Formation of molecular oxygen in ultracold O + OH reaction

We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic and reactive cross sections as well as the vibrational and rotational populations of the product O2 molecules are reported. A J-shifting approximation is used to compute the rate coefficients. At temperatures T = 10 - 100 mK for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, T < 1 mK, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at T=0.3 K, at higher temperatures, the quantum calculations predict a larger rate coefficient than the classical model, in agreement with experimental data for the O + OH reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about 6.10^{-12} cm^3 molecule^{-1} s^{-1}, a value comparable to that of barrierless alkali-metal atom - dimer systems and about a factor of five larger than that of the tunneling dominated F + H2 reaction.Comment: 9 pages, 8 figure

Controlling the quantum stereodynamics of ultracold bimolecular reactions

Chemical reaction rates often depend strongly on stereodynamics, namely the orientation and movement of molecules in three-dimensional space. An ultracold molecular gas, with a temperature below 1 uK, provides a highly unusual regime for chemistry, where polar molecules can easily be oriented using an external electric field and where, moreover, the motion of two colliding molecules is strictly quantized. Recently, atom-exchange reactions were observed in a trapped ultracold gas of KRb molecules. In an external electric field, these exothermic and barrierless bimolecular reactions, KRb+KRb -> K2+Rb2, occur at a rate that rises steeply with increasing dipole moment. Here we show that the quantum stereodynamics of the ultracold collisions can be exploited to suppress the bimolecular chemical reaction rate by nearly two orders of magnitude. We use an optical lattice trap to confine the fermionic polar molecules in a quasi-two-dimensional, pancake-like geometry, with the dipoles oriented along the tight confinement direction. With the combination of sufficiently tight confinement and Fermi statistics of the molecules, two polar molecules can approach each other only in a "side-by-side" collision, where the chemical reaction rate is suppressed by the repulsive dipole-dipole interaction. We show that the suppression of the bimolecular reaction rate requires quantum-state control of both the internal and external degrees of freedom of the molecules. The suppression of chemical reactions for polar molecules in a quasi-two-dimensional trap opens the way for investigation of a dipolar molecular quantum gas. Because of the strong, long-range character of the dipole-dipole interactions, such a gas brings fundamentally new abilities to quantum-gas-based studies of strongly correlated many-body physics, where quantum phase transitions and new states of matter can emerge.Comment: 19 pages, 4 figure

Experimental investigation of ultracold atom-molecule collisions

Ultracold collisions between Cs atoms and Cs2 dimers in the electronic ground state are observed in an optically trapped gas of atoms and molecules. The Cs2 molecules are formed in the triplet ground state by cw-photoassociation through the outer well of the 0g-(P3/2) excited electronic state. Inelastic atom-molecule collisions converting internal excitation into kinetic energy lead to a loss of Cs2 molecules from the dipole trap. Rate coefficients are determined for collisions involving Cs atoms in either the F=3 or F=4 hyperfine ground state and Cs2 molecules in either highly vibrationally excited states (v'=32-47) or in low vibrational states (v'=4-6) of the a ^3 Sigma_u^+ triplet ground state. The rate coefficients beta ~10^{-10} cm^3/s are found to be largely independent of the vibrational and rotational excitation indicating unitary limited cross sections.Comment: 4 pages, 3 figures, submitted for publicatio

Dipolar collisions of polar molecules in the quantum regime

Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range, and spatially anisotropic. This is in stark contrast to the dilute gases of ultracold atoms, which have isotropic and extremely short-range, or "contact", interactions. The large electric dipole moment of polar molecules can be tuned with an external electric field; this provides unique opportunities such as control of ultracold chemical reactions, quantum information processing, and the realization of novel quantum many-body systems. In spite of intense experimental efforts aimed at observing the influence of dipoles on ultracold molecules, only recently have sufficiently high densities been achieved. Here, we report the observation of dipolar collisions in an ultracold molecular gas prepared close to quantum degeneracy. For modest values of an applied electric field, we observe a dramatic increase in the loss rate of fermionic KRb molecules due to ultrcold chemical reactions. We find that the loss rate has a steep power-law dependence on the induced electric dipole moment, and we show that this dependence can be understood with a relatively simple model based on quantum threshold laws for scattering of fermionic polar molecules. We directly observe the spatial anisotropy of the dipolar interaction as manifested in measurements of the thermodynamics of the dipolar gas. These results demonstrate how the long-range dipolar interaction can be used for electric-field control of chemical reaction rates in an ultracold polar molecule gas. The large loss rates in an applied electric field suggest that creating a long-lived ensemble of ultracold polar molecules may require confinement in a two-dimensional trap geometry to suppress the influence of the attractive dipolar interactions

