Magnetically controlled exchange process in an ultracold atom-dimer mixture

Modeling Photoassociative Spectra of Ultracold NaK + K

A model for photoassociation of ultracold atoms and molecules is presented and applied to the case of 39K and 23Na39K bosonic particles. The model relies on the assumption that photoassociation is dominated by long-range atom-molecule interactions well outside the chemical bond region. The frequency of the photoassociation laser is chosen close to a bound-bound rovibronic transition from the X1Σ+ ground state toward the metastable b3Π lowest excited state of 23Na39K, allowing us to neglect any other excitation, which could hinder the photoassociation detection. The energy level structure of the long-range 39K···23Na39K excited super-dimer is computed in the space-fixed frame by solving coupled-channel equations, involving the coupling between the 23Na39K internal rotation and the mechanical rotation of the super-dimer complex. A quite rich structure is obtained, and the corresponding photoassociation rates are presented. Other possible photoassociation transitions are discussed in the context of the proposed model.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Hyperfine Magnetic Substate Resolved State-to-State Chemistry

We extend state-to-state chemistry to a realm where besides vibrational, rotational, and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect, which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of ^{87}Rb atoms forming weakly bound Rb_{2} molecules. Here, we find the propensity rule that the total m_{F} quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other reactions and inelastic collisions and will allow for novel insights into few-body processes.

Nonadiabatic Ultracold Quantum Reactive Scattering of Hydrogen with Vibrationally Excited HD(v = 5-9)

The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD(v = 5-9) → H + HD(v', j') reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry. Prominent shape resonances appear at higher collision energies (100 mK to 20 K), which could be measured experimentally. Significant geometric phase effects are also reported on the resonance energies and lifetimes. In particular, an enhancement (suppression) of the l = 1 (l = 2) shape resonances for HD(v = 5, 6) is predicted for even symmetry relative to those of odd symmetry.

Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ^{23}Na^{40}K Molecules

Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ^{23}Na^{40}K ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.

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.

Cooling of atoms using an optical frequency comb

We report on laser cooling of neutral rubidium atoms by using a single mode of a frequency comb. Cooling is achieved on a dipole-allowed transition at 780 nm in a one-dimensional retro-reflected beam geometry. Temperatures are measured using standard time-of-flight imaging. We show the dependence of the temperature on the cooling time, intensity and detuning of the frequency comb. The lowest temperature achieved is approximately equal to the Doppler temperature and is limited by the intensity of the comb mode driving the cooling transition. Additionally, we verify the analogy between frequency comb and continuous-wave laser cooling. Our work is a step towards laser cooling of atoms with strong cycling transitions in the vacuum ultraviolet, such as hydrogen, deuterium and antihydrogen, where generation of continuous-wave laser light is limited by current laser technology. Achieving efficient cooling at these wavelengths would significantly improve the precision of optical frequency standards, enable measurements of fundamental constants with unprecedented accuracy, improve tests of charge, parity, and time reversal symmetry, and open the way to achieving quantum degeneracy width new atomic species.

Reaction kinetics of ultracold molecule-molecule collisions

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. Here, we investigate a single-channel reaction of two Li₂-Feshbach molecules where one of the molecules dissociates into two atoms 2AB ⇒ AB + A + B. The process is a prototype for a class of four-body collisions where two reactants produce three product particles. We measure the collisional dissociation rate constant of this process as a function of collision energy/temperature and scattering length. We confirm an Arrhenius-law dependence on the collision energy, an a⁴ power-law dependence on the scattering length a and determine a universal four body reaction constant.

Unraveling the Stereodynamics of Cold Controlled HD-H_{2} Collisions

Measuring inelastic rates with partial-wave resolution requires temperatures close to a Kelvin or below, even for the lightest molecule. In a recent experiment, Perreault, Mukherjee, and Zare [Nat. Chem. 10, 561 (2018).NCAHBB1755-433010.1038/s41557-018-0028-5] studied collisional relaxation of excited HD molecules in the v=1, j=2 state by para- and ortho-H_{2} at a temperature of about 1 K, extracting the angular distribution of scattered HD in the v=1, j=0 state. By state preparation of the HD molecules, control of the angular distribution of scattered HD was demonstrated. Here, we report a first-principles simulation of that experiment which enables us to attribute the main features of the observed angular distribution to a single L=2 partial-wave shape resonance. Our results demonstrate important stereodynamical insights that can be gained when numerically exact quantum scattering calculations are combined with experimental results in the few-partial-wave regime.

