We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar 40 K 87 Rb molecules [1,2].Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold 40 K and 87 Rb atoms.Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X 1 + and a 3 + vibrational levels.We find excellent agreement with the hyperfine structure observed in experimental data.In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition.This allowed us to investigate its effect on the vibrationally averaged transition dipole moment to the lowest rovibrational level of the X 1 + state.Finally, we obtained an estimate of the polarizability of the initial and final rovibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules.Contents 1. Introduction 2 2. Coupled-channel calculation of the ground states 4 3. Multi-channel calculation of the excited states 8 4. Dynamic polarizability of the ground state vibrational levels 11
We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar 40 K 87 Rb molecules [1,2].Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold 40 K and 87 Rb atoms.Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X 1 + and a 3 + vibrational levels.We find excellent agreement with the hyperfine structure observed in experimental data.In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition.This allowed us to investigate its effect on the vibrationally averaged transition dipole moment to the lowest rovibrational level of the X 1 + state.Finally, we obtained an estimate of the polarizability of the initial and final rovibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules.Contents 1. Introduction 2 2. Coupled-channel calculation of the ground states 4 3. Multi-channel calculation of the excited states 8 4. Dynamic polarizability of the ground state vibrational levels 11
Ultracold bialkali polar molecules play a leading part at the frontline of quantum physics. They recently attract a lot of attention in the field of ultracold quantum chemistry, quantum many-body physics and quantum simulations. The key for their success is the rich internal level structure with rotational and vibrational degrees of freedom and their large electric dipole moments. Still, only a handful of molecular species are available at ultracold temperatures until now, although it is highly desirable to produce new molecular species to further expand the range of applications. Besides direct laser cooling methods for molecules, the assembly of heteronuclear ground-state molecules from ultracold atomic mixtures is the most promising approach for the creation of polar molecules. It includes the formation of weakly bound Feshbach molecules from the diatomic mixture and the subsequent two-photon stimulated Raman adiabatic passage (STIRAP) transfer to the rovibrational ground state. This creation strategy has been successfully demonstrated for the first time in the pioneering experiments at JILA with ultracold 40K87Rb molecules. Since then, only a few more molecular species from different alkali atoms have been created, namely 6Li23Na, 23Na40K, 23Na87Rb and 87Rb133Cs. In this thesis, I report the successful creation of a new species of ultracold polar ground-state molecules: 23Na39K. Starting from an ultracold mixture of bosonic 23Na and 39K atoms, weakly bound molecules are created. For this purpose, a Feshbach resonance in a high angular momentum scattering channel is chosen, experimentally identified and characterized. Close to this resonance the weakly bound Feshbach molecules are formed using resonant radio frequency radiation. For the two-photon ground-state transfer, a unique, highly specialized two-color laser system is designed and realized. It is used for one- and two-photon spectroscopy to identify the relevant transitions for the ground-state transfer. Based on the obtained data, a local model of the singlet-triplet mixed excited state manifolds is developed, with which the hyperfine structure and the magnetic field dependence is predicted with high accuracy. According to these findings, a suitable pathway to a single hyperfine ground state is chosen considering selection rules and experimental conditions such as laser polarization and beam alignment. To precisely determine the two-photon resonance condition for STIRAP, electromagnetically induced transparency measurements are performed. The ground-state transfer is then performed using STIRAP. The experimental findings regarding the STIRAP are successfully supported theoretically by a model based on a five-level master equation. The pure molecular gas shows evidence for two-body dominated loss mechanisms, such as sticky four-body collisions. The molecule-atom mixture of 23Na39K+39K reveals an unexpectedly low loss rate coefficient although sticky three-body collisions are assumed to occur. This behavior demands further investigations regarding different hyperfine collisional chan-nels and magnetic field regions.
We have studied interspecies scattering in an ultracold mixture of 87Rb and 133Cs atoms, both in their lowest-energy spin states. The three-body loss signatures of 30 incoming s- and p-wave magnetic Feshbach resonances over the range 0 to 667 G have been cataloged. Magnetic field modulation spectroscopy was used to observe molecular states bound by up to 2.5 $\text{MHz}\ifmmode\times\else\texttimes\fi{}h$. We have created RbCs Feshbach molecules using two of the resonances. Magnetic moment spectroscopy along the magnetoassociation pathway from 197 to 182 G gives results consistent with the observed and calculated dependence of the binding energy on magnetic field strength. We have set up a coupled-channel model of the interaction and have used direct least-squares fitting to refine its parameters to fit the experimental results from the Feshbach molecules, in addition to the Feshbach resonance positions and the spectroscopic results for deeply bound levels. The final model gives a good description of all the experimental results and predicts a large resonance near 790 G, which may be useful for tuning the interspecies scattering properties. Quantum numbers and vibrational wave functions from the model can also be used to choose optimal initial states of Feshbach molecules for their transfer to the rovibronic ground state using stimulated Raman adiabatic passage.
