Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, as they can be experimentally studied with unprecedented control, yet display dynamics that are highly complex. Here, we report the full product state distribution for the reaction 2KRb $\rightarrow$ K$_2$ + Rb$_2$. Ultracold preparation of the reactants grants complete control over their initial quantum degrees of freedom, while state-resolved, coincident detection of both products enables the measurement of scattering probabilities into all 57 allowed rotational state-pairs. Our results show an overall agreement with a state-counting model based on statistical theory, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit, which we precisely determine to be $9.7711^{+0.0007}_{-0.0005}$ cm$^{-1}$, as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a valuable benchmark for quantum dynamics calculations beyond the current state-of-the-art.
Ultracold ground-state molecules can be formed from ultracold atoms via photoassociation followed by a spontaneous emission process. Typically, the molecular products are distributed over a range of final states. Here, we propose to use an optical cavity with high cooperativity to selectively enhance the population of a pre-determined final state by controlling the spontaneous emission. During this process, a photon will be emitted into the cavity mode. Detection of this photon heralds a single reaction. We discuss the efficiency and the dynamics of cavity-assisted molecule formation in the fr…
We study the reaction kinetics of chemical processes occurring in the ultracold regime and systematically investigate their dynamics. Quantum entanglement is found to play a key role in driving an ultracold reaction towards a dynamical equilibrium. In case of multiple concurrent reactions Hamiltonian chaos dominates the phase space dynamics in the mean field approximation.
Advances in atomic, molecular, and optical (AMO) physics techniques allowed the cooling of simple molecules down to the ultracold regime ($\lesssim$ 1 mK), and opened the opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Fur…
Rapid progress in atomic, molecular, and optical (AMO) physics techniques enabled the creation of ultracold samples of molecular species and opened opportunities to explore chemistry in the ultralow temperature regime. In particular, both the external and internal quantum degrees of freedom of the reactant atoms and molecules are controlled, allowing studies that explored the role of the long range potential in ultracold reactions. The kinetics of these reactions have typically been determined using the loss of reactants as proxies. To extend such studies into the short-range, we developed an …
Impurity physics is a traditional topic in condensed matter physics that nowadays is being explored in the field of ultracold gases. Among the different classes of impurities, we focus on charged impurities in an ultracold bath. When a single ion is brought in contact with an ultracold gas it is subjected to different reactive processes that can be understood from a cold chemistry approach. In this work, we present an outlook of approaches for the dynamics of a single ion in a bath of ultracold atoms or molecules, complementing the usual many-body approaches characteristic of impurity physics …
Photoassociation of ultracold atoms is shown to lead to alignment of the product molecules along the excitation laser polarization axis. We theoretically investigate pulsed photoassociation of $^{87}Rb$ atoms into a specific weakly-bound level of the a $^3Σ_u^+$ metastable electronic state and find both stationary and time-dependent field-free alignment. Although a transform-limited pulse yields significant alignment, a frequency-chirped pulse dramatically enhances the molecular formation rate at the cost of a slight decrease in the alignment. Employing multiple pulses synchronized with the vi…
We propose a new method for the production of ultracold molecular ions. This method utilizes sympathetic cooling due to the strong collisions between appropriately chosen molecular ions and laser-cooled neutral atoms to realize ultracold, internal ground-state molecular ions. In contrast to other experiments producing cold molecular ions, our proposed method efficiently cools both the internal and external molecular ion degrees of freedom. The availability of an ultracold, absolute ground-state sample of molecular ions would have broad impact to fields as diverse as quantum chemistry, astrophy…
This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. …
We demonstrate the occurrence of oscillatory reactions in the ultra-cold chemistry of atom-molecular Bose-Einstein condensate. Nonlinear oscillations in the mean-field dynamics occur for a specific range of elliptic modulus, giving rise to both in- and out-phase modulations in the atom-molecule population density. The reaction front velocity is found to be controlled by photoassociation, which also regulates the condensate density. Two distinct pair of in-phase bright localized gap solitons are found as exact solutions, existence of one of which necessarily requires a background. Cnoidal atomi…
The study of ultracold molecules tightly trapped in an optical lattice can expand the frontier of precision measurement and spectroscopy, and provide a deeper insight into molecular and fundamental physics. Here we create, probe, and image microkelvin $^{88}$Sr$_2$ molecules in a lattice, and demonstrate precise measurements of molecular parameters as well as coherent control of molecular quantum states using optical fields. We discuss the sensitivity of the system to dimensional effects, a new bound-to-continuum spectroscopy technique for highly accurate binding energy measurements, and prosp…
We report results for reaction and vibrational quenching of the collision D with para-H$_2$($v,j=0$) and ortho-H$_2$($v,j=1$) at cold and ultracold temperatures. We investigate the effect of nuclear spin symmetry for barrier dominated processes ($0\le v\le 4$) and for one barrierless case ($v=5$). We find resonant structures for energies in the range corresponding to 0.01--10 K, which depend on the nuclear spin of H$_2$, arising from contributions of specific partial waves. We discuss the implications on the results in this benchmark system for ultracold chemistry.
