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, the electric field dependence of the collision rates follows automatically. We present examples for reactive species such as KRb, and non-reactive species, such as RbCs.
We present and analyze a toolbox for the controlled manipulation of ultracold polar molecules, consisting of detection of molecules, atom-molecule entanglement, and engineering of dissipative dynamics. Our setup is based on fast chemical reactions between molecules and atoms leading to a quantum Zeno-based collisional blockade in the system. We demonstrate that the experimental parameters for achieving high fidelities can be found using a straightforward numerical optimization. We exemplify our approach for a system comprised of NaK molecules and Na atoms and we discuss the consequences of res…
The creation of ultracold molecules is currently limited to diatomic species. In this letter we present a theoretical description of the photoassociation of ultracold atoms and molecules to create ultracold excited triatomic molecules, thus being a novel example of light-assisted ultracold chemical reaction. The calculation of the photoassociation rate of ultracold Cs atoms with ultracold Cs$_2$ molecules in their rovibrational ground state is reported, based on the solution of the quantum dynamics involving the atom-molecule long-range interactions, and assuming a model potential for the shor…
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.
Heteronuclear alkali-metal dimers represent the class of molecules of choice for creating samples of ultracold molecules exhibiting an intrinsic large permanent electric dipole moment. Among them, the KCs molecule, with a permanent dipole moment of 1.92~Debye still remains to be observed in ultracold conditions. Based on spectroscopic studies available in the literature completed by accurate quantum chemistry calculations, we propose several optical coherent schemes to create ultracold bosonic and fermionic KCs molecules in their absolute rovibrational ground level, starting from a weakly boun…
We explore the feasibility of optically forming long-range tetratomic and larger polyatomic molecules in their ground electronic state from ultracold pairs of polar molecules aligned by external fields. Depending on the relative orientation of the interacting diatomic molecules, we find that a tetratomic can be formed either as a weakly bound complex in a very extended halo state or as a pure long-range molecule composed of collinear or nearly-collinear diatomic molecules. The latter is a novel type of tetratomic molecule comprised of two diatomic molecules bound at long intermolecular range a…
Progress on researches in the field of molecules at cold and ultracold temperatures is reported in this review. It covers extensively the experimental methods to produce, detect and characterize cold and ultracold molecules including association of ultracold atoms, deceleration by external fields and kinematic cooling. Confinement of molecules in different kinds of traps is also discussed. The basic theoretical issues related to the knowledge of the molecular structure, the atom-molecule and molecule-molecule mutual interactions, and to their possible manipulation and control with external fie…
We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N=0 and N=2 rotational levels, is engineered which exploits the unique Rydberg electron-molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck-Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.
We investigate the use of microwave radiation to produce a repulsive shield between pairs of ultracold polar molecules and prevent collisional losses that occur when molecular pairs reach short range. We carry out coupled-channels calculations on RbCs+RbCs and CaF+CaF collisions in microwave fields. We show that effective shielding requires predominantly circular polarization, but can still be achieved with elliptical polarization that is around 90% circular.
We produce ultracold dense trapped samples of 87Rb133Cs molecules in their rovibrational ground state, with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with efficiencies of 90%. We observe the onset of hyperfine-changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift of the transition frequencies as a function of applied electric field shows the strongly dipolar character of the RbCs ground-state molecule. Our results open up the prospect of realizing stable bosoni…
Photoassociation (PA) is a powerful technique to synthesize molecules directly and continuously from cold and ultracold atoms into deeply bound molecular states. In freespace, however, PA efficiency is constrained by the number of spontaneous decay channels linking the initial excited molecular state to a sea of final (meta)stable rovibronic levels. Here, we propose a novel scheme based on molecules strongly coupled to a guided photonic mode in a photonic crystal waveguide that turns PA into a powerful tool for near deterministic formation of ultracold molecules in their ground rovibrational l…
We present a rigorous study of vibrational relaxation in p-H2 + p-H2 collisions at cold and ultracold temperatures and identify an efficient mechanism of ro-vibrational energy transfer. If the colliding molecules are in different rotational and vibrational levels, the internal energy may be transferred between the molecules through an extremely state-selective process involving simultaneous conservation of internal energy and total rotational angular momentum. The same transition in collisions of distinguishable molecules corresponds to the rotational energy transfer from one vibrational state…
We present an architecture for the quantum simulation of many-body spin interactions based on ultracold polar molecules trapped in optical lattices. Our approach employs digital quantum simulation, i.e., the dynamics of the simulated system is reproduced by the quantum simulator in a stroboscopic pattern, and allows to simulate both coherent and dissipative dynamics. We discuss the realization of Kitaev's toric code Hamiltonian, a paradigmatic model involving four-body interactions, and we analyze the requirements for an experimental implementation.
