Observation of Feshbach-like resonances in collisions between ultracold molecules

Field-linked resonances of polar molecules

Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances¹, which have been extensively studied in various platforms^1-7, are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance^8-10. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances^11-14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium-potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole-dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids¹⁵ and molecular supersolids¹⁶, as well as assembling ultracold polyatomic molecules.

A Feshbach resonance in collisions between triplet ground-state molecules

Collisional resonances are important tools that have been used to modify interactions in ultracold gases, for realizing previously unknown Hamiltonians in quantum simulations¹, for creating molecules from atomic gases² and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions^3-7 and collisions between Feshbach molecules, which are very weakly bound^8-10. Whether such resonances exist for ultracold ground-state molecules has been debated owing to the possibly high density of states and/or rapid decay of the resonant complex^11-15. Here we report a very pronounced and narrow (25 mG) Feshbach resonance in collisions between two triplet ground-state NaLi molecules. This molecular Feshbach resonance has two special characteristics. First, the collisional loss rate is enhanced by more than two orders of magnitude above the background loss rate, which is saturated at the p-wave universal value, owing to strong chemical reactivity. Second, the resonance is located at a magnetic field where two open channels become nearly degenerate. This implies that the intermediate complex predominantly decays to the second open channel. We describe the resonant loss feature using a model with coupled modes that is analogous to a Fabry-Pérot cavity. Our observations provide strong evidence for the existence of long-lived coherent intermediate complexes even in systems without reaction barriers and open up the possibility of coherent control of chemical reactions.

Creation of an ultracold gas of triatomic molecules from an atom–diatomic molecule mixture

In recent years, there has been notable progress in the preparation and control of ultracold gases of diatomic molecules. The next experimental challenge is the production of ultracold polyatomic molecular gases. Here, we report the creation of an ultracold gas of 23 Na 40 K 2 triatomic molecules from a mixture of ground-state sodium-23–potassium-40 ( 23 Na 40 K) molecules and potassium-40 ( 40 K) atoms. The triatomic molecules were created by adiabatic magneto-association through an atom–diatomic molecule Feshbach resonance. We obtained clear evidence for the creation of triatomic molecules by directly detecting them using radio-frequency dissociation. Approximately 4000 triatomic molecules with a high-peak phase-space density of 0.05 could be created. The ultracold triatomic molecules can serve as a launchpad to probe the three-body potential energy surface and may be used to prepare quantum degenerate triatomic molecular gases.

Transition from an atomic to a molecular Bose-Einstein condensate

Molecular quantum gases (that is, ultracold and dense molecular gases) have many potential applications, including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing^1-3. For molecules, to reach the quantum regime usually requires efficient cooling at high densities, which is frequently hindered by fast inelastic collisions that heat and deplete the population of molecules^4,5. Here we report the preparation of two-dimensional Bose-Einstein condensates (BECs) of spinning molecules by inducing pairing interactions in an atomic condensate near a g-wave Feshbach resonance⁶. The trap geometry and the low temperature of the molecules help to reduce inelastic loss, ensuring thermal equilibrium. From the equation-of-state measurement, we determine the molecular scattering length to be + 220(±30) Bohr radii (95% confidence interval). We also investigate the unpairing dynamics in the strong coupling regime and find that near the Feshbach resonance the dynamical timescale is consistent with the unitarity limit. Our work demonstrates the long-sought transition between atomic and molecular condensates, the bosonic analogue of the crossover from a BEC to a Bardeen-Cooper-Schrieffer (BCS) superfluid in a Fermi gas^7-9. In addition, our experiment may shed light on condensed pairs with orbital angular momentum, where a novel anisotropic superfluid with non-zero surface current is predicted^10,11, such as the A phase of ³He.

Inelastic collisions of ultracold triplet Rb2 molecules in the rovibrational ground state

Exploring and controlling inelastic and reactive collisions on the quantum level is a main goal of the developing field of ultracold chemistry. For this, the preparation of precisely defined initial atomic and molecular states in tailored environments is necessary. Here we present experimental studies of inelastic collisions of metastable ultracold Rb₂ molecules in an array of quasi-1D potential tubes. In particular, we investigate collisions of molecules in the absolute lowest triplet energy level where any inelastic process requires a change of the electronic state. Remarkably, we find similar decay rates as for collisions between rotationally or vibrationally excited triplet molecules where other decay paths are also available. The decay rates are close to the ones for universal reactions but vary considerably when confinement and collision energy are changed. This might be exploited to control the collisional properties of molecules.

Investigating the collisional behaviour of molecules on the quantum level is the key in understanding and controlling chemical reactions. Here the authors measure inelastic collision rates for ultracold Rb₂ dimers in precisely defined quantum states and show that the rates can be tuned via external parameters.

