collisions provide linear couplings between fictitious condensate oscillators, leading to possibilities of achieving a globally coupled quantum optomechanical network with an integrated atom chip. Potential applications range from simulating collective nonequilibrium dynamics in fields well past physics to probing unique properties of quantum mixtures.