We have produced ultracold heteronuclear YbRb$^*$ molecules in a combined magneto-optical trap by photoassociation. The formation of electronically excited molecules close to the dissociation limit was observed by trap loss spectroscopy in mixtures of $^{87}$Rb with $^{174}$Yb and $^{176}$Yb. The molecules could be prepared in a series of vibrational levels with resolved rotational structure, allowing for an experimental determination of the long-range potential in the electronically excited state.
Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.
We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22,000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of $1.0(4) \times 10^{12}$ cm$^{-3}$. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D. Dipolar systems of NaCs molecu…
We investigate the presence of Feshbach resonances in ultracold alkali-dialkali reactive collisions. Quantum scattering calculations are performed on a new Na_3 quartet potential energy surface. An analysis of scattering features is performed through a systematic variation of the nonadditive three-body interaction potential. Our results should provide useful information for interpreting future atom-molecule collision experiments.
We show that the excitation of long-range Rydberg molecules in a three-dimensional optical lattice can be used as a position- and time-sensitive probe of the site occupancy in the system. To this end, we detect the ions which are continuously generated by the decay of the formed Rydberg molecules. While a superfluid gas shows molecule formation for all parameters, a Mott insulator with $n=1$ filling reveals a strong suppression of the number of formed molecules. In the limit of weak probing, the technique can be used to probe the superfluid to Mott-insulator transition in real-time. Our method…
We report here on the production of an ultracold gas of tightly bound Rb2 molecules in the ro-vibrational triplet ground state, close to quantum degeneracy. This is achieved by optically transferring weakly bound Rb2 molecules to the absolute lowest level of the ground triplet potential with a transfer efficiency of about 90%. The transfer takes place in a 3D optical lattice which traps a sizeable fraction of the tightly bound molecules with a lifetime exceeding 200 ms.
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. …
By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac-field is increased, the long-range well becomes deeper and can support a certain numbers of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescale…
We create fermionic dipolar $^{23}$Na$^6$Li molecules in their triplet ground state from an ultracold mixture of $^{23}$Na and $^6$Li. Using magneto-association across a narrow Feshbach resonance followed by a two-photon STIRAP transfer to the triplet ground state, we produce $3\,{\times}\,10^4$ ground state molecules in a spin-polarized state. We observe a lifetime of $4.6\,\text{s}$ in an isolated molecular sample, approaching the $p$-wave universal rate limit. Electron spin resonance spectroscopy of the triplet state was used to determine the hyperfine structure of this previously unobserve…
We theoretically explore photoassociation by Adiabatic Passage of two colliding cold ^{85}Rb atoms in an atomic trap to form an ultracold Rb_2 molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of ~2*10^7 pulses of moderate intensities, each lasting ~750 ns, can photoassociate a large fraction of the atomic ensemble at t…
We demonstrate coherent control of both the rotational and hyperfine state of ultracold, chemically stable $^{87}$Rb$^{133}$Cs molecules with external microwave fields. We create a sample of ~2000 molecules in the lowest hyperfine level of the rovibronic ground state N = 0. We measure the transition frequencies to 8 different hyperfine levels of the N = 1 state at two magnetic fields ~23 G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population tr…
Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the tw…
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topo…
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…
Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a n…
Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, {\it i.e.} in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhance molecular formation rates by several orders of magnitude. We illustrate this effect in heteronuclear systems, and find giant rate coefficients even in deeply bound levels. We also give a simple analytical expression for the photoassociation rates, and discuss future applications of the Feshbach Opti…
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…
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…
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…
In recent experiments on ultracold matter, molecules have been produced from ultracold atoms by photoassociation, Feshbach resonances, and three-body recombination. The created molecules are translationally cold, but vibrationally highly excited. This will eventually lead them to be lost from the trap due to collisions. We propose shaped laser pulses to transfer these highly excited molecules to their ground vibrational level. Optimal control theory is employed to find the light field that will carry out this task with minimum intensity. We present results for the sodium dimer. The final targe…
We have produced large samples of ultracold $^{88}$Sr$_2$ molecules in the electronic ground state in an optical lattice. The molecules are bound by 0.05 cm$^{-1}$ and are stable for several milliseconds. The fast, all-optical method of molecule creation via intercombination line photoassociation relies on a near-unity Franck-Condon factor. The detection uses a weakly bound vibrational level corresponding to a very large dimer. This is the first of two steps needed to create Sr$_2$ in the absolute ground quantum state. Lattice-trapped Sr$_2$ is of interest to frequency metrology and ultracold …
In this Chapter, we give an introduction into experiments with Feshbach molecules and their applications. In particular, we discuss the various creation and detection methods, and the internal-state manipulation of such molecules. We highlight two topics, namely Feshbach molecules in the halo regime and the application of Feshbach molecule to achieve ultracold gases of molecules in the rovibrational ground state. Our illustrative examples are mainly based on work performed at Innsbruck University.