Note: High turn density magnetic coils with improved low pressure water cooling for use in atom optics

We describe a magnetic coil design utilizing concentrically wound electro-magnetic insulating (EMI) foil (25.4 μm Kapton backing and 127 μm thick layers). The magnetic coils are easily configurable for different coil sizes, while providing large surfaces for low-pressure (0.12 bar) water cooling. The coils have turn densities of ~5 mm(-1) and achieve a maximum of 377 G at 2.1 kW driving power, measured at a distance 37.9 mm from the axial center of the coil. The coils achieve a steady-state temperature increase of 36.7°C/kW.

Efficient continuous-duty Bitter-type electromagnets for cold atom experiments

We present the design, construction, and characterization of Bitter-type electromagnets which can generate high magnetic fields under continuous operation with efficient heat removal for cold atom experiments. The electromagnets are constructed from a stack of alternating layers consisting of copper arcs and insulating polyester spacers. Efficient cooling of the copper is achieved via parallel rectangular water cooling channels between copper layers with low resistance to flow; a high ratio of the water-cooled surface area to the volume of copper ensures a short length scale (~1 mm) to extract dissipated heat. High copper fraction per layer ensures high magnetic field generated per unit energy dissipated. The ensemble is highly scalable and compressed to create a watertight seal without epoxy. From our measurements, a peak field of 770 G is generated 14 mm away from a single electromagnet with a current of 400 A and a total power dissipation of 1.6 kW. With cooling water flowing at 3.8 l/min, the coil temperature only increases by 7 °C under continuous operation.

Experimental methods of molecular matter-wave optics

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.

Deviation from universality in collisions of ultracold 6Li2 molecules

Collisions of 6Li2 molecules with free 6Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li2 closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance and decay via two-body collisions with Li2, Li, and Na. For Li2 + Li2 and Li2 + Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li2 + Li is exceptionally small, with an upper bound 10 times smaller than the universal prediction. This can be explained by the low density of available decay states in systems of light atoms [G. Quéméner, J.-M. Launay, and P. Honvault, Phys. Rev. A 75, 050701 (2007)], for which such collisions have not been studied before.

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.

One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions

We deal with the three-dimensional Gross-Pitaevskii equation which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation,controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.

Magnetically controlled exchange process in an ultracold atom-dimer mixture

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.

Quantum noise in the collective abstraction reaction A + B2-->AB + B

We demonstrate theoretically that the collective abstraction reaction A + B2-->AB + B can be realized efficiently with degenerate bosonic or fermionic matter waves. We show that this is dominated by quantum fluctuations, which are critical in triggering its initial stages with the appearance of macroscopic nonclassical correlations of the atomic and molecular fields as a result. This study opens up a promising new regime of quantum-degenerate matter-wave chemistry.

Collisions between tunable halo dimers: exploring an elementary four-body process with identical bosons

We study inelastic collisions in a pure, trapped sample of Feshbach molecules made of bosonic cesium atoms in the quantum halo regime. We measure the relaxation rate coefficient for decay to lower-lying molecular states and study the dependence on scattering length and temperature. We identify a pronounced loss minimum with varying scattering length along with a further suppression of loss with decreasing temperature. Our observations provide insight into the physics of a few-body quantum system that consists of four identical bosons at large values of the two-body scattering length.

Modulational instability of a trapped Bose-Einstein condensate with two- and three-body interactions

We investigate analytically and numerically the modulational instability of a Bose-Einstein condensate with both two- and three-body interatomic interactions and trapped in an external parabolic potential. Analytical investigations performed lead us to establish an explicit time-dependent criterion for the modulational instability of the condensate. The effects of the potential as well as of the quintic nonlinear interaction are studied. Direct numerical simulations of the Gross-Pitaevskii equation with two- and three-body interactions describing the dynamics of the condensate agree with the analytical predictions.

Metastable feshbach molecules in high rotational states

We experimentally demonstrate Cs2 Feshbach molecules well above the dissociation threshold, which are stable against spontaneous decay on the time scale of 1 s. An optically trapped sample of ultracold dimers is prepared in a high rotational state and magnetically tuned into a region with a negative binding energy. The metastable character of these molecules arises from the large centrifugal barrier in combination with negligible coupling to states with low rotational angular momentum. A sharp onset of dissociation with increasing magnetic field is mediated by a crossing with a lower rotational dimer state and facilitates dissociation on demand with a well-defined energy.

Coherent atom-trimer conversion in a repulsive Bose-Einstein condensate

We show that the use of a generalized atom-molecule dark state permits the enhanced coherent creation of triatomic molecules in a repulsive atomic Bose-Einstein condensate, with further enhancement being possible in the case of heteronuclear trimers via the constructive interference between two chemical reaction channels.

