= Two-mode fermionic paired vacuum
{title2=$|\widetilde0\rangle=u|0\rangle+v a^\dagger b^\dagger|0\rangle$}
= Paired fermionic vacuum
{synonym}
The normalized <vacuum state> annihilated by $c=ua-vb^\dagger$ and $d=va^\dagger+ub$, for positive $u,v$ with $u^2+v^2=1$. Since $(a^\dagger b^\dagger)^2=0$, it can also be written $u\exp[(v/u)a^\dagger b^\dagger]|0\rangle$. Acting with either <annihilation operator> makes the two terms cancel. Its original <occupation numbers> each have <expected value> $v^2$ and its pair amplitude is $\langle ab\rangle=-uv$. It has even <fermion parity> although the original total <number operator> is not sharp. For the <two-orbital fermionic pairing Hamiltonian>, it is the unique <ground state> of <energy> $\varepsilon-\sqrt{\varepsilon^2+\Delta^2}$.
Back to article page