We report on two-photon photoassociation (PA) spectroscopy of ultracold heteronuclear LiRb molecules. This is used to determine the binding energies of the loosely bound levels of the electronic ground singlet and the lowest triplet states of LiRb. We observe strong two-photon PA lines with power broadened line widths greater than 20 GHz at relatively low laser intensity of 30 W/cm$^{2}$. The implication of this observation on direct atom to molecule conversion using stimulated Raman adiabatic passage (STIRAP) is discussed and the prospect for electronic ground state molecule production is the…
We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields, taking account of the hyperfine structure due to the nuclear spins. We consider the molecules 41K87Rb and 7Li133Cs, which are the targets of current experiments and demonstrate two extremes of large and small nuclear quadrupole coupling. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine …
We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of non-degenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states ex…
Ultracold LiCs molecules in the absolute ground state X$^1Σ^+$, v"=0, J"=0 are formed via a single photo-association step starting from laser-cooled atoms. The selective production of v"=0, J"=2 molecules with a 50-fold higher rate is also demonstrated. The rotational and vibrational state of the ground state molecules is determined in a setup combining depletion spectroscopy with resonant-enhanced multi-photon ionization time-of-flight spectroscopy. Using the determined production rate of up to 5x10^3 molecules/s, we describe a simple scheme which can provide large samples of externally and i…
Trapping ultracold molecules in conservative traps is essential for applications -- such as quantum state-controlled chemistry, quantum simulations, and quantum information processing. These applications require high densities or phase-space densities. We report magnetic trapping of NaLi molecules in the triplet ground state at high density ($\approx 10^{11} \; \rm{cm}^{-3}$) and ultralow temperature ($\approx 1\;{\rm μK}$). Magnetic trapping at these densities allows studies on both atom-molecule and molecule-molecule collisions in the ultracold regime in the absence of trapping light, which …
Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr$_2$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr$_2$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr \cite{Zelevinsky2008}. Th…
We demonstrated that final states of ultracold scattering between atom and molecule can be selectively produced using dynamic magnetic fields of multiple frequencies. The mechanism of the dynamic magnetic field control is based on a generalized quantum Zeno effect for the selected scattering channels. In particular, we use an atom-molecule spin flip scattering to show that the transition to the selected final spin projection of the molecule in the inelastic scattering can be suppressed by dynamic modulation of coupling between the Floquet engineered initial and final states.
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance a…
We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10-14 cm3 s-1. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)], and do not require cancelation of the long-range dipole-dipole interaction that is vital to many app…
We theoretically study non-destructive detection of ultracold molecules, using a Fabry-Perot cavity. Specifically, we consider vacuum Rabi splitting where we demonstrate the use of collective strong coupling for detection of molecules with many participating energy levels. We also consider electromagnetically induced transparency and transient response of light for the molecules interacting with a Fabry-Perot cavity mode, as a mean for non-destructive detection. We identify the parameters that are required for the detection of molecules in the cavity electromagnetically induced transparency co…
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite $f$-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art \textit{ab initio} model.
We propose a process to convert ultracold metastable Cs$_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}Σ_{u}^{+} \sim b ^{3}Π_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs$_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay ba…
We propose a new approach to excite ion-pair states of ultracold dimers. The central idea is a two-step process where first long-range Rydberg molecules are formed by photoassociation, which are then driven by stimulated emission towards the ion-pair state, a process bearing features of a photo-induced harpooning reaction. We assess the feasibility of this approach through a detailed experimental and theoretical study on a specific system, p-wave-scattering dominated long-range Rydberg molecules in caesium, and discuss potential applications for the study of strongly correlated plasmas consist…
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 study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in t…
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 efficient all-optical creation of an ultracold gas of alkaline-earth-metal dimers, $^{88}\rm{Sr}_2$, in their absolute ground state. Starting with weakly bound singlet molecules formed by narrow-line photoassociation in an optical lattice, followed by stimulated Raman adiabatic passage (STIRAP) via a singlet-dominant channel in the $(1)0_u^+$ excited potential, we prepare pure samples of more than 5500 molecules in $X^1Σ_g^+(v=0,J=0)$. We observe two-body collisional loss rates close to the universal limit for both the least bound and most bound vibrational states in $X^1Σ_g^+$. We d…
