Feshbach resonance

[1] It is a feature of many-body systems in which a bound state is achieved if the coupling(s) between at least one internal degree of freedom and the reaction coordinates, which lead to dissociation, vanish.

The opposite situation, when a bound state is not formed, is a shape resonance.

Feshbach resonances have become important in the study of cold atoms systems, including Fermi gases and Bose–Einstein condensates (BECs).

[2] In the context of scattering processes in many-body systems, the Feshbach resonance occurs when the energy of a bound state of an interatomic potential is equal to the kinetic energy of a colliding pair of atoms.

In experimental settings, the Feshbach resonances provide a way to vary interaction strength between atoms in the cloud by changing scattering length, asc, of elastic collisions.

For atomic species that possess these resonances (like K39 and K40), it is possible to vary the interaction strength by applying a uniform magnetic field.

Among many uses, this tool has served to explore the transition from a BEC of fermionic molecules to weakly interacting fermion-pairs the BCS in Fermi clouds.

For the BECs, Feshbach resonances have been used to study a spectrum of systems from the non-interacting ideal Bose gases to the unitary regime of interactions.

We consider now a second reaction channel, denoted by D, which is closed for large values of R. Let this potential curve

[2] In ultracold atomic experiments, the resonance is controlled via the magnetic field and we assume that the kinetic energy

As the magnetic field is swept through the resonance, the states in the open and closed channel can also mix and a large number of atoms, sometimes near 100% efficiency, convert to Feshbach molecules.

Other methods include inducing stimulated emission through an oscillating magnetic field and atom-molecule thermalization.

[2] In molecules, the nonadiabatic couplings between two adiabatic potentials build the avoided crossing (AC) region.

The rovibronic resonances in the AC region of two-coupled potentials are very special, since they are not in the bound state region of the adiabatic potentials, and they usually do not play important roles on the scatterings and are less discussed.

Yu Kun Yang et al studied this problem in the New J. Phys.

[3] Exemplified in particle scattering, resonances in the AC region are comprehensively investigated.

The effects of resonances in the AC region on the scattering cross sections strongly depend on the nonadiabatic couplings of the system, it can be very significant as sharp peaks, or inconspicuous buried in the background.

More importantly, it shows a simple quantity proposed by Zhu and Nakamura to classify the coupling strength of nonadiabatic interactions, can be well applied to quantitatively estimate the importance of resonances in the AC region.

Such a state is called 'virtual'"[5] and may be further contrasted to a shape resonance depending on the angular momentum.

The interatomic potential of the open (red) and closed (blue) channel are shown. When the incoming energy of the free atoms, given by the dotted line, is approximately equivalent to that of the bound state in the closed channel, a temporary molecular state can form.