This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole-dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime. We discuss in detail the recent experimental progress in realizing and studying strongly interacting systems of polar molecules trapped in optical lattices, with particular emphasis on the study of interacting spin systems and non-equilibrium quantum magnetism. Finally, we conclude with a brief discussion of the future prospects for studies of strongly interacting dipolar molecules.
We report the creation of ultracold bosonic dipolar $^{23}\textrm{Na}^{39}\textrm{K}$ molecules in their absolute rovibrational ground state. Starting from weakly bound molecules immersed in an ultracold atomic mixture, we coherently transfer the dimers to the rovibrational ground state using an adiabatic Raman passage. We analyze the two-body decay in a pure molecular sample and in molecule-atom mixtures and find an unexpectedly low two-body decay coefficient for collisions between molecules and $^{39}\textrm{K}$ atoms in a selected hyperfine state. The preparation of bosonic $^{23}\textrm{Na…
The quantum mechanical few-body problem at ultracold energies poses severe challenges to theoretical techniques, particularly when long-range interactions are present that decay only as a power-law potential. In this paper we review the techniques and progress in studies of universal few-body physics for ultracold atoms, particularly those related to long-range interactions.
Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we use microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probe collisions in three dimensions. The correct combination of microwave frequency and power creates an effective repulsive shield, which suppresses the inelastic loss rate by a factor of six, in agreement with theoretical calculations. The demonstrated mic…
We describe the formation of fermionic NaLi Feshbach molecules from an ultracold mixture of bosonic 23Na and fermionic 6Li. Precise magnetic field sweeps across a narrow Feshbach resonance at 745 G result in a molecule conversion fraction of 5% for our experimental densities and temperatures, corresponding to a molecule number of 5*10^4. The observed molecular decay ifetime is 1.3 ms after removing free Li and Na atoms from the trap.
We report the creation of ultracold bosonic $^{23}$Na$^{87}$Rb Feshbach molecules via magneto-association. By ramping the magnetic field across an interspecies Feshbach resonance, at least 4000 molecules can be produced out of the near degenerate ultracold mixture. Fast loss due to inelastic atom-molecule collisions is observed, which limits the pure molecule number, after residual atoms removal, to 1700. The pure molecule sample can live for 21.8(8) ms in the optical trap, long enough for future molecular spectroscopy studies toward coherently transferring to the singlet ro-vibrational ground…
We report the observation of a dimer-dimer inelastic collision resonance for ultracold Feshbach molecules made of bosonic sodium and rubidium atoms. This resonance, which we attribute to the crossing of the dimer-dimer threshold with a heteronuclear tetramer state, manifests itself as a pronounced inelastic loss peak of dimers when the interspecies scattering length between the constituent atoms is tuned. Near this resonance, a strong modification of the temperature dependence of the dimer-dimer scattering is observed. Our result provides insight into the heteronuclear four-body system consist…
We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between $^2Σ$ CaF molecules in the absolute ground state $|X,v=0, N=0,F=0\rangle$, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of $7(4) \times 10^{-11} \text{cm}^{3}/\text{s}$, which is below, but close to the predicted universal loss rate.
Understanding ultracold collisions involving molecules is of fundamental importance for current experiments, where inelastic collisions typically limit the lifetime of molecular ensembles in optical traps. Here we present a broad study of optically trapped ultracold RbCs molecules in collisions with one another, in reactive collisions with Rb atoms, and in nonreactive collisions with Cs atoms. For experiments with RbCs alone, we show that by modulating the intensity of the optical trap, such that the molecules spend 75% of each modulation cycle in the dark, we partially suppress collisional lo…
In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two dimensional geometry can be reduced by usi…
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…
We report on the formation of ultracold fermionic Feshbach molecules of $^{23}$Na$^{40}$K, the first fermionic molecule that is chemically stable in its ground state. The lifetime of the nearly degenerate molecular gas exceeds 100 ms in the vicinity of the Feshbach resonance. The measured dependence of the molecular binding energy on the magnetic field demonstrates the open-channel character of the molecules over a wide field range and implies significant singlet admixture. This will enable efficient transfer into the singlet vibrational ground state, resulting in a stable molecular Fermi gas …
We present investigations of the formation rate and collisional stability of lithium Feshbach molecules in an ultracold three-component mixture composed of two resonantly interacting fermionic 6-Li spin states and bosonic 174-Yb. We observe long molecule lifetimes (> 100 ms) even in the presence of a large ytterbium bath and extract reaction rate coefficients of the system. We find good collisional stability of the mixture in the unitary regime, opening new possibilities for studies and probes of strongly interacting quantum gases in contact with a bath species.
