Cold Collisions Research Articles

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms.

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H2 molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.

Two types of highly efficient electrostatic traps for single loading or multi-loading of polar molecules**Project supported by the National Natural Science Foundation of China (Grant Nos. 11834003, 91536218, 11034002, 11274114, 11504112, and 11874151), the National Key Basic Research and Development Program of China (Grant No. 2011CB921602), the Fundamental Research Funds for the Central Universities, China, Shanghai Pujiang Talents Plan, China

Two novel electrostatic traps named octopole-based disk electrostatic trap (ODET) and tubular-based disk electrostatic trap (TDET) are proposed for trapping cold polar molecules in low-field-seeking states. Using MgF as the target molecule, single loading and multi-loading methods are numerically simulated with varied incident velocities of slow molecular beams in the two types of traps, respectively. In ODET, with an incident velocity of 10 m/s, a highest loading efficiency of 78.4% or 99.9% has been achieved under the single loading or multi-loading operation mode. In TDET, with an incident velocity of 11 m/s, a highest loading efficiency of 81.6% or 106.5% has been achieved using the two loading methods, respectively. With such high loading efficiencies, the trapped cold molecules can be applied in the researches of cold collisions, high precision spectroscopy, and precision measurements. Especially, together with a blue-detuned hollow beam, the new electrostatic traps proposed here offer a new platform for the following gradient-intensity cooling of MgF molecules, which may provide a new way to produce high density ultracold molecules.

Interactions and charge-transfer dynamics of anAl+ion immersed in ultracold Rb and Sr atoms

Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooled alkaline-earth ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge transfer dynamics of an Al$^+$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)$^+$ and (Al+Sr)$^+$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge transfer dynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.

Investigation of cold atom collision frequency shift measured by rapid adiabatic passage in cesium fountain clock

Cold collision frequency shift is one of the major systematic effects which limit the frequency uncertainty of the cesium fountain atomic clock. It is proportional to the effective atomic density, which is defined as the average density over the initial spacial and velocity distribution. The measurement of the frequency shift is based on a differential method, in which the fountain clock is operated with two different atomic densities, i.e. high density and low density, in turn. The clock frequency without collision shift can be achieved by linear extrapolation with the frequencies and density ratios of two states. For the density ratio is estimated with the atom number, it plays a crucial role in generating atoms with same density distribution for reducing systematic uncertainty in cold collision frequency shift estimation. The rapid adiabatic passage method is used in Cesium fountain clock to realize homogeneous transition probability, which modulates the amplitude and frequency of microwave continuously to prepare atom sample. To investigate the precision of this method, theoretical analysis and experimental measurement are both used here. An equation of deviation is derived from the time evolution of Bloch vector. The vector rotates at angular speed <i>Ω</i> with the rotation axis processing at lower angular speed. The deviations in the two directions on the surface of Bloch sphere are determined by the equations which are similar to wave equations, and can be simplified into wave equations when the deviations are sufficiently small. It is shown in the equations that the deviations are stimulated by angular velocity and angular acceleration of the precession, and is inversely proportional to the square of <i>Ω</i>. Further calculation shows that the deviation becomes smaller when the amplitude of microwave frequency and Rabi frequency are close to each other. It is then confirmed experimentally. The effects of some other parameters, such as the pulse length and time delay, on transition probability are also measured, showing that the RAP method is insensitive to these parameters up to a large scope. The precision of RAP method is dominated by three factors. The first factor is the product of rotating angular speed <i>Ω</i> and pulse length <i>T</i>, i.e. <i>ΩT</i>: The increase of <i>ΩT</i> can reduce the uncertainty to a satisfactory degree. The second factor is the uncertainty of resonant frequency, so the measurement is required to be precise. The third factor is the unexpected atoms which are not selected by the microwave, and may be attributed to pulling light. After optimizing the parameters, the ratio of low density to high density can approach to 0.5 with 3 × 10<sup>–3</sup> uncertainty, which leads to a systematic relative uncertainty of cold collision shift up to 1.6 × 10<sup>–16</sup>.

Cold collisions of with Li and Rb atoms in hybrid traps

We present a theoretical investigation of reactive and non-reactive collisions of Li and Rb atoms with molecular anions at low temperatures in the context of sympathetic cooling in hybrid trap experiments. Based on accurate potential energy surfaces for the singlet and triplet states of the Li– and Rb– systems, we show that the associative electronic detachment reaction is inefficient but that it occurs with a large rate for collisions involving excited states of either Li/Rb or . We also investigate rotationally inelastic collisions in order to explore the cooling of the translational and rotational degrees of freedom of in hybrid ion-atom traps. The effect of micromotion is taken into account by considering Tsallis distributions of collision energies. We show that the translational cooling occurs much more rapidly than rotational cooling and that the presence of excited atoms leads to losses of anions on a timescale comparable to that of rotational cooling.

Long-range versus short-range effects in cold molecular ion-neutral collisions

The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N{}_{2}^{+} and O{}_{2}^{+} ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.