Symmetry and the geometric phase in ultracold hydrogen-exchange reactions

Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states, one can always find final states where it does. For the isotopic counterpart reactions, these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. It is shown how this equivalence can be used to define a constant which quantifies the GP effect and can be obtained solely from experimentally observable rates. This equivalence reflects the important role that discrete symmetries play in ultracold chemistry and highlights the key role that ultracold reactions can play in understanding fundamental aspects of chemical reactivity more generally.

Universality and chaoticity in ultracold K+KRb chemical reactions

A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K₂Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.

Studying chemical reactions near zero temperature in detail is challenging both in theory and practice. Here the authors report an explicit quantum mechanical study of the benchmark ultracold reaction between a K atom and a KRb molecule, important for future controlled chemistry experiments.

Observation of Rydberg-Atom Macrodimers: Micrometer-Sized Diatomic Molecules

Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme is employed to form these molecules in states, which correlate to np(n+1)s dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair states. We show that a full model is required to accurately predict the occurrence of bound Rydberg macrodimers. The macrodimers are distinguished from repulsive molecular states by their behavior with respect to spontaneous ionization and possible decay channels are discussed.

Production of high density molecular beams with wide velocity scanning

We describe modifications of a pulsed rotating supersonic beam source that improve performance, particularly increasing the beam density and sharpening the pulse profiles. As well as providing the familiar virtues of a supersonic molecular beam (high intensity, narrowed velocity distribution, and drastic cooling of rotation and vibration), the rotating source enables scanning the translational velocity over a wide range. Thereby, beams of any atom or molecule available as a gas can be slowed or speeded. Using Xe beams in the slowing mode, we have obtained lab speeds down to about 40 ± 5 m/s with density near 10(11) cm(-3) and in the speeding mode lab speeds up to about 660 m/s and density near 10(14) cm(-3). We discuss some congenial applications. Providing low lab speeds can markedly enhance experiments using electric or magnetic fields to deflect, steer, or further slow polar or paramagnetic molecules. The capability to scan molecular speeds facilitates merging velocities with a codirectional partner beam, enabling study of collisions at very low relative kinetic energies, without requiring either beam to be slow.

Reactive scattering calculations for (87)Rb+(87)RbHe→Rb2((3)Σ(u)(+),v)+He from ultralow to intermediate energies

We investigate atom-diatom reactive collisions, as a preliminary step,in order to assess the possibility of forming Rb(2) molecules in their lowest triplet electronic state by cold collisions of rubidium atoms on the surface of helium nanodroplets [corrected]. A simple model related to the well-known Rosen treatment of linear triatomic molecules [N. Rosen, J. Chem. Phys. 1, 319 (1933)] in relative coordinates is used, allowing to estimate reactive probabilities for different values of the total angular momentum. The best available full dimensional potential energy surface [Guillon et al., J. Chem. Phys. 136, 174307 (2012)] is employed through the calculations. Noticeable values of the probabilities in the ultracold regime, which numerically fulfill the Wigner threshold law, support the feasibility of the process. The rubidium dimer is mainly produced at high vibrational states, and the reactivity is more efficient for a bosonic helium partner than when the fermion species is considered.

Quantum reactive scattering of ultracold NH(X (3)Σ(-)) radicals in a magnetic trap

We investigate the ultracold reaction dynamics of magnetically trapped NH(X (3)Σ(-)) radicals using rigorous quantum scattering calculations involving three coupled potential energy surfaces. We find that the reactive NH+NH cross section is driven by a short-ranged collisional mechanism, and its magnitude is only weakly dependent on magnetic field strength. Unlike most ultracold reactions observed so far, the NH+NH scattering dynamics is nonuniversal. Our results indicate that chemical reactions can cause more trap loss than spin-inelastic NH+NH collisions, making molecular evaporative cooling more difficult than previously anticipated.

