# 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?

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

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.

See also the answer.

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I like the link to the answer, as an amature physics buff I sure would like to see where a Bosenova fits into all those figures and what is hapening to those electrons. ps. I did a search for bosenove on this forum and nothing came up. Did I go wrong somewhere? –  Jitter Oct 4 '13 at 13:49
@Jitter Interesting, I just know such phenomenon exists. I doubt that it is captured by GPE, so a more general theory might required. I dont think it has been asked, so you might ask such a question here to see whether other out there can answer your question. –  hwlau Oct 4 '13 at 15:44
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