Long-range vs. short-range effects in cold molecular ion-neutral collisions: Charge exchange of Rb with N+2 and O+2

Long-range vs. short-range effects in cold molecular ion-neutral collisions: Charge exchange of Rb with N+2 and O+2

Ion beam trap design looks to capture beams of merged cations and anions

Simulations show that proposed hybrid electrostatic ion beam trap would be capable of cold collisions at low relative velocities between reactants.

Time delays in ultracold atomic and molecular collisions

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.

Cooling of fermionic $$^{83}\hbox {Kr}$$ and bosonic $$^{84}\hbox {Kr}$$ isotopes in a magneto-optical trap

Simultaneous laser cooling of two isotopes of krypton, \(^{83}\hbox {Kr}\) and \(^{84}\hbox {Kr}\), is reported here in a two-isotope magneto-optical trap (TIMOT). The number of cold metastable \(^{83}\hbox {Kr}\) atoms in this TIMOT is dependent on the power of the repumping laser beams used, which is maximised for our set-up by varying the powers of repumping lasers. These studies may be useful to investigate cold collisions between fermionic \(^{83}\hbox {Kr}\) and bosonic \(^{84}\hbox {Kr}\) atoms in the metastable state.

Quantum control of molecular rotation

The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two- and many-body scenarios, thereby allowing to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information, to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, we recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control --- from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting.

Long-term trapping of Stark-decelerated molecules

Trapped cold molecules represent attractive systems for precision-spectroscopic studies and for investigations of cold collisions and chemical reactions. However, achieving their confinement for sufficiently long timescales remains a challenge. Here, we report the long-term trapping of Stark-decelerated OH radicals in their X2Π3/2 (ν = 0, J = 3/2, MJ = 3/2, f) state in a permanent magnetic trap. The trap environment is cryogenically cooled to a temperature of 17 K to suppress black-body-radiation-induced pumping of the molecules out of trappable quantum states and collisions with residual background gas molecules which usually limit the trap lifetime. The cold molecules are thus confined on timescales approaching minutes, an improvement of up to two orders of magnitude compared with room temperature experiments, at translational temperatures of ∼25 mK. The present results pave the way for new experiments using trapped cold molecules in precision spectroscopy, in studies of slow chemical processes at low energies and in the quantum technologies.

General mathematical formulation of scattering processes in atom-diatomic collisions in the RmatReact methodology.

Accurately modelling cold and ultracold reactive collisions occurring over deep potential wells, such as [Formula: see text], requires the development of new theoretical and computational methodologies. One potentially useful framework is the R-matrix method adopted widely for electron-molecule collisions which has more recently been applied to non-reactive heavy-particle collisions such as Ar-Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photoassociation, photodissociation, charge exchange and reactive scattering using the R-matrix method. Of particular note is that the inner region, of central importance to calculable R-matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

Metamorphism and the evolution of subduction on Earth

AbstractSubduction is a component of plate tectonics, which is widely accepted as having operated in a manner similar to the present-day back through the Phanerozoic Eon. However, whether Earth always had plate tectonics or, if not, when and how a globally linked network of narrow plate boundaries emerged are matters of ongoing debate. Earth's mantle may have been as much as 200–300 °C warmer in the Mesoarchean compared to the present day, which potentially required an alternative tectonic regime during part or all of the Archean Eon. Here we use a data set of the pressure (P), temperature (T), and age of metamorphic rocks from 564 localities that vary in age from the Paleoarchean to the Cenozoic to evaluate the petrogenesis and secular change of metamorphic rocks associated with subduction and collisional orogenesis at convergent plate boundaries. Based on the thermobaric ratio (T/P), metamorphic rocks are classified into three natural groups: high T/P type (T/P > 775 °C/GPa, mean T/P ~1105 °C/GPa), intermediate T/P type (T/P between 775 and 375 °C/GPa, mean T/P ~575 °C/GPa), and low T/P type (T/P < 375 °C/GPa, mean T/P ~255 °C/GPa). With reference to published thermal models of active subduction, we show that low T/P oceanic metamorphic rocks preserving peak pressures >2.5 GPa equilibrated at P–T conditions similar to those modeled for the uppermost oceanic crust in a wide range of active subduction environments. By contrast, those that have peak pressures <2.2 GPa may require exhumation under relatively warm conditions, which may indicate subduction of young oceanic lithosphere or exhumation during the initial stages of subduction. However, low T/P oceanic metamorphic rocks with peak pressures of 2.5–2.2 GPa were exhumed from depths where, in models of active subduction, the slab and overriding plate change from being decoupled (at lower P) to coupled (at higher P), possibly suggesting a causal relationship. In relation to secular change, the widespread appearance of low T/P metamorphism in the Neoproterozoic represents a “modern” style of cold collision and deep slab breakoff, whereas rare occurrences of low T/P metamorphism in the Paleoproterozoic may reveal atypical localized regions of cold collision. Low T/P metamorphism is not known from the Archean geological record, but the absence of blueschists in particular is unlikely to reflect secular change in the composition of the oceanic crust. In addition, the premise that the formation of lawsonite requires abnormally low thermal gradients and the postulate that oceanic subduction-related rocks register significantly lower maximum pressures than do continental subduction-related rocks, and imply different mechanisms of exhumation, are not supported. The widespread appearance of intermediate T/P and high T/P metamorphism at the beginning of the Neoarchean, and the subsequent development of a clear bimodality in tectono-thermal environments are interpreted to be evidence of the stabilization of subduction during a transition to a globally linked network of narrow plate boundaries and the emergence of plate tectonics.