A first principles study of the dynamics of $^6$Li($^{2}$S) + $^6$Li$^{174}$Yb($^2Σ^+$)$ \to ^6$Li$_2(^1Σ^+$) + $^{174}$Yb($^1$S) reaction is presented at cold and ultracold temperatures. The computations involve determination and analytic fitting of a three-dimensional potential energy surface for the Li$_2$Yb system and quantum dynamics calculations of varying complexities, ranging from exact quantum dynamics within the close-coupling scheme, to statistical quantum treatment, and universal models. It is demonstrated that the two simplified methods yield zero-temperature limiting reaction rat…
Photodissociation of a molecule produces a spatial distribution of photofragments determined by the molecular structure and the characteristics of the dissociating light. Performing this basic chemical reaction at ultracold temperatures allows its quantum mechanical features to dominate. In this regime, weak applied fields can be used to control the reaction. Here, we photodissociate ultracold diatomic strontium in magnetic fields below 10 G and observe striking changes in photofragment angular distributions. The observations are in excellent qualitative agreement with a multichannel quantum c…
We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\to$ HD+H collisions with rovibrational quantum state resolution of the…
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 and/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 dis…
The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss the first generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by: (1) modifying the product energy levels thus potentially reshaping the product distributions; and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strengt…
We present development of a genetic algorithm for fitting potential energy curves of diatomic molecules to experimental data. Our approach does not involve any functional form for fitting, which makes it a general fitting procedure. In particular, it takes in a guess potential, perhaps from an $ab \ initio$ calculation, along with experimental measurements of vibrational binding energies, rotational constants, and their experimental uncertainties. The fitting procedure is able to modify the guess potential until it converges to better than 1% uncertainty, as measured by $\barχ^2$. We present t…
While attaining external field control of bimolecular chemical reactions has long been a coveted goal of physics and chemistry, the role of hyperfine interactions and dc magnetic fields in achieving such control has remained elusive. We develop an extended coupled-channel statistical theory of barrierless atom-diatom chemical reactions, and apply it to elucidate the effects of magnetic fields and hyperfine interactions on the ultracold chemical reaction Li($^2\text{S}_{1/2}$) + CaH($^2Σ^+$) $\to$ LiH($^1Σ^+$) + Ca($^1\text{S}_{0}$) on a newly developed set of ab initio potential energy surface…
A versatile apparatus for simultaneous trapping of multiple species of ultracold atoms and ions to enable studies of low energy collisions and cold chemistry
Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond-rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extensio…
Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to trea…
Chemistry in the ultracold regime enables fully quantum-controlled interactions between atoms and molecules, leading to the discovery of the hidden mechanisms in chemical reactions which are usually curtained by thermal averaging in the high temperature. Recently a couple of diatomic molecules have been cooled to ultracold regime based on laser cooling techniques, but the chemistry associated with these simple molecules is highly limited. In comparison, free radicals play a major role in many important chemical reactions, but yet to be cooled to submillikelvin temperature. Here we propose a no…
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 re…
Electronically non-adiabatic effects play an important role in many chemical reactions. How these effects manifest in cold and ultracold chemistry remain largely unexplored. Here, through first principles non-adiabatic quantum dynamics calculations of the Li + LiNa $\to$ Li$_2$ + Na chemical reaction, it is shown that non-adiabatic dynamics induces quantum interference effects that dramatically alter the ultracold rotationally resolved reaction rate coefficients. The interference effect arises from a conical intersection between the ground and an excited electronic state that is energetically …
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 fo…
The present paper is related to a talk presented during the Symposium on Coherent Control and Ultracold Chemistry held during the Sixth Congress of the International Society for Theoretical Chemical Physics (ISTCP-VI, July 2008). The talk was entitled "Electronic structure properties of alkali dimers and trimers. Prospects for alignment of ultracold molecules". Here we report on the electrostatic repulsion forces of the ionic cores at short separation, involved when the potential energy surfaces of alkali trimers are calculated with a quantum chemistry approach based on effective large-core po…
With the creation of ultracold atoms and molecules, a new type of chemistry - "resonance" chemistry - emerges: chemical reactions can occur when the energy of colliding atoms and molecules matches a bound state of the combined molecule (Feshbach resonance). This chemistry is rather similar to reactions that take place in nuclei at low energies. In this paper we suggest some problems for future experimental and theoretical work related to the resonance chemistry of ultracold molecules. Molecular Bose-Einstein condensates are particularly interesting because in this system collisions and chemica…
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable $^{23}$Na$^{40}$K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, $J{=}1$, we observe collisional lifetimes of more than $3\, \rm s$, comparable to those in the rovibrational ground state…