In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^
Within the scope of this thesis, the production of ultracold molecules at a temperature of a few µK with various isotopes of rubidium (Rb) and ytterbium (Yb) was examined by means of photoassociation spectroscopy and magnetic Feshbach resonances in combined conservative traps. The long-term goal of this experiment is the production of ultracold RbYb molecules in the rovibronic ground state.
It was possible to produce electronically excited ^{87}Rb ^{176}Yb molecules in a novel hybrid trap (HT) at a combined temperature of 1.7 µK by means of 1-photon photoassociation close to the Rb D1 line at 795 nm. This HT takes advantage of the different magnetic properties of Rb and Yb and allows for independent trapping and manipulation of the atomic species. It combines an Ioffe-Pritchard type magnetic trap for Rb and a near-resonant optical dipole trap for Yb. The excited molecular ^2 Pi_1/2 state could be characterized further extending previous works in a combined MOT and vibrational levels reaching binding energies up to E_b=-h x 2.2 THz could be assigned by trap-loss spectroscopy.
Almost every detected vibrational state consists of two resonances that could be assigned to the molecular analogue of the hyperfine structure of ^{87}Rb. An important experimental observation is a decrease in hyperfine splitting with increasing binding energy of a vibrational level. For the deepest found vibrational state the hyperfine splitting amounts only 70 % of the atomic value (817 MHz) which emphasizes a gradual passage from weakly to tightly bound molecules.
Furthermore, detailed attempts were undertaken to induce magnetic Feshbach resonances in ^{85}Rb and different Yb isotopes, especially ^{171}Yb in a crossed optical dipole trap at 1064 nm at temperatures of 10 µK. For this purpose, a homogeneous magnetic field was applied and scanned in small steps over the range of 495 G... 640 G. Unfortunately, our efforts were without success. Additionally, well known as well as not yet reported Rb_2 Feshbach resonances in ^{85}Rb and ^{87}Rb were detected. These resonances allowed for a detailed analysis of the typical behaviour of Feshbach resonances.
The first experimental realization of photoassociation spectroscopy in a conservative is also a major step towards the ultimate project goal of producing ultracold RbYb molecules in the electronic ground state. A spatial confinement, which is in principle possible in the HT, is a prerequisite for transferring the molecules to the rovibronic ground state, e.g. with the help of a STIRAP process.
This thesis reports the creation and trapping of 87RbCs molecules in the absolute ground state with a temperature of 1 uK. We build a tunable narrow-linewidth laser system at 1550 nm and 980 nm, using a single high-finesse optical cavity as a reference for both colours. We use fibre-coupled electro-optic modulators to continuously tune both lasers. These allow a novel measurement of the free spectral range of the cavity to better than 1 part in 10^6. We perform one- and two-photon spectroscopy on 87RbCs Feshbach molecules and identify a suitable intermediate state for transfer to the molecular ground state. We measure the electric dipole moment of the molecular ground state as 1.225(3)(8) D, and demonstrate the highest lab-frame dipole moment of any ultracold molecular system at the time of measurement. We transfer the molecules to the electronic, rovibrational and hyperfine ground state using stimulated Raman adiabatic passage, with 88% efficiency. We measure the transition strengths and excited state linewidth for this transfer route. We develop a model for the transfer which includes the effect of laser linewidth, and find excellent agreement with experimental data. The molecular sample is trapped in an optical dipole potential, and has a lifetime of 0.89(6) s. We reference the STIRAP lasers to a novel design of frequency comb which uses difference frequency generation to cancel the carrier-envelope offset. We use this to measure the binding energy of the molecules as h x 114 268 135.24(4)(3) MHz. To our knowledge, this is the most precise determination of the dissociation energy of a molecule to date. Finally, we report progress toward loading the molecules into a 1D optical lattice at 1064 nm. We develop the tools and methods to characterise a lattice, and demonstrate trapping of Feshbach molecules in both a 1D optical lattice and a harmonic optical potential at 1064 nm.
We propose a mechanism to produce ultracold polar molecules with microwave fields. It converts trapped ultracold atoms into vibrationally excited molecules by a single microwave transition and entirely depends on the existence of a permanent dipole moment in the molecules. As opposed to production of molecules by photoassociation or magnetic-field Feshbach resonances, our method does not rely on properties of excited states or existence of Feshbach resonances. We determine conditions for optimal creation of polar molecules in vibrationally excited states of the ground-state potential by changing frequency and intensity of the microwave field. We also explore the possibility to produce vibrationally cold molecules by combining the microwave field with an optical Raman transition or by applying a microwave field to Feshbach molecules. The production mechanism is illustrated for KRb and RbCs.