Stereodynamical Control of a Quantum Scattering Resonance in Cold Molecular Collisions.

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

Cold collision and the determination of the X2Σ1/2(v = 1, N = 1) → A2Π1/2(v′ = 0, J′ = 1/2) frequency with buffer-gas-cooled MgF molecules

We report a detailed experimental study of the cold collision of magnesium mono-fluoride (MgF) with buffer gas and compare the cryogenic molecular beam source of two different inner structures of cell. The collision cross section with helium is measured to be ∼0.8×10−14cm2 at 7.5 K, which is suitable for buffer-gas cooling. The absorption spectrum around 368.7 nm at low-lying rotational states is assigned and the accurate frequency of X2Σ1/2(v = 1, N = 1) → A2Π1/2(v′ = 0, J′ = 1/2) transition is determined to be 812.959246 THz, which is essential for constructing the quasi-closed cycling between vibrational states. Our study is an important complement to laser cooling of MgF molecules.

Cold hybrid ion-atom systems

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

The Clusterization Technique: A Systematic Search for the Resonance Energies Obtained via Padé.

Atomic and molecular resonances play an important role in many physical processes, hence developing theoretical tools to properly calculate these states is required. Recently, we introduced a method for calculating the electronic resonance complex energies from stabilization graphs via analytical continuation, specifically, using the Padé approximant. This method was shown to be efficient, for example, in interpreting the results of cold molecular collisions. However, we observed that the complex energies obtained by Padé depend on the selected set of input points from the stabilization graph. In addition, unphysical solutions (noise) may appear and need to be eliminated. Therefore, applying the method to systems in which the resonance values are unavailable is difficult. The excited Li-He* Feshbach states, for which autoionization was recently observed, present such a challenge. Herein, we introduce a statistical approach to single out the resonance energy from the false solutions by identifying it as a cluster of Padé solutions. This clusterization technique was applied to study several electronic resonance states, for which we obtained excellent agreement with available data (exact or other theoretical solutions and an experimental result). Following this, the technique successfully identified the most likely Li-He* Feshbach resonance energy. Moreover, we concluded that large input sets generate much noise while restricting the number of points facilitates clusterization, which makes this approach more attractive, since input points are obtained from computationally demanding electronic-structure calculations. Overall, the use of analytical continuation via Padé, along with the statistical technique presented herein, offers an efficient approach to calculate resonances.

Controlling rotational quenching rates in cold molecular collisions.

The relative orientation and alignment of colliding molecules plays a key role in determining the rates of chemical processes. Here, we examine in detail a prototypical example: rotational quenching of HD in cold collisions with H2. We show that the rotational quenching rate from j = 2 → 0, in the v = 1 vibrational level, can be maximized by aligning the HD along the collision axis and can be minimized by aligning the HD at the so called magic angle. This follows from quite general helicity considerations and suggests that quenching rates for other similar systems can also be controlled in this manner.

Generation of high-energy-resolved NH3 molecular beam by a Stark decelerator with 179 stages**Project supported by the National Natural Science Foundation of China (Grant Nos. 91536218, 11034002, 11274114, 11504112, and 11504318), the National Basic Research Program of China (Grant No. 2011CB921602), the Fundamental Research Funds for the Central Universities, China, Shanghai Pujiang Talents Plan, China (Grant No. 18PJ1403100), and Exploration Funds

We demonstrate the production of cold, slow NH3 molecules from a supersonic NH3 molecular beam using our electrostatic Stark decelerator consisting of 179 slowing stages. By using this long Stark decelerator, a supersonic NH3 molecular beam can be easily decelerated to trappable velocities. Here we present two modes for operating the Stark decelerator to slow the supersonic NH3 molecules. The first is the normal mode, where all 179 stages are used to decelerate molecules, and it allows decelerating the NH3 molecular beam from 333 m/s to 18 m/s, with a final temperature of 29.2 mK. The second is the deceleration-bunch mode, which allows us to decelerate the supersonic NH3 beam from 333 m/s to 24 m/s, with a final temperature of 2.9 mK. It is clear that the second mode promises to produce colder (high-energy-resolution) molecular samples than the normal mode. Three-dimensional Monte Carlo simulations are also performed for the experiments and they show a good agreement with the observed results. The deceleration-bunch operation mode presented here can find applications in the fields of cold collisions, high-resolution spectroscopy, and precision measurements.