We report the full control over the internal states of ultracold $^{23}$Na$^{87}$Rb molecules, including vibrational, rotational and hyperfine degrees of freedom. Starting from a sample of weakly bound Feshbach molecules, we realize the creation of molecules in single hyperfine levels of both the rovibrational ground and excited states with a high-efficiency and high-resolution stimulated Raman adiabatic passage. Starting from the rovibrational and hyperfine ground state, we demonstrate rotational and hyperfine control with one- and two-photon microwave spectroscopy. This achievement of fully …
We report the successful production of an ultracold sample of absolute ground-state $^{23}$Na$^{87}$Rb molecules. Starting from weakly-bound Feshbach molecules formed via magneto-association, the lowest rovibrational and hyperfine level of the electronic ground state is populated following a high efficiency and high resolution two-photon Raman process. The high purity absolute ground-state samples have up to 8000 molecules and densities of over $10^{11}$ cm$^{-3}$. By measuring the Stark shifts induced by external electric fields, we determined the permanent electric dipole moment of the absol…
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.
Measuring the statistical correlations of individual quantum objects provides an excellent way to study complex quantum systems. Ultracold molecules represent a powerful platform for quantum science due to their rich and controllable internal degrees of freedom. However, the detection of correlations between single molecules in an ultracold gas has yet to be demonstrated. Here we observe the Hanbury Brown and Twiss effect in a gas of bosonic $^{23}$Na$^{87}$Rb, enabled by the realization of a quantum gas microscope for molecules. We detect the characteristic bunching correlations in the densit…
We show that radiofrequency (RF) radiation may be used to create Feshbach resonances in ultracold gases of alkali-metal atoms at desired magnetic fields that are convenient for atomic cooling and degeneracy. For the case of $^{39}$K+$^{133}$Cs, where there are no RF-free resonances in regions where Cs may be cooled to degeneracy, we show that a resonance may be created near 21~G with 69.2~MHz RF radiation. This resonance is almost lossless with circularly polarized RF, and the molecules created are long-lived even with plane-polarized RF.
We report measurements of the ac polarizabilities of ultracold ground-state $^{23}\rm{Na}^{87}\rm{Rb}$ molecules. While the polarizability of the ground rotational state $J = 0$ is isotropic, that of the first excited rotational state $J = 1$ is anisotropic and depends strongly on the light polarization angle. We obtain both polarizabilities precisely by combining trap oscillation frequency measurement and high resolution rotational spectroscopy driven by microwave. With the optimized light polarization angle and intensity combination, the nonuniformity of the differential ac Stark shift betwe…
We report on the creation of ultracold 84Sr2 molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain 4x10^4 molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow 1S0-3P1 intercombination transition, using a vibrational level of the 0u potential as intermediate state. In preparation of our molecule association scheme, we have determined the binding energies of the last vibrational l…
We investigate the effect of far-off-resonant trapping light on ultracold bosonic RbCs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating …
The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.
For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum…
Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1) seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of $T_2^* = 3.3(6)$~s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor…
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…
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 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.
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 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 the production of ultracold 7Li85Rb molecules by photoassociation (PA) below the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We perform PA spectroscopy in a dual-species 7Li-85Rb magneto-optical trap (MOT) and detect the PA resonances using trap loss spectroscopy. We observe several strong PA resonances corresponding to the last few bound states, assign the lines and derive the long range C6 dispersion coefficients for the Li (2s 2S1/2) + Rb (5p 2P1/2) asymptote. We also report an excited-state molecule formation rate (P_LiRb) of ~10^7 s^-1 and a PA rate coefficient (K_PA) of ~4x10^-11 …
We report the production of ultracold heteronuclear 7Li85Rb molecules in excited electronic states by photoassociation (PA) of ultracold 7Li and 85Rb atoms. PA is performed in a dual-species 7Li-85Rb magneto-optical trap (MOT) and the PA resonances are detected using trap loss spectroscopy. We identify several strong PA resonances below the Li (2s 2S1/2) + Rb (5p 2P3/2) asymptote and experimentally determine the long range C6 dispersion coefficients. We find a molecule formation rate (P_LiRb) of 3.5x10^7 s^-1 and a PA rate coefficient (K_PA) of 1.3x10^-10 cm^3/s, the highest among heteronuclea…
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 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…
We study the dissociation of Feshbach molecules in ultracold Fermi gases with spin-orbit (SO) coupling. Since SO coupling can induce quantum transition between the Feshbach molecules and the fully polarized Fermi gas, the Feshbach molecules can be dissociated by the SO coupling. We experimentally realized this new type of dissociation in ultracold gases of 40K atoms with SO coupling created by Raman beams, and observed that the dissociation rate is highly non-monotonic on both the positive and negative Raman-detuning sides. Our results show that the dissociation of Feshbach molecules can be co…
In this review, we discuss the impact of the development of lasers on ultracold atoms and molecules and their applications. After a brief historical review of laser cooling and Bose-Einstein condensation, we present important applications of ultra cold atoms, including time and frequency metrology, atom interferometry and inertial sensors, atom lasers, simulation of condensed matter systems, production and study of strongly correlated systems, and production of ultracold molecules.
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…
