10
$\begingroup$

In one of the two main theoretical approaches used in describing ultracold Fermi gases and the BEC-BCS crossover, the so-called BCS-Leggett approach, the starting point is the BCS trial wavefunction:

$$ \mid BCS \rangle \equiv \prod_{\mathbf{k}} \left( u_{\mathbf{k}} + v_{\mathbf{k}} P^\dagger_{\mathbf{k}} \right) \mid 0 \rangle $$

where the $P^\dagger_{\mathbf{k}}$ operator creates a Cooper pair. It is often asserted that this wavefunction, which may seem tailored for a BCS-like problem, has far greater validity and can also be successfully exploited in describing the BEC-BCS crossover (see for instance: http://arxiv.org/abs/cond-mat/0404274).

Even looking at the original articles by Leggett and Eagles (cited in the reference above) I cannot see why $\mid BCS \rangle$ should be valid in the BEC regime: I am looking for a review article (or even a textbook) addressing this issue.

$\endgroup$
5
$\begingroup$

You can gain some intuition from looking at the density distribution function in momentum space which for the $|BCS\rangle$ is given by $n_k=v^{2}_k$. In the BCS limit one finds approximately the filled Fermi sphere, while in the BEC limit $n_k\sim 1/(1+[ka]^2)^2$ which is proportional to the square of the Fourier transform of the dimer wave function. For this reason in the BEC limit the state $|BCS\rangle$ describes a condensate of dimers. You can find a little bit more about this question in http://arxiv.org/abs/0706.3360

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.