# Annual Review of Cold Atoms and Molecules: Volume 3 by Kirk W Madison, Kai Bongs, Visit Amazon's Lincoln D Carr

By Kirk W Madison, Kai Bongs, Visit Amazon's Lincoln D Carr Page, search results, Learn about Author Central, Lincoln D Carr, , Ana Maria Rey, Hui Zhai

The purpose of this publication is to comprise evaluate articles describing the most recent theoretical and experimental advancements within the box of chilly atoms and molecules. Our desire is this sequence will advertise study via either highlighting fresh breakthroughs and by means of outlining essentially the most promising study instructions within the field.

Readership: examine scientists together with graduate scholars and top point undergraduate scholars.

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Parish Following Ref. 68, we define the pairing order parameter qN VNn1 n2 cq−kn2 ↓ ckn1 ↑ , =g (47) k,n 1 ,n 2 and assume that fluctuations around this are small, thus obtaining the meanfield Hamiltonian, Hˆ MF = ( kn † − µ)cknσ cknσ k,n,σ + † VNn1 n2 ckn c† 1 ↑ q−kn 2 ↓ qN k,n 1 ,n 2 q,N ∗ qN + VNn3 n4 cq−k n3 ↓ ck n4 ↑ − | k ,n 3 ,n 4 2 qN | g . (48) If we further assume that the ground state has a uniform order parameter without nodes so that qN = δq0 δ N0 0 , then Eq. (48) only contains a single unknown parameter 0 .

2. Thus, in 2D, the BCS and BEC regimes correspond, respectively, 1 and k F a2D 1, where the pair size is much greater than the to k F a2D inter-particle spacing in the former case, and much smaller in the latter. The dimensionless parameter k F a2D automatically implies that there are two ways of achieving the BCS-BEC crossover: by varying the interactions or by varying the density. Note, however, that this is not the case for 3D contact interactions, since a two-body bound state does not exist for arbitrarily weak attraction, and the scattering length can change sign.

1. Quasi-2D case Given that experiments deal with quasi-2D Fermi gases, it is important to understand the effect of a finite confinement length on Tc . This is in general a challenging problem to address throughout the BCS-Bose crossover, but it is possible to estimate the dependence on ε F /ωz in the BCS limit. Using the mean-field approach for the quasi-2D system described in Sec. 2, one obtains a natural generalization of the Thouless criterion to quasi-2D:76 − 1 = g k,n (V0n1 n2 )2 1 ,n 2 tanh βc ξkn1 /2 + tanh βc ξkn2 /2 , 2(ξkn 1 + ξkn2 ) (66) where g is the strength of the 3D contact interaction, βc = 1/Tc , and ξkn = kn −µ.