This article reviews the current state of the art in the field of cold and ultracold molecules and demonstrates that chemical reactions, inelastic collisions and dissociation of molecules at subKelvin temperatures can be manipulated with external electric or magnetic fields. The creation of ultracold molecules may allow for spectroscopy measurements with extremely high precision and tests of fundamental symmetries of nature, quantum computation with molecules as qubits, and controlled chemistry. The probability of chemical reactions and collisional energy transfer can be very large at temperat…
We present numerical results for rate coefficients of reaction and vibrational quenching in the collision of H with D$_2(v,j)$ at cold and ultracold temperatures. We explore both ortho-D$_2(j\!=\!0)$ and para-D$_2(j\!=\!1)$ for several initial vibrational states $(v\leq 5)$, and find resonant structures in the energy range 0.01--10 kelvin, which are sensitive to the initial rovibrational state $(v,j)$. We compare the reaction rates for D$_2$+H with our previously obtained results for the isotopologue reaction H$_2$+D, and discuss the implications of our detailed study of this benchmark system …
We perform a systematic investigation of the electronic properties of the $^2Σ^+$ ground state of Li-alkaline-earth dimers. These molecules are proposed as possible candidates for quantum simulation of lattice-spin models. We apply powerful quantum chemistry coupled-cluster methods with large basis sets to calculate potential energies, permanent dipole moment, and electron density distributions for LiBe, LiMg, LiCa, LiSr, and LiYb. Our results reveal a surprising irregularity in the dissociation energy and bond length with an increase in the reduced mass of the molecule. At the same time the p…
In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem - that based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose-Einstein Condensates form angulons, and therefore can be described …
There is substantial interest in producing samples of ultracold molecules for possible applications in quantum computation, quantum simulation of condensed matter systems, precision measurements, controlled chemistry, and high precision spectroscopy. A crucial step to obtaining large samples of ultracold, trapped molecules is developing a means to bridge the gap between typical molecular source velocities (~150-600 m/s) and velocities for which trap loading or confinement is possible (~5-20 m/s). Here we show deceleration of a beam of neutral strontium monofluoride (SrF) molecules using radiat…
Controlling the pathways and outcomes of reactions is a broadly pursued goal in chemistry. In gas phase reactions, this is typically achieved by manipulating the properties of the reactants, including their translational energy, orientation, and internal quantum state. In contrast, here we influence the pathway of a reaction via its intermediate complex, which is generally too short-lived to be affected by external processes. In particular, the ultracold preparation of potassium-rubidium (KRb) reactants leads to a long-lived intermediate complex (K$_2$Rb$_2^*$), which allows us to steer the re…
Chemical reactions at ultracold temperature provide an ideal platform to study chemical reactivity at the fundamental level, and to understand how chemical reactions are governed by quantum mechanics. Recent years have witnessed the remarkable progress in studying ultracold chemistry with ultracold molecules. However, these works were limited to exothermic reactions. The direct observation of state-to-state ultracold endothermic reaction remains elusive. Here we report on the investigation of endothermic and nearly thermoneutral atom-exchange reactions in an ultracold atom-dimer mixture. By de…
Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, who…
Interactions between cold ions and atoms have been proposed for use in implementing quantum gates\cite{Idziaszek2007}, probing quantum gases\cite{Sherkunov2009}, observing novel charge-transport dynamics\cite{Cote2000}, and sympathetically cooling atomic and molecular systems which cannot be laser cooled\cite{Smith2005,Hudson2009}. Furthermore, the chemistry between cold ions and atoms is foundational to issues in modern astrophysics, including the formation of stars, planets, and interstellar clouds\cite{Smith1992}, the diffuse interstellar bands\cite{Reddy2010}, and the post-recombination ep…
Coherence, the stability of the relative phase between quantum states, lies at the heart of quantum mechanics. Applications such as precision measurement, interferometry, and quantum computation are enabled by physical systems that have quantum states with robust coherence. With the creation of molecular ensembles at sub-$μ$K temperatures, diatomic molecules have become a novel system under full quantum control. Here, we report on the observation of stable coherence between a pair of nuclear spin states of ultracold fermionic NaK molecules in the singlet rovibrational ground state. Employing m…
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…
The development of the magneto-optical trap revolutionized the fields of atomic and quantum physics by providing a simple method for the rapid production of ultracold, trapped atoms. A similar technique for producing a diverse set of dense, ultracold diatomic molecular species will likewise transform the study of strongly interacting quantum systems, precision measurement, and physical chemistry. We demonstrate one- and two-dimensional transverse laser cooling and magneto-optical trapping of the polar molecule yttrium (II) oxide (YO). Using a quasicycling optical transition we observe transver…
The goal of the present article is to review the major developments that have led to the current understanding of molecule-field interactions and experimental methods for manipulating molecules with electromagnetic fields. Molecule-field interactions are at the core of several, seemingly distinct, areas of molecular physics. This is reflected in the organization of this article, which includes sections on Field control of molecular beams, External field traps for cold molecules, Control of molecular orientation and molecular alignment, Manipulation of molecules by non-conservative forces, Ultr…
Automatic Differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that automatic differentiation can be used to compute gradients with respect to any parameter through…
