Feshbach

Feshbach resonance is a quantum mechanical phenomenon in which a bound state in a closed reaction channel interacts with the continuum of scattering states in an open channel. The effect is named after the physicist Hermann Feshbach, who described it in the context of multichannel scattering.

In multichannel scattering, the coupling between channels allows a resonance to occur when the energy of a bound state in the closed channel matches the energy of the two free particles in the open channel. This coupling causes a rapid variation in the scattering amplitude and, in particular, a dramatic change of the s-wave scattering length.

In ultracold atomic physics, magnetic Feshbach resonances provide a practical means to tune interactions. Different channels have different magnetic moments, so applying an external magnetic field B shifts the relative energy of the bound state with respect to the open-channel threshold. The dependence of the scattering length on B is often written as a(B) = a_bg [1 - Δ/(B - B0)], where a_bg is the background scattering length, B0 the resonance position, and Δ the width. Broad resonances offer wide tunability, while narrow resonances require more precise control.

Applications of Feshbach resonances include control of interactions in Bose-Einstein condensates and degenerate Fermi gases, formation of weakly bound diatomic molecules known as Feshbach molecules, and exploration of phenomena such as the BEC-BCS crossover and Efimov states. The concept has become a central tool in experimental and theoretical studies of strongly interacting quantum systems.

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