Resonant collisional shielding of reactive molecules using electric fields

Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. Here, we demonstrate extreme tunability of chemical reaction rates by using an external electric field to shift excited collision channels of ultracold molecules into degeneracy with the initial collision channel. In this situation, resonant dipolar interactions mix the channels at long range, dramatically altering the intermolecular potential. We prepare fermionic potassium-rubidium (KRb) molecules in their first excited rotational state and observe a three orders-of-magnitude modulation of the chemical reaction rate as we tune the electric field strength by a few percent across resonance. In a quasi-two-dimensional geometry, we accurately determine the contributions from the three lowest angular momentum projections of the collisions. Using the resonant features, we shield the molecules from loss and suppress the reaction rate by up to an order of magnitude below the background value, realizing a long-lived sample of polar molecules in large electric fields.Comment: 17+4 pages, 4+1 figure

Determination of the moments of the proton charge density

A global analysis of proton electric form factor experimental data from Rosenbluth separation and low squared four-momentum transfer experiments is discussed for the evaluation of the spatial moments of the proton charge density based on the recently published integral method \cite{Hob20}. Specific attention is paid to the evaluation of the systematic errors of the method, particularly the sensitivity to the choice of the mathematical expression of the form factor fitting function. Within this comprehensive analysis of proton electric form factor data, the moments of the proton charge density are determined for integer order moments, particularly: $\langle r^2 \rangle$=0.682(02)$_{Sta.}$(11)$_{Sys.}$~fm$^2$, $\langle r^3 \rangle$=0.797(10)$_{Sta.}$(58)$_{Sys.}$~fm$^3$, and $\langle r^4 \rangle$=1.02(05)$_{Sta.}$(31)$_{Sys.}$~fm$^4$. This analysis leads to the proton charge radius 0.8459(12)$_{Sta.}$(76)$_{Sys.}$~fm once relativistic effects are taken into account.Comment: 10 pages, 3 figure

Long range forces between polar alkali diatoms aligned by external electric fields

Long range electrostatic, induction and dispersion coefficients including terms of order $R^{-8}$ have been calculated by the sum over states method using time dependent density functional theory. We also computed electrostatic moments and static polarizabilities of the individual diatoms up to the octopole order using coupled cluster and density functional theory. The laboratory-frame transformed electrostatic moments and van der Waals coefficients corresponding to the alignment of the diatomic molecules were found. We use this transformation to obtain the coupling induced by an external DC electric field, and present values for all XY combinations of like polar alkali diatomic molecules with atoms from Li to Cs. Analytic solutions to the dressed-state laboratory-frame electrostatic moments and long range intermolecular potentials are also given for the DC low-field limit

Tuning of dipolar interactions and evaporative cooling in a three-dimensional molecular quantum gas

Ultracold polar molecules possess long-range, anisotropic and tunable dipolar interactions, providing opportunities to probe quantum phenomena that are inaccessible with existing cold gas platforms. However, experimental progress has been hindered by the dominance of two-body loss over elastic interactions, which prevents efficient evaporative cooling. Although recent work has demonstrated controlled interactions by confining molecules to a two-dimensional geometry, a general approach for tuning molecular interactions in a three-dimensional stable system has been lacking. Here we demonstrate tunable elastic dipolar interactions in a bulk gas of ultracold 40K87Rb molecules in three dimensions, facilitated by an electric field-induced shielding resonance that suppresses the reactive loss by a factor of 30. This improvement in the ratio of elastic to inelastic collisions enables direct thermalization. The thermalization rate depends on the angle between the collisional axis and the dipole orientation controlled by an external electric field, a direct manifestation of the anisotropic dipolar interaction. We achieve evaporative cooling mediated by the dipolar interactions in three dimensions. This work demonstrates full control of a long-lived bulk quantum gas system with tunable long-range interactions, paving the way for the study of collective quantum many-body physics