"Stückelberg interferometry" with ultracold molecules

We report on the realization of a time-domain "Stückelberg interferometer", which is based on the internal-state structure of ultracold Feshbach molecules. Two subsequent passages through a weak avoided crossing between two different orbital angular momentum states in combination with a variable hold time lead to high-contrast population oscillations. This allows for a precise determination of the energy difference between the two molecular states. We demonstrate a high degree of control over the interferometer dynamics. The interferometric scheme provides new possibilities for precision measurements with ultracold molecules.

Dynamics of the O(3P) + H2 reaction at low temperatures: comparison of quasiclassical trajectory with quantum scattering calculations

Quasiclassical trajectory and quantum-mechanical scattering calculations are reported for the O((3)P) + H(2)(X (1)Sigma(g) (+);upsilon = 1-3,j = 0)-->OH(X (2)Pi) + H((2)S) reaction at energies close to the reaction threshold. The dynamics of the reaction have been investigated for zero total angular momentum using the lowest (3)A" potential-energy surface developed by Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)] and its recent extensions by Brandao et al. [J. Chem. Phys. 121, 8861 (2004)] which provide an improved description of the van der Waals interaction. Good agreement is observed for this system between quasiclassical and quantal results for incident kinetic energies above the tunneling regime. Quantum-mechanical calculations also confirm recent theoretical predictions of a strong collision-energy dependence of the OH(v(') = 0)OH(v' = 1) product branching ratio in the O((3)P) + H(2)(v = 1) reaction, which explains the differences observed in OH vibrational populations between experiments using different O((3)P) sources.

Coherent optical transfer of Feshbach molecules to a lower vibrational state

Using the technique of stimulated Raman adiabatic passage (STIRAP) we have coherently transferred ultracold (87)Rb(2) Feshbach molecules into a more deeply bound vibrational quantum level. Our measurements indicate a high transfer efficiency of up to 87%. Because the molecules are held in an optical lattice with not more than a single molecule per lattice site, inelastic collisions between the molecules are suppressed and we observe long molecular lifetimes of about 1 s. Using STIRAP we have created quantum superpositions of the two molecular states and tested their coherence interferometrically. These results represent an important step towards Bose-Einstein condensation of molecules in the vibrational ground state.

Long-lived Feshbach molecules in a three-dimensional optical lattice

We have created and trapped a pure sample of Feshbach molecules in a three-dimensional optical lattice. Compared to previous experiments without a lattice, we find dramatic improvements such as long lifetimes of up to 700 ms and a near unit efficiency for converting tightly confined atom pairs into molecules. The lattice shields the trapped molecules from collisions and, thus, overcomes the problem of inelastic decay by vibrational quenching. Furthermore, we have developed an advanced purification scheme that removes residual atoms, resulting in a lattice in which individual sites are either empty or filled with a single molecule in the vibrational ground state of the lattice.

Atom-molecule collisions in an optically trapped gas

Cold inelastic collisions between confined cesium (Cs) atoms and Cs2 molecules are investigated inside a CO2 laser dipole trap. Inelastic atom-molecule collisions can be observed and measured with a rate coefficient of approximately 2.6 x 10(-11) cm3 s(-1), mainly independent of the molecular rovibrational state populated. Lifetimes of purely atomic and molecular samples are essentially limited by rest gas collisions. The pure molecular trap lifetime ranges 0.3-1 s, 4 times smaller than the atomic one, as is also observed in a pure magnetic trap. We give an estimation of the inelastic molecule-molecule collision rate to be approximately 10(-11) cm3 s(-1).

Experimental investigation of ultracold atom-molecule collisions

Ultracold collisions between Cs atoms and Cs2 dimers in the electronic ground state are observed in an optically trapped gas of atoms and molecules. The Cs2 molecules are formed in the triplet ground state by cw photoassociation through the outer well of the 0-(g) (P3/2) excited electronic state. Inelastic atom-molecule collisions converting internal excitation into kinetic energy lead to a loss of Cs2 molecules from the dipole trap. Rate coefficients are determined for collisions involving Cs atoms in either the F=3 or F=4 hyperfine ground state, and Cs2 molecules in either highly vibrationally excited states (nu'=32-47) or in low vibrational states (nu'=4-6) of the a3 summation(u)+ triplet ground state. The rate coefficients beta approximately 10(-10) cm3/s are found to be largely independent of the vibrational and rotational excitation indicating unitary limited cross sections.

Calculation of accurate permanent dipole moments of the lowest Σ+1,3 states of heteronuclear alkali dimers using extended basis sets

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction.

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.