Dynamics of individual rotational states in an electrostatic guide for neutral molecules

The guiding properties of individual rotational states of deuterated ammonia inside an electrostatic hexapole guide are presented. The guide is combined with resonance enhanced multiphoton ionization detection to assess the guiding probabilities and velocity distributions as a function of the rotational quantum numbers J and K. Due to the differences in the effective dipole moment these states are prepared at significantly different translational temperatures. A model is presented that describes the velocity-distribution for individual M-sublevels, and this model is also used to determine a rotational-state dependent translational temperature. Furthermore, the hexapole field has been replaced by a dipole field in order to obtain a band-pass velocity filter. However, the resulting change in the final velocity distribution is similar to that obtained from a hexapole guide but with increased backing pressure, leading to collisional acceleration of the slow molecules.

Rotational predissociation of extremely weakly bound atom-molecule complexes produced by Feshbach resonance association

We study the rotational predissociation of atom-molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e., when the predissociating state is just above the excited state threshold.

Homo- and heteronuclear alkali metal trimers formed on helium nanodroplets. Part II. Femtosecond spectroscopy and spectra assignments

Homo- and heteronuclear alkali quartet trimers of type K(3-n)Rb(n) (n = 0,1,2,3) formed on helium nanodroplets are probed by one-color femtosecond (fs) photoionization (PI) spectroscopy. The obtained frequencies are assigned to vibrations in different electronic states in comparison to high level ab initio calculations of the involved potentials including pronounced Jahn-Teller and spin-orbit couplings. Despite the fact that the resulting complex vibronic structure of the heavy alkali molecules complicates the comparison of experiment and theory we find good agreement for many of the observed lines for all species.

Sympathetic cooling of polyatomic molecules with S-state atoms in a magnetic trap

We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with (1)S(0) atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH(2)(X(3)B(1)) (methylene) and nine other triatomic radicals in cold (3)He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest that it may be possible to create ultracold gases of polyatomic molecules by sympathetic cooling with alkaline-earth atoms in a magnetic trap.

Universal model for exoergic bimolecular reactions and inelastic processes

From a rigorous multichannel quantum-defect formulation of bimolecular processes, we derive a fully quantal and analytic model for the total rate of exoergic bimolecular reactions or inelastic processes that is applicable over a wide range of temperatures including the ultracold regime. The theory establishes a connection between the ultracold chemistry and the regular chemistry by showing that the same theory that gives the quantum threshold behavior agrees with the classical Gorin model at higher temperatures. In between, it predicts that the rates for identical bosonic molecules and distinguishable molecules would first decrease with temperature outside of the Wigner threshold region, before rising after a minimum is reached.

Note: A helical velocity selector for continuous molecular beams

We report on a modern realization of the classic helical velocity selector for gas phase particle beams. The device operates stably under high vacuum conditions at rotational frequencies limited only by commercial dc motor capabilities. Tuning the rotational frequency allows selective scanning over a broad velocity band. The width of the selected velocity distributions at full-width-half-maximum is as narrow as a few percent of the selected mean velocity and independent of the rotational speed of the selector. The selector generates low vibrational noise amplitudes comparable to mechanically damped state-of-the-art turbo-molecular pumps and is therefore compatible with vibration sensitive experiments like molecule interferometry.

Sympathetic cooling of molecular ions in selected rotational and vibrational states produced by threshold photoionization

We present a new method for the generation of rotationally and vibrationally state-selected, translationally cold molecular ions in ion traps. Our technique is based on the state-selective threshold photoionization of neutral molecules followed by sympathetic cooling of the resulting ions with laser-cooled calcium ions. Using N₂(+) ions as a test system, we achieve >90% selectivity in the preparation of the ground rovibrational level and state lifetimes on the order of 15 minutes limited by collisions with background-gas molecules. The technique can be employed to produce a wide range of apolar and polar molecular ions in the ground and excited rovibrational states. Our approach opens up new perspectives for cold quantum-controlled ion-molecule-collision studies, frequency-metrology experiments with state-selected molecular ions and molecular-ion qubits.

Atom-dimer scattering in a three-component Fermi gas

Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12+|3→|23+|1. Such a suppression is caused by interference between different decay paths and demonstrates the possibility of using Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.