What is BCs-BEC crossover Interpolation between fermionic superfluids to bosonic superfluids Transition from loosely bound Cooper pairs to tightly bound molecules The schematic excitation spectrum BCS intermediate BEC ◎a ●● ○o
What is BCS-BEC Crossover ◼ Interpolation between fermionic superfluids to bosonic superfluids ◼ Transition from loosely bound Cooper pairs to tightly bound molecules. ◼ The schematic excitation spectrum:
Physical picture of BCS-BEC crossover Pairs are formed before condensation E nergy gap is different from order acD) parameter a This combination defines bcs-bec crossover
Physical picture of BCS-BEC crossover ◼ Pairs are formed before condensation. ◼ Energy gap is different from order parameter. ◼ This combination defines BCS-BEC crossover
BCS-BEC crossover at t=0 Based on BCS-Leggett ground state BCS)=Tu+vs* ck) Self-consistently solve for chemical potential 2E g Ek IkEa l/k
BCS-BEC crossover at T=0 ◼ Based on BCS-Leggett ground state ◼ Self-consistently solve for chemical potential ( ) + − + = + k k k k k 0 , , BCS u v c c E g 1 2 1 = − k k = − k k k E n 1
Generalization of bcs-bec crossover to finite temperatures: GOG pairing fluctuation t-matrix(ladder approx. for non-condensed pairs to=:+ +·· pg tn(Q1+8@),tlo)=2G(0-K)G(K) g a Fermion self-energy pg ∑三
Generalization of BCS-BEC Crossover to finite temperatures: G0G pairing fluctuation ◼ t-matrix (ladder approx.) for non-condensed pairs ◼ Fermion self-energy = − + = K p g Q G Q K G K g Q g t Q , ( ) ( ) ( ) 1 ( ) ( ) 0
Properties of GOG Pair fluctuations It reduce to bcs mean field at t=o It generates pseudogap at finite t a The superfluid transition is a continuous transition Consistency requires a gauge invariant linear response theory
Properties of G0G Pair fluctuations ◼ It reduce to BCS mean field at T=0 ◼ It generates pseudogap at finite T ◼ The superfluid transition is a continuous transition. ◼ Consistency requires a gauge invariant linear response theory