Bose-Einstein Condensation In Feshbach Resonance

Bose-Einstein condensate (BEC) is that a large number of identical particles occupy the same quantum state. If the considered microscopic particles are bosons, they must obey the Bose-Einstein statistics. Statistics Bose and Fermi - Dirac statistics are the two different statistics methods. Because of the Pauli exclusion principle, the same quantum state at most can be occupied by more than one microscopic particle. BEC phenomenon is fundamentally different from classical statistics; the unique quantum correlation effects of BEC play a crucial role.Bose first proposed this problem. He considered the statistics of photons with zero static mass in 1924 [1]. Einstein realized the importance of this idea. Einstein quickly extended this idea to the circumstances for particles with non-zero mass [2]. Einstein Further described the condensation of ideal Bose gases in 1925.How to deal with the interaction is a very important topic for the BEC problem. In 1947, the Russian physicists Bogolubov explored the BEC possibility a weak coupling non-ideal Bose gases [4]. In 1961, Gross and Pitaevskii further proposed that BEC phase transition. The BEC wave function satisfied the famous Gross - Pitaevskii equation. Its mathematical structure is very similar to non-linear Schr'odinger equations.In 1995, with the breakthrough of cryogenic technology, three experimental groups observed the BEC phenomenon of the weak coupling Bose gases seventy years later after Bose and Albert Einstein predicted. These were considered the most important physics experiments in 20th century, and were awarded the Nobel Prize in Physics quickly in 2001. From then on, it gave a new important physics research direction. The study for the BEC phenomenon is in a golden era now. The first part of this paper is a briefly review on the BEC phenomenon about Boson gases.In 2004, the international physics started an unprecedented upsurge for the BEC realized in fermions systems. It is thought that there will not BEC for fermions system because it is well known fermions obey the Fermi statistics quite different from the Bose statistics. But if there is any effective attractive interaction such as in solid metal through exchanging virtual phonons, the like-charged electrons will be paired and condensed in the momentum space. This is the well-known BCS mechanism. To realize the BEC with...