Interspecies Feshbach resonances

Feshbach resonances are an extremely valuable tool for ultracold atom experiments. They occur, when the colliding atoms can couple to a bound molecular state belonging to a different atomic asymptote. This situation can be artificially brought about by applying a homogeneous magnetic field that introduces a Zeeman energy due to the magnetic moment of the atoms. When the magnetic moment of a bound molecular state and the combined magnetic moment of the colliding atoms is different, the Zeeman energy is different for the two states and they can be shifted relative to each other (left image). At the magnetic field that corresponds to energetic degeneracy, the scattering length of the system changes dramatically an can be tuned to any value between plus and minus infinity (right image).

Optical Dipole Trap

In order to apply a homogeneous magnetic field, the atoms need to be loaded into a trap that does not use the magnetic field coils. We therefore use an optical dipole trap based on a 10W Yb:YAG fiber laser running at 1064 nm that is focussed onto the atomic clouds. Since the light is far red-detuned from the atomic transitions, they only experience a potential energy proportional to the light intensity without scattering of photons. The magnetic field coils can then be used to apply the magnetic field. We use a horizontally crossed beam geometry in order to localize the atoms in the center of the magnetic field coils. Since they are so small, field gradients across the cloud, reducing the magnetic field resolution, need to be considered. The image shows fermionic Li atoms inside a single beam dipole trap with a long aspect ratio (top) and the crossed geometry where most atoms are in the crossing volume (bottom).

State Preparation

Feshbach resonances do not necessarily appear in all spin combinations. We therefore need to prepare the atoms in specific states, usually the absolute ground state, e.g. |1,+1> for bosonic Rubidium and Lithium and |1/2,+1/2> for fermionic Lithium. This can be done with very efficiently by coupling e.g. the initial state |2,+2> with radio frequency or microwave field to the desired lower state |1,+1>. In case of 7Li the frequency is about 803 MHz. By ramping this frequency across the resonance, nearly all atoms can be transferred into the absolute ground state.

The transfer efficiency can be analyzed by a Stern-Gerlach experiment in which an magnetic field gradient is applied during free fall. The different magnetic momenta then cause a splitting of the cloud of atoms into the different magnetic substates. (a) A cloud of pure |2,+2> Li without any sweep. (b) After a sweep nearly 100% of the atoms are in the |1,+1> state. (c) Applying the same sweep again restores the initial population distribution.

6Li-87Rb Feshbach Resonances

On July 5th 2007, we observed for the first time in the Fermi-Bose system Feshbach resonances. This was achieved by monitoring the atom numbers after a fixed storage time at different magnetic fields. In the vicinity of a Feshbach resonance, the collision rate increases thereby also increasing inelastic three-body recombination. For our conditions, Li-Rb-Rb three-body collisions are the dominant loss channel. We found a narrow (a) and a broad (b) Feshbach resonance in the magnetic field range from 0..1200G for 6Li and 87Rb atoms in their respective hyperfine ground states |F,mF=1/2,+1/2> and |1,+1>. The magnetic field values where they occur represent important benchmarks for an accurate determination of the interspecies interaction potentials. The broad resonance at 1067G can be used to accurately control the interspecies scattering length.

7Li-87Rb Feshbach Resonances

The first Feshbach resonances in the Bose-Bose system were observed on March 23th 2008. Five loss features were observed in total, four of which could be unambiguously assigned to heteronuclear interspecies Feshbach resonances of the 7Li-87Rb system. Both atoms are in their absolute groundstate |F,mF=1,+1>. Of particular interest is the extremely broad s-wave Feshbach resonance located at 649G with a tuning width of almost 200G making very precise control of the scattering parameters possible.

Catalytic Enhancement of 6Li p-wave Feshbach Resonances

In the Fermi-Bose mixture, the fermions are spin-polarized and do not interact through s-wave collisions due to the Pauli exclusion principle. The next higher partial wave, the p-wave, is allowed, but due to its centrifugal barrier, these collisions are highly suppressed at ultracold temperatures. Nonetheless, at 158G there occurs a p-wave resonance in the Li subsystem that makes is possible to introduce strong Li-Li collisions through the p-wave channel. The presence of Rb inside the trap introduces another loss mechanism through inelastic Li-Li-Rb collisions (right), thereby enhancing the visibility of the p-wave resonance compared to a pure Li cloud where only Li-Li-Li collisions can occur (left).

Interaction Potentials

Based in our measurements of the background scattering lengths as well as the positions of Feshbach resonances, the interaction potentials were reconstructed to a high degree of precision. These calculations were performed both in the groups of Eberhard Tiemann (U Hannover) and Alejandro Saenz (HU Berlin). These potentials form the basis for scattering length tuning curves as well as for photoassociation schemes to produce deeply bound polar molecules.