# 2N Fermions $\stackrel{?}{=}$ N Bosons

We know that we do have composite particles (for example Atoms) made of fermions or bosons or mixture of them with fermionic or bosonic statistics. So why can't a gas of $2N$ fermions become a gas of $N$ bosons and condense to the lowest state at low temperature (just like what happens in superfluidity and superconductivity)?

• – Ben Crowell Oct 10 '13 at 14:35

• @richard: Deborah Jin's experiment required temperatures of $10^{-8}$K, and even then it took the assistance of a magnetic field to increase the pairing energy. The error in your stat mech calculations by ignoring the process is pretty small :-) – John Rennie Oct 10 '13 at 6:55
• If the attractive interaction between the fermion is strong enough, there might be a bound-state, and the fermions form a bosonic molecule. These molecules can then Bose-Einstein condense. One can continuously go from the BCS regime (loosely bound Cooper pair) to the BEC regime (strongly bound molecules), this is the BCS-BEC cross-over. If the interaction is strictly repulsive, the system stays a Fermi liquid down to $T=0$. – Adam Oct 10 '13 at 13:29