# Why People talk so much about Feshbach resonance while dealing with Bose-Einstein Condensate (BEC)?

Why People talk so much about Feshbach resonance while dealing with Bose-Einstein Condensate (BEC)?

Why not tune the system near the resonance and measure the effect on BEC formation?

• Could you please elaborate? It's not quite clear what your question is. – Emilio Pisanty Mar 6 '13 at 11:48

Feshbach resonance is important to BEC because it allows the adjustment of the interaction between atoms.

At low energy regime, the BEC dynamics can be described by the mean field Gross–Pitaevskii equation: $$i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2 \psi + V\psi + \frac{4\pi \hbar^2 a_s}{m}|\psi|^2 \psi \tag{1}$$

The $\psi$ is usually called the marcoscopic order parameter of BEC. When compared with the Schroedinger equation, there is an extra non-linear term for the interaction between atoms. The adjustability of the s-wave scattering length $a_s$ therefore allows controlling the nonlinear dynamics of BEC and its ground state wavefunction.

With Feshbach resonance, it is possible to change $a_s$ of atoms by over two orders of magnitude. Therefore, it is an important control technique to realize different BEC experiments in dilute atomic gas. As described clearly in the book, "Bose-Einstein Condensation in Dilute Gases", Pathick and Smith:

These resonances have become an important tool in investigations of the basic atomic physics of cold atoms, because they make it possible to vary the effective interaction by adjusting an external parameter such as the magnetic field. The use of magnetically tunable Feshbach resonances has played an important role in the production of cold molecules and the superfluid state of strongly interacting